statistics 1.3 homework answers

Chapter 1: Sampling and Data

Chapter 1 Homework

Homework from 1.2.

For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

The population is all of the clients of the fitness center. A sample of the clients that use the fitness center for a given week. The average amount of time that all clients exercise in one week. The average amount of time that a sample of clients exercises in one week. The amount of time that a client exercises in one week. Examples are: 2 hours, 5 hours, and 7.5 hours –>

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

• all children who take ski or snowboard lessons
• a group of these children
• the population mean age of children who take their first snowboard lesson
• the sample mean age of children who take their first snowboard lesson
• X = the age of one child who takes his or her first ski or snowboard lesson
• values for X , such as 3, 7, and so on

A cardiologist is interested in the mean recovery period of her patients who have had heart attacks.

the cardiologist’s patients a group of the cardiologist’s patients the mean recovery period of all of the cardiologist’s patients the mean recovery period of the group of the cardiologist’s patients X = the mean recovery period of one patient values for X, such as 10 days, 14 days, 20 days, and so on –>

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

• the clients of the insurance companies
• a group of the clients
• the mean health costs of the clients
• the mean health costs of the sample
• X = the health costs of one client
• values for X , such as 34, 9, 82, and so on

A politician is interested in the proportion of voters in his district who think he is doing a good job.

all voters in the politician’s district a random selection of voters in the politician’s district the proportion of voters in this district who think this politician is doing a good job the proportion of voters in this district who think this politician is doing a good job in the sample X = the number of voters in the district who think this politician is doing a good job Yes, he is doing a good job. No, he is not doing a good job. –>

A marriage counselor is interested in the proportion of clients she counsels who stay married.

• all the clients of this counselor
• a group of clients of this marriage counselor
• the proportion of all her clients who stay married
• the proportion of the sample of the counselor’s clients who stay married
• X = the number of couples who stay married

Political pollsters may be interested in the proportion of people who will vote for a particular cause.

all voters (in a certain geographic area) a random selection of all the voters the proportion of voters who are interested in this particular cause the proportion of voters who are interested in this particular cause in the sample X = the number of voters who are interested in this particular cause yes, no –>

A marketing company is interested in the proportion of people who will buy a particular product.

• all people (maybe in a certain geographic area, such as the United States)
• a group of the people
• the proportion of all people who will buy the product
• the proportion of the sample who will buy the product
• X = the number of people who will buy it
• buy, not buy

Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

• all Lake Tahoe Community College students
• all Lake Tahoe Community College English students
• all Lake Tahoe Community College students in her classes
• all Lake Tahoe Community College math students

Consider the following:

[latex]X[/latex] = number of days a Lake Tahoe Community College math student is absent

In this case, X is an example of a:

• population.

The instructor’s sample produces a mean number of days absent of 3.5 days. This value is an example of a:

More Homework from 1.2

For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

number of tickets sold to a concert

quantitative discrete, 150

percentage of body fat

quantitative continuous, 19.2% –>

favorite baseball team

qualitative, Oakland A’s

time in line to buy groceries

quantitative continuous, 7.2 minutes –>

number of students enrolled at Evergreen Valley College

quantitative discrete, 11,234 students

most-watched television show

qualitative, Dancing with the Stars –>

brand of toothpaste

qualitative, Crest

distance to the closest movie theater

quantitative continuous, 8.32 miles –>

age of executives in Fortune 500 companies

quantitative continuous, 47.3 years

number of competing computer spreadsheet software packages

quantitative discrete, three –>

Use the following information to answer the next two exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.

“Number of times per week” is what type of data?

• qualitative
• quantitative discrete
• quantitative continuous

“Duration (amount of time)” is what type of data?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

• Using complete sentences, list three things wrong with the way the survey was conducted.
• Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

The survey would not be a true representation of the entire population of air travelers.

Conducting the survey on a holiday weekend will not produce representative results.

• Conduct the survey during different times of the year.

Conduct the survey using flights to and from various locations.

Conduct the survey on different days of the week.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Answers will vary. Sample Answer: Randomly choose 25 colleges in the state. Use all statistics classes from each of the chosen colleges in the sample. This can be done by listing all the colleges together with a two-digit number starting with 00 then 01, etc. The list of colleges can be found on Wikipedia. http://en.wikipedia.org/wiki/List_of_colleges_and_universities_in_California Use a random number generator to pick 25 colleges. –>

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Answers will vary. Sample Answer: You could use a systematic sampling method. Stop the tenth person as they leave one of the buildings on campus at 9:50 in the morning. Then stop the tenth person as they leave a different building on campus at 1:50 in the afternoon.

List some practical difficulties involved in getting accurate results from a telephone survey.

Answers will vary. Sample Answer: Not all people have a listed phone number. Many people hang up or do not respond to phone surveys. –>

List some practical difficulties involved in getting accurate results from a mailed survey.

Answers will vary. Sample Answer: Many people will not respond to mail surveys. If they do respond to the surveys, you can’t be sure who is responding. In addition, mailing lists can be incomplete.

With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey.

Ask everyone to include their age then take a random sample from the data. Include in the report how the survey was conducted and why the results may not be accurate. –>

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is

• cluster sampling
• stratified sampling
• simple random sampling
• convenience sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was:

• simple random

Name the sampling method used in each of the following situations:

convenience cluster stratified systematic simple random

A “random survey” was conducted of 3,274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had 💲2,000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users.

• Do you consider the sample size large enough for a study of this type? Why or why not?

Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute’s road show called “America’s Smithsonian.”

• With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
• With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

Yes, in polling, samples that are from 1,200 to 1,500 observations are considered large enough and good enough if the survey is random and is well done. We do not have enough information to decide if this is a random sample from the U.S. population. No, this is a convenience sample taken from individuals who visited an exhibition in the Angeles Convention Center. This sample is not representative of the U.S. population. It is possible that the two sample statistics, 48% and 66% are larger than the true parameters in the population at large. In any event, no conclusion about the population proportions can be inferred from this convenience sample. –>

The Gallup-Healthways Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

• Do you have any health problems that prevent you from doing any of the things people your age can normally do?
• During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
• In the last seven days, on how many days did you exercise for 30 minutes or more?
• Do you have health insurance coverage?

In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent postcards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards.

• Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time.
• What effect does the low response rate have on the reliability of the sample?
• Are these problems examples of sampling error or nonsampling error?
• During the same year, George Gallup conducted his own poll of 30,000 prospective voters. His researchers used a method they called “quota sampling” to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

The country was in the middle of the Great Depression, and many people could not afford these “luxury” items and therefore were not able to be included in the survey. Samples that are too small can lead to sampling bias. sampling error stratified

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI’s Uniform Crime Report . One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in [link] could explain this connection?

Causality: The fact that two variables are related does not guarantee that one variable is influencing the other. We cannot assume that crime rate impacts education level or that education level impacts crime rate.

Confounding: There are many factors that define a community other than education level and crime rate. Communities with high crime rates and high education levels may have other lurking variables that distinguish them from communities with lower crime rates and lower education levels. Because we cannot isolate these variables of interest, we cannot draw valid conclusions about the connection between education and crime. Possible lurking variables include police expenditures, unemployment levels, region, average age, and size.

YouPolls is a website that allows anyone to create and respond to polls. One question posted April 15 asks:

“Do you feel happy paying your taxes when members of the Obama administration are allowed to ignore their tax liabilities?” 1

As of April 25, 11 people responded to this question. Each participant answered “NO!”

Which of the potential problems with samples discussed in this module could explain this connection?

Self-Selected Samples: Only people who are interested in the topic are choosing to respond. Sample Size Issues: A sample with only 11 participants will not accurately represent the opinions of a nation. Undue Influence: The question is wording in a specific way to generate a specific response. Self-Funded or Self-Interest Studies: This question was generated to support one person’s claim and it was designed to get the answer that the person desires. –>

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.” 2

The Pew Research Center for People and the Press admits:

“The percentage of people we interview – out of all we try to interview – has been declining over the past decade or more.” 3

• What are some reasons for the decline in response rate over the past decade?
• Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.
• Possible reasons: increased use of caller id, decreased use of landlines, increased use of private numbers, voice mail, privacy managers, hectic nature of personal schedules, decreased willingness to be interviewed
• When a large number of people refuse to participate, then the sample may not have the same characteristics of the population. Perhaps the majority of people willing to participate are doing so because they feel strongly about the subject of the survey.

Bringing It Together

Seven hundred and seventy-one distance learning students at Long Beach City College responded to surveys in the 2010-11 academic year. Highlights of the summary report are listed in [link] .

• What percentage of the students surveyed do not have a computer at home?
• About how many students in the survey live at least 16 miles from campus?
• If the same survey were done at Great Basin College in Elko, Nevada, do you think the percentages would be the same? Why?

4% 13% Not necessarily. Long Beach City is the seventh largest college in California, and it has an enrollment of approximately 27,000 students. On the other hand, Great Basin College has its campuses in rural northeastern Nevada, and its enrollment of about 3,500 students. –>

Several online textbook retailers advertise that they have lower prices than on-campus bookstores. However, an important factor is whether the Internet retailers actually have the textbooks that students need in stock. Students need to be able to get textbooks promptly at the beginning of the college term. If the book is not available, then a student would not be able to get the textbook at all, or might get a delayed delivery if the book is back ordered.

A college newspaper reporter is investigating textbook availability at online retailers. He decides to investigate one textbook for each of the following seven subjects: calculus, biology, chemistry, physics, statistics, geology, and general engineering. He consults textbook industry sales data and selects the most popular nationally used textbook in each of these subjects. He visits websites for a random sample of major online textbook sellers and looks up each of these seven textbooks to see if they are available in stock for quick delivery through these retailers. Based on his investigation, he writes an article in which he draws conclusions about the overall availability of all college textbooks through online textbook retailers.

Write an analysis of his study that addresses the following issues: Is his sample representative of the population of all college textbooks? Explain why or why not. Describe some possible sources of bias in this study, and how it might affect the results of the study. Give some suggestions about what could be done to improve the study.

Answers will vary. Sample answer: The sample is not representative of the population of all college textbooks. Two reasons why it is not representative are that he only sampled seven subjects and he only investigated one textbook in each subject. There are several possible sources of bias in the study. The seven subjects that he investigated are all in mathematics and the sciences; there are many subjects in the humanities, social sciences, and other subject areas (for example: literature, art, history, psychology, sociology, business) that he did not investigate at all. It may be that different subject areas exhibit different patterns of textbook availability, but his sample would not detect such results.

He also looked only at the most popular textbook in each of the subjects he investigated. The availability of the most popular textbooks may differ from the availability of other textbooks in one of two ways:

• the most popular textbooks may be more readily available online, because more new copies are printed, and more students nationwide are selling back their used copies, OR
• the most popular textbooks may be harder to find available online, because more student demand exhausts the supply more quickly.

In reality, many college students do not use the most popular textbooks in their subject, and this study gives no useful information about the situation for those less popular textbooks.

He could improve this study by:

• expanding the selection of subjects he investigates so that it is more representative of all subjects studied by college students, and
• expanding the selection of textbooks he investigates within each subject to include a mixed representation of both the most popular and less popular textbooks.

HOMEWORK from 1.3

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

• Fill in the blanks in [link] .
• What percent of students take exactly two courses?
• What percent of students take one or two courses?

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in [link] .

• What percent of adults flossed six times per week?
• What percentage flossed at most three times per week?

Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2 5 7 2 2 10 20 15 0 7 0 20 5 12 15 12 4 5 10 .

[link] was produced.

• Fix the errors in [link] . Also, explain how someone might have arrived at the incorrect number(s).
• Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.”
• Fix the statement in b to make it correct.
• What fraction of the people surveyed have lived in the U.S. five or seven years?
• What fraction of the people surveyed have lived in the U.S. at most 12 years?
• What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
• What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive?

The Frequencies for 15 and 20 should both be two and the Relative Frequencies should both be

The mistake could be due to copying the data down wrong. The Cumulative Relative Frequency for five years should be 0.4737. The mistake is due to calculating the Relative Frequency instead of the Cumulative Relative Frequency. The Cumulative Relative Frequency for 15 years should be 0.8947 The 47% is the Cumulative Relative Frequency, not the Relative Frequency. 47% of the people surveyed have lived in the U.S. for five years or less.

How much time does it take to travel to work? [link] shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

The sum of the travel times is 1,173.1. Divide the sum by 50 to calculate the mean value: 23.462. Because each state’s travel time was measured to the nearest tenth, round this calculation to the nearest hundredth: 23.46.

Forbes magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least 💲5 per share, and have reported annual revenue between 💲5 million and 💲1 billion. [link] shows the ages of the chief executive officers for the first 60 ranked firms.

• What is the frequency for CEO ages between 54 and 65?
• What percentage of CEOs are 65 years or older?
• What is the relative frequency of ages under 50?
• What is the cumulative relative frequency for CEOs younger than 55?
• Which graph shows the relative frequency and which shows the cumulative relative frequency?

26 (This is the count of CEOs in the 55 to 59 and 60 to 64 categories.) 12% (number of CEOs age 65 or older ÷ total number of CEOs) 14/60; 0.23; 23% 0.45 Graph A represents the cumulative relative frequency, and Graph B shows the relative frequency. –>

Use the following information to answer the next two exercises: [link] contains data on hurricanes that have made direct hits on the U.S. Between 1851 and 2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm.

What is the relative frequency of direct hits that were category 4 hurricanes?

• Not enough information to calculate

What is the relative frequency of direct hits that were AT MOST a category 3 storm?

HOMEWORK from 1.4

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

Explanatory variable: amount of sleep

Response variable: performance measured in assigned tasks

Treatments: normal sleep and 27 hours of total sleep deprivation

Experimental Units: 19 professional drivers

Lurking variables: none – all drivers participated in both treatments

Random assignment: treatments were assigned in random order; this eliminated the effect of any “learning” that may take place during the first experimental session

Control/Placebo: completing the experimental session under normal sleep conditions

Blinding: researchers evaluating subjects’ performance must not know which treatment is being applied at the time

An advertisement for Acme Investments displays the two graphs in [link] to show the value of Acme’s product in comparison with the Other Guy’s product. Describe the potentially misleading visual effect of these comparison graphs. How can this be corrected?

The graphs do not show scales of values. We do not know the period of time each graph represents; they may show data from different years. We also do not know if the vertical scales on each graph are equivalent. The scales may have been adjusted to exaggerate or minimize trends. There is no reliable information to be gleaned from these graphs, and setting them up as examples of performance is misleading. –>

The graph in [link] shows the number of complaints for six different airlines as reported to the US Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

You cannot assume that the numbers of complaints reflect the quality of the airlines. The airlines shown with the greatest number of complaints are the ones with the most passengers. You must consider the appropriateness of methods for presenting data; in this case displaying totals is misleading.

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1.1 Definitions of Statistics, Probability, and Key Terms

For each of the following situations, indicate whether it would be best modeled with a mathematical model or a statistical model. Explain your answers.

• driving time from New York to Florida
• departure time of a commuter train at rush hour
• distance from your house to school
• temperature of a refrigerator at any given time
• weight of a bag of rice at the store

For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

A cardiologist is interested in the mean recovery period of her patients who have had heart attacks.

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

A politician is interested in the proportion of voters in his district who think he is doing a new good job.

A marriage counselor is interested in the proportion of clients she counsels who stay married.

Political pollsters may be interested in the proportion of people who will vote for a particular cause.

A marketing company is interested in the proportion of people who will buy a particular product.

Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

• all Lake Tahoe Community College students
• all Lake Tahoe Community College English students
• all Lake Tahoe Community College students in her classes
• all Lake Tahoe Community College math students

Consider the following

X X = number of days a Lake Tahoe Community College math student is absent.

In this case, X is an example of which of the following?

The instructor’s sample produces a mean number of days absent of 3.5 days. This value is an example of which of the following?

1.2 Data, Sampling, and Variation in Data and Sampling

For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

number of tickets sold to a concert

percent of body fat

favorite baseball team

time in line to buy groceries

number of students enrolled at Evergreen Valley College

most-watched television show

brand of toothpaste

distance to the closest movie theatre

age of executives in Fortune 500 companies

number of competing computer spreadsheet software packages

Use the following information to answer the next two exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.

Number of times per week is what type of data?

• qualitative
• quantitative discrete
• quantitative continuous

Duration (amount of time) is what type of data?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

• Using complete sentences, list three things wrong with the way the survey was conducted.
• Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

List some practical difficulties involved in getting accurate results from a telephone survey.

List some practical difficulties involved in getting accurate results from a mailed survey.

With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey.

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is which of the following?

• cluster sampling
• stratified sampling
• simple random sampling
• convenience sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was which of the following?

• simple random

Name the sampling method used in each of the following situations:

• A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport’s service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers who are sitting near gates and not taking naps while they wait.
• A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class.
• The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
• The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books.
• A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

A random survey was conducted of 3,274 people of the microprocessor generation —people born since 1971, the year the microprocessor was invented. It was reported that 48 percent of those individuals surveyed stated that if they had $2,000 to spend, they would use it for computer equipment. Also, 66 percent of those surveyed considered themselves relatively savvy computer users.

• Do you consider the sample size large enough for a study of this type? Why or why not?
• Based on your gut feeling , do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why? Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute's road show called “America’s Smithsonian.”
• With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
• With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

The Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

• Do you have any health problems that prevent you from doing any of the things people your age can normally do?
• During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
• In the last seven days, on how many days did you exercise for 30 minutes or more?
• Do you have health insurance coverage?

In advance of the 1936 presidential election, a magazine released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards.

• Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time.
• What effect does the low response rate have on the reliability of the sample?
• Are these problems examples of sampling error or nonsampling error?
• During the same year, another pollster conducted a poll of 30,000 prospective voters. These researchers used a method they called quota sampling to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI's Uniform Crime Report . One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in Data, Sampling, and Variation in Data and Sampling could explain this connection?

A website that allows anyone to create and respond to polls had a question posted on April 15 which asked:

“Do you feel happy paying your taxes when members of the Obama administration are allowed to ignore their tax liabilities?” 5

As of April 25, 11 people responded to this question. Each participant answered “NO!”

Which of the potential problems with samples discussed in this module could explain this connection?

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.” 6

The Pew Research Center for People and the Press admits

“The percentage of people we interview—out of all we try to interview—has been declining over the past decade or more.” 7

• What are some reasons for the decline in response rate over the past decade?
• Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.

1.3 Frequency, Frequency Tables, and Levels of Measurement

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below.

• Fill in the blanks in Table 1.37 .
• What percent of students take exactly two courses?
• What percent of students take one or two courses?

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in Table 1.38 .

• Fill in the blanks in Table 1.38 .
• What percent of adults flossed six times per week?
• What percent flossed at most three times per week?

Nineteen immigrants to the United States were asked how many years, to the nearest year, they have lived in the United States The data are as follows: 2, 5, 7, 2, 2, 10, 20, 15, 0, 7, 0, 20, 5, 12, 15, 12, 4, 5, 10.

Table 1.39 was produced.

• Fix the errors in Table 1.39 . Also, explain how someone might have arrived at the incorrect number(s).
• Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the United States for 5 years.”
• Fix the statement in b to make it correct.
• What fraction of the people surveyed have lived in the United States five or seven years?
• What fraction of the people surveyed have lived in the United States at most 12 years?
• What fraction of the people surveyed have lived in the United States fewer than 12 years?
• What fraction of the people surveyed have lived in the United States from five to 20 years, inclusive?

How much time does it take to travel to work? Table 1.40 shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

A business magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. Table 1.41 shows the ages of the chief executive officers for the first 60 ranked firms.

• What is the frequency for CEO ages between 54 and 65?
• What percentage of CEOs are 65 years or older?
• What is the relative frequency of ages under 50?
• What is the cumulative relative frequency for CEOs younger than 55?
• Which graph shows the relative frequency and which shows the cumulative relative frequency?

Use the following information to answer the next two exercises: Table 1.42 contains data on hurricanes that have made direct hits on the United States. Between 1851-2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm.

What is the relative frequency of direct hits that were category 4 hurricanes?

• not enough information to calculate

What is the relative frequency of direct hits that were AT MOST a category 3 storm?

1.4 Experimental Design and Ethics

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

An advertisement for Acme Investments displays the two graphs in Figure 1.14 to show the value of Acme’s product in comparison with the Other Guy’s product. Describe the potentially misleading visual effect of these comparison graphs. How can this be corrected?

The graph in Figure 1.15 shows the number of complaints for six different airlines as reported to the U.S. Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

An epidemiologist is studying the spread of the common cold among college students. He is interested in how the temperature of the dorm room correlates with the incidence of new infections. How can he design an observational study to answer this question? If he chooses to use surveys in his measurements, what type of questions should he include in the survey?

• 5 lastbaldeagle. Retrieved from http://www.youpolls.com/details.aspx?id=12328.
• 6 Keeter, S., et al. (2006). Gauging the impact of growing nonresponse on estimates from a national RDD telephone survey. Public Opinion Quarterly, 70 (5). Retrieved from http://hbanaszak.mjr.uw.edu.pl/TempTxt/Links/GAUGING%20THE%20IMPACT%20OF%20GROWING.pdf.
• 7 Pew Research Center. (n.d.). Frequently asked questions. Retrieved from http://www.pewresearch.org/methodology/u-s-survey-research/frequently-asked-questions/#dont-you-have-trouble-getting-people-to-answer-your-polls.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Statistics
• Publication date: Mar 27, 2020
• Location: Houston, Texas
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• Section URL: https://openstax.org/books/statistics/pages/1-homework

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Immigrants make up the largest share of the population in over 150 years and continue to shape who we are as canadians.

Released: 2022-10-26

Canada has a long history of immigration. Millions of people from all over the world have chosen, and continue to choose, Canada as their new home. In 2021, more than 8.3 million people, or almost one-quarter (23.0%) of the population, were, or had ever been, a landed immigrant or permanent resident in Canada. This was the largest proportion since Confederation, topping the previous 1921 record of 22.3%, and the highest among the G7.

Given that the population of Canada continues to age and fertility is below the population replacement level , today immigration is the main driver of population growth . If these trends continue, based on Statistics Canada's recent population projections , immigrants could represent from 29.1% to 34.0% of the population of Canada by 2041.

The COVID -1 9 pandemic highlighted the contribution that immigrants make to Canada's labour market. With job vacancies in late 2021 hitting 80% higher than pre-pandemic levels , and the working population aging, immigration is even more critical to the labour market than ever before. Recent immigrants, whose age structure is younger than the general population, constitute a pool of workers who can help mitigate the impacts of labour shortages in a number of sectors and regions across the country. From 2016 to 2021, immigrants accounted for four-fifths of labour force growth . More and more immigrants have pre-admission experience in Canada, and a large share of recent immigrants were selected for their ability to contribute to Canada's economy.

Immigrants come from many different countries, bringing with them their cultural, ethnic, linguistic and religious heritage. In the past, the majority of immigrants in Canada came from Europe. However, over the past 50 years, the share of new immigrants from Europe has declined, with the share of new immigrants who were born in Asia (including the Middle East) increasing. Over time, Asia has become the top source region of new immigrants, and this trend continued in 2021. The share of new immigrants from Africa also increased. Together, immigrants, Indigenous peopl e—w ho have walked this land for thousands of years, before Europeans settled her e—a nd their descendants have helped shape Canada as it is known today.

Today, Statistics Canada is releasing the sixth set of results from the 2021 Census, which provide an updated statistical portrait of the immigrant population. The census is one of the most comprehensive sources of data on immigrants living in Canada, allowing for comparability over time and at various levels of geography.

Governments at all level s—f rom federal to provincial, territorial and municipa l—a s well as many other non-governmental and community organizations will use this information to develop and evaluate immigration policies and programs, and to plan and implement education, health care, housing and other services.

Almost one in four people (23.0%) counted during the 2021 Census are or have been a landed immigrant or permanent resident in Canada. This was the highest proportion since Confederation, topping the previous record of 22.3% in 1921, and the largest proportion among G7 countries.

Just over 1.3 million new immigrants settled permanently in Canada from 2016 to 2021, the highest number of recent immigrants recorded in a Canadian census.

The share of recent immigrants settling in Atlantic Canada almost tripled in 15 years, rising from 1.2% in 2006 to 3.5% in 2021.

Over half of recent immigrants living in Canada were admitted under the economic category. Of these 748,120 economic immigrants, just over one-third (34.5%) were selected through skilled worker programs and another one-third (33.6%) through the Provincial Nominee Program.

The proportion of immigrants who first came to Canada temporarily on work or study permits or as asylum claimants before being admitted as permanent residents was especially high among recent immigrants who settled since 2016 (36.6%).

Asia, including the Middle East, remained the continent of birth for most recent immigrants (62.0%).

Almost one in five recent immigrants (18.6%) were born in India, making it the leading country of birth for recent immigration to Canada.

In contrast, the share of recent immigrants from Europe continued to decline, falling from 61.6% in 1971 to 10.1% in 2021.

The vast majority (92.7%) of recent immigrants are able to conduct a conversation in either English or French.

The share of second-generation Canadians (children of immigrants) younger than 15 years with at least one foreign-born parent rose from 26.7% in 2011 to 31.5% in 2021.

Canada's population growth driven by the record number of new immigrants admitted from 2016 to 2021 

Infographic 1  nearly one in four people in canada are immigrants, the highest proportion of the population in more than 150 years.

The rising proportion of immigrants is mainly driven by the record number of new immigrants who came to Canada from 2016 to 2021, despite fewer immigrants being admitted in 2020 because of the border and travel restrictions implemented in response to the pandemic.

From 2016 to 2021, Canada's population living in private households grew by 5.4%, and new, or recent, immigrants accounted for 71.1% of that growth.

Over 1.3 million recent immigrants were permanently admitted from January 1, 2016 to May 11, 2021, accounting for 15.9% of all immigrants living in Canada in 2021.

When combined with those already established here, more than 8.3 million people, or 23.0% of the population, were or had ever been a landed immigrant or permanent resident of Canada in 2021.

Immigration is expected to continue to increase in the decades to come. According to Statistics Canada's recent population projections , immigrants could represent from 29.1% to 34.0% of the total population by 2041.

Close to two-thirds of recent immigrants are of core working age

Infographic 2  close to two-thirds of recent immigrants are of core working age, rejuvenating canada's aging population.

While Canada has the highest share of the total population aged 15 to 64 among G7 countries, at 64.8%, the country's working population has never been older . According to the recent census release on age and type of dwelling, more than one in five people were closing in on retirement age (55 to 64 years), an all-time high. There were also more people aged 55 to 64 than young adults aged 15 to 24.

While immigration ultimately cannot stop the population aging process, it has a rejuvenating effect on the population in Canada overall. Since people usually migrate when they are young, the vast majority (95.8%) of recent immigrants to Canada from 2016 to 2021 were under the age of 65.

Just over 1 in 10 recent immigrants were youth and young adults aged 15 to 24 (10.9%), while most (64.2%) were in the core working age group of 25 to 54. A much smaller proportion of recent immigrants (3.6%) were aged 55 to 64.

Children younger than 15 years of age, who may one day join the labour force, represented 17.1% of recent arrivals to Canada. Immigration over the near term will ease the labour force crunch in Canada.

More immigrants are now working in Canada than before the pandemic, and, from 2016 to 2021, immigration contributed to 79.9% of the growth in Canada's labour force . The labour market outcomes of immigrants have improved in recent years, and since 2016, the employment rate among immigrants has risen by 2.0 percentage points, while the Canadian-born population has experienced a decrease of 2.0 percentage points.

Although more immigrants are employed in Canada, challenges remain, especially regarding skill utilization. From 2001 to 2016, the percentage of university-educated recent immigrants working in a job requiring a university degree decreased and was well below the proportion of their Canadian-born counterparts. Recent policy changes have been implemented to improve labour market outcomes for new immigrants and to increase the responsiveness of immigration to labour market demand. The census release in November 2022 will allow for further analysis of the education levels of Canada's recent immigrants and their skill uptake in the labour market.

More than half of recent immigrants are admitted under the economic category

In Canada, immigrants are selected according to three broad objectives: to enhance and promote economic development, to reunite families, and to fulfill the country's international obligations and uphold its humanitarian tradition.

Immigrants admitted under the economic category are selected based upon their potential economic contribution to meet labour market needs, or to create economic opportunities by owning, operating or investing in a business or through self-employment. In 2021, more than half (56.3%) of recent immigrants living in Canada were admitted under the economic category, either as the principal applicant or the dependant.

Among the broad types of economic immigration programs , more than one-third (34.5%) of new economic immigrants admitted from 2016 to 2021 were selected under one of the skilled worker programs. A similar proportion were selected under the Provincial Nominee Program, which is a program where people who have skills, education and work experience are nominated to contribute to the economy of a specific province or territory.

The proportion of economic immigrants admitted under the Provincial Nominee Program has increased since the first Provincial Nominee Program agreement was signed in Manitoba in 1996. Of those new economic immigrants admitted from 2016 to 2021, 33.6% were Provincial Nominee Program candidates, compared with 3.7% of those economic immigrants admitted from 2001 to 2005 and still living in Canada.

Manitoba (90.2%) had the highest share of recent economic immigrants selected as provincial nominees, followed by Saskatchewan (87.3%) and Prince Edward Island (84.7%). Provincial nominees also accounted for the majority of recent economic immigrants in Nova Scotia (66.4%), New Brunswick (63.7%), Yukon (62.9%), the Northwest Territories (56.8%) and Newfoundland and Labrador (53.3%).

In Canada, nine provinces and two territories have established their own Provincial Nominee Program. The exceptions are Quebec and Nunavut. Quebec has administered its own economic immigration programs since 1991 through the Canada–Quebec Accord , which gives the province more autonomy over the selection and integration of its immigrants. In 2021, 46.4% of recent immigrants who lived in Quebec were admitted under a skilled worker program.

Just under 61,000 recent refugees came from Syria, attesting to Canada's international commitments and its long-standing humanitarian tradition

According to the 2021 Census, there were 218,430 new refugees admitted as permanent residents from 2016 to 2021 and still present in Canada at the time of the census. The primary places of birth of refugees have changed considerably over the decades, in tandem with conflicts and international events. These changes are reflected in the profile of refugees who are still in the country today.

For example, from 1980 to 1990, most refugees came from Viet Nam, Poland and El Salvador.

From 1991 to 2000, Sri Lanka, Bosnia and Herzegovina and Iran accounted for the largest share of refugees admitted to Canada.

From 2001 to 2010, Colombia, Afghanistan and Iraq were the main countries of birth of refugees who settled in Canada during that period.

In 2015, the Government of Canada committed to bringing Syrian refugees to the country. At the time of the 2016 Census, close to 27,000 Syrian refugees had already been admitted to Canada over the previous five years . From 2016 to 2021, 60,795 new Syrian-born refugees were admitted and living in Canada, accounting for over one-quarter (27.8%) of the new refugees in the country.

Iraq (15,505), Eritrea (13,965), Afghanistan (9,490) and Pakistan (7,810) were the other most common countries of birth for new refugees from 2016 to 2021.

The majority of refugees were resettled in Canada after a recommendation by the United Nations Refugee Agency, a designated referral organization or a private sector sponsor.

Close to 85,000 immigrants were recognized as protected persons in Canada and became permanent residents from 2016 to 2021 following an asylum claim in Canada for themselves or their family members.

More than one-third of recent immigrants have pre-admission experience

Infographic 3  more than one-third of recent immigrants have pre-admission experience.

Pre-admission experience is gained when immigrants first come to Canada temporarily on work or study permits or as asylum claimants before seeking permanent residence. This process is called " two-step immigration " and it can ease an immigrant's integration into the Canadian labour market and improve earnings in both the short and long term. The two-step immigration process has the objective to improve outcomes for immigrants, employers, society and the economy, giving both the receiving country and the potential immigrant the opportunity to test the situation before making the move permanent.

Among immigrants admitted since 1980 and where pre-admission experience information was available, one-quarter (25.2%) had lived temporarily in Canada before their admission as permanent residents or landed immigrants.

Given the increase in the number of temporary foreign workers and international students, as well as the expansion of some economic immigrant programs (for example, the Canadian Experience Class and the Provincial Nominee Program), two-step immigration is more common among recent immigrants. In 2021, over one-third (36.6%) of immigrants admitted in the previous five years had gone through this process, compared with 17.9% among longer-term immigrants (those admitted from 2001 to 2005).

Most (62.9%) immigrants admitted since 1980 with pre-admission experience had acquired a temporary work permit. This was especially true among immigrants who recently settled in the country permanently (77.3%). There are many benefits associated with pre-admission experience. It plays a key role in lifting immigrants' wages , as it provides pathways for immigrants to acquire language skills and knowledge of the Canadian labour market. Immigrants with prior experience in Canada have contributed to recent improvements in labour force outcomes among new immigrants .

Increasing shares of recent immigrants settling outside Canada's three largest urban centres

In 2021, over 9 in 10 recent immigrants lived in one of Canada's 41 census metropolitan areas ( CMAs ), which are large urban centres of over 100,000 residents. As was the trend over the past 50 years, Toronto (29.5%), Montréal (12.2%) and Vancouver (11.7%) continued to welcome the most recent immigrants in 2021.

However, the share of recent immigrants who have settled in Canada's three largest urban centres continued to decline, falling from 56.0% in 2016 to 53.4% in 2021—with the most pronounced decrease in Montréal, where the share went from 14.8% in 2016 to 12.2% in 2021.

In contrast, an increasing number of recent immigrants have settled outside these key urban centres, strengthening population growth in urban centres outside Canada's three largest CMAs . For example, the share of recent immigrants who settled in Ottawa–Gatineau rose from 3.1% in 2016 to 4.4% in 2021, while it almost doubled in Kitchener–Cambridge–Waterloo (from 1.2% in 2016 to 2.1% in 2021; see Table 1).

Additionally, 4.4% of recent immigrants settled in small urban areas (census agglomerations) and 3.2% of recent immigrants settled in rural areas (outside CMAs and census agglomerations) in 2021.

New immigrants often settle in regions where they have existing social networks, economic and employment opportunities and enjoy the general appeal of the area . Several immigration programs and investments were also designed to help balance the geographical distribution of recent immigrants across the country and encourage settlement in both small and large metropolitan areas.

The share of recent immigrants settling in Atlantic Canada has nearly tripled since 2006

The share of recent immigrants settling in Atlantic Canada has almost tripled, rising from 1.2% in 2006 to 3.5% in 2021. Over this 15-year period, the share of recent immigrants rose in Nova Scotia (from 0.6% to 1.6%), New Brunswick (from 0.4% to 1.2%), Prince Edward Island (from 0.1% to 0.4%) and Newfoundland and Labrador (from 0.1% to 0.3%).

As is the case in other provinces, the settlement of recent immigrants is especially notable in the large urban centres of the Atlantic provinces. Between one-third and one-half of all immigrants living in Moncton (48.4%), Fredericton (39.2%), Saint John (36.2%), Halifax (35.2%) and St. John's (32.5%) were admitted from 2016 to 2021.

The Atlantic Immigration Program ( AIP ) was launched in 2017 as an employer-driven program to speed the growth of Atlantic Canada's economy and to test new approaches to attract and retain skilled immigrants in the region in key sectors.

The program helps temporary foreign workers and international graduates wanting to live and work in one of the four Atlantic provinces gain permanent residency. Immigration, Refugees and Citizenship Canada ( IRCC ) has reported that since its inception, the AIP has brought thousands of new permanent residents to Atlantic Canada. Participating employers have made over 9,800 job offers in key sectors, including health care, accommodation and food services, and manufacturing.

IRCC reported that the vast majority of AIP applicants were still living in the region after one year. The AIP and other similar programs could play a role in population growth and economic development of various regions across the country.

This new economic admission category for immigrants has been included in the 2021 Census.

Map 1  The Atlantic provinces welcomed higher shares of recent immigrants in Canada than the previous censuses, while Quebec and the Prairies saw their shares decrease

Following the drop in global oil prices in 2014 and increased unemployment in Alberta, the proportion of new immigrants settling in Alberta fell from 17.1% in 2016 to 14.5% in 2021. Nevertheless, this was well above the proportion observed in 2006, when 9.3% of new immigrants made Alberta their home.

New immigrants represented almost one-third of the immigrant population of Regina (32.5%) and Saskatoon (31.2%) in 2021.

The territories (Yukon, the Northwest Territories and Nunavut) had the lowest numbers of recent immigrants in Canada. In 2021, 2,175 new immigrants, or 0.2% of all recent immigrants to the country, settled in the territories. This proportion has remained stable since 2011.

Changes in the place of birth of immigrants over time contribute to Canada's linguistic and ethnocultural landscape

Infographic 4  almost two-thirds of recent immigrants were born in asia, including the middle east.

The places of birth of immigrants and refugees to Canada have changed over time, in tandem with changing immigration policies as well as international events, contributing to the diversity of Canadian society.

For decades, Asia (including the Middle East) has accounted for the largest share of recent immigrants. This proportion has grown, with Asian-born immigrants making up a record-high 62.0% of recent immigrants admitted from 2016 to 2021—whereas in 1971, 12.1% of recent immigrants were from Asia.

The share of recent immigrants born in Europe continued its 50-year downward trend. In 2021, 1 in 10 recent immigrants (10.1%) were from Europe, a proportion about six times lower than in 1971 (61.6%).

Largest proportion of new immigrants comes from India

Infographic 5  nearly one in five recent immigrants were born in india, the highest proportion from a single place of birth since 1971 .

For the first time, India took the top spot as the primary place of birth of new immigrants to Canada (18.6% of recent immigrants from 2016 to 2021), followed by the Philippines (11.4%) and China (8.9%).

The last time that such a high proportion of immigrants came from a single place of birth was during the 1971 Census, when 20.9% of all recent immigrants came from the United Kingdom.

The picture of immigration varies in Canada by place of birth, period of immigration, admission category and place of residence. See this interactive chart for more information on how immigration varies by region.

Over 450 mother tongues reported on the census, as newcomers contribute to linguistic diversity

The wide variety of source regions of immigrants contributes to the linguistic diversity in Canada . In 2021, 69.4% of recent immigrants did not report having English or French as their mother tongue, that is, the first language they learned in childhood that is still understood. In the context of this release, languages other than English and French are also referred to as "non-official languages." Arabic (10.3%), Tagalog (8.4%), Mandarin (7.9%), and Punjabi (6.5%) were the non-official languages reported most often as mother tongues by recent immigrants, either alone or with another language.

In 2021, nearly one in four recent immigrants (24.4%) reported English as their mother tongu e—a lone or with another language. This proportion was up from 18.2% in 2016. Those immigrants reporting English as their mother tongue predominately came from India (20.5%), the Philippines (12.5%), the United States (10.3%) and Nigeria (10.2%).

Of recent immigrants, 6.5% reported French as their mother tongue, either alone or with another language, the same proportion as in 2016. These recent immigrants were largely coming from France (30.3%), Cameroon (11.5%), Côte d'Ivoire (8.4%), Algeria (5.8%) and the Democratic Republic of the Congo (5.7%).

The vast majority of recent immigrants can conduct a conversation in either English or French

Although a large proportion (69.4%) of the recent immigrants reported only having non-official languages as their mother tongue, the vast majority (92.7%) of the more than 1.3 million recent immigrants reported being able to conduct a conversation in English or French.

Among those recent immigrants who did not report English or French as their mother tongue, nearly two-thirds (62.3%) reported speaking at least one of the two official languages regularly at home, either alone or with another language, reflecting one aspect of the integration of these newcomers. More specifically, almost half (47.8%) reported speaking only English with a non-official language regularly at home, while 7.4% reported speaking only English, 3.3% reported speaking only French with a non-official language and 1.2% reported speaking only French regularly at home.

The percentage of immigrants who spoke English or French regularly at home was even higher among immigrants who had been in Canada longer. In 2021, 76.4% of immigrants who settled in the country before the 1980s and whose mother tongue was not an official language spoke English or French regularly at home, either alone or with another language.

The knowledge or predominant use of English or French generally leads immigrants to one of Canada's two official language communities in the public sphere, and even the private sphere. The first official language spoken ( FOLS ) is a general indicator of this linguistic orientation.

Outside Quebec, almost 9 in 10 recent immigrants (89.1%) had only English as their FOLS . The share of recent immigrants settling outside Quebec with only French as their FOLS was 2.1%, while 1.3% reported both English and French as their FOLS . The share of recent immigrants outside Quebec with neither English nor French was 7.5%.

In Quebec, over half (54.5%) of recent immigrants had only French as their FOLS in 2021. The share of recent immigrants to Quebec with both English and French as their FOLS was 14.7% in 2021, and just over one in four (25.5%) had only English as their FOLS . The share of recent immigrants in Quebec with neither English nor French as their FOLS was 5.3%.

For more information on the linguistic integration of immigrants, stay tuned for the release on language at work. New census data will be available in November 2022.

Immigrants also contribute to the ethnic, cultural and religious diversity of the country. For more information, the Daily article titled " The Canadian census: A rich portrait of the country's religious and ethnocultural diversity " is available today.

The vast majority of immigrants, recent or established, live in a major urban centre

Infographic 6  10 of canada's 41 large urban centres have a higher proportion of immigrants than all of canada.

The provinces and territories, especially the urban centres where immigrants are initially settled, often remain the place they call home, contributing to the urbanization of the country .

The vast majority (92.2%) of immigrants in 2021 lived in a CMA . In comparison, just over two-thirds (67.7%) of those born in Canada lived in a CMA .

The fact that most established immigrants and recent immigrants choose to settle in large urban centres has had a profound impact on Canada's cities. New immigrants tend to join existing immigrant communities already established throughout the country, especially in its largest cities. Family, friends, jobs, housing and lifestyle are some of the key factors that immigrants consider when selecting their new home.

The large urban centre of Toronto has the largest proportion of immigrants overall. In 2021, close to half (46.6%) of the population living in the Toronto CMA were immigrants. Immigrants made up more than half of the residents of four municipalities in the Toronto CMA : Markham (58.6%), Richmond Hill (58.2%), Mississauga (53.2%) and Brampton (52.9%).

Vancouver had the second-largest proportion of immigrants, at 41.8%. Within the large urban centre of Vancouver, immigrants accounted for three-fifths (60.3%) of the population of Richmond and half (50.4%) of Burnaby's population.

Among Canada's 41 largest urban centres, the proportion of immigrants was above the national average of 23.0% in Calgary (31.5%), Abbotsford–Mission (26.1%), Edmonton (26.0%), Kitchener–Cambridge–Waterloo (25.8%), Hamilton (25.6%), Winnipeg (25.4%), Montréal (24.3%) and Windsor (23.3%).

According to 2022 results from the Canadian Social Survey, most new immigrants still value having family in the area. At the same time, the location of jobs, businesses and education prospects, as well as housing, are also among the top key factors considered by immigrants as reasons for settling in specific cities.

The fact that recent immigrants are increasingly choosing to settle outside of the large urban centres of Toronto, Montréal and Vancouver may partly reflect the higher shelter and housing costs and availability in these cities, as Toronto and Vancouver reported the highest rates of unaffordable housing in the 2021 Census. According to the census release on housing , shelter costs across Canada, especially for renters, have been rising since 2016. Despite improved housing affordability overall, over one in five immigrants (21.0%) spent at least 30% of their income on shelter costs. In comparison, 13.2% of non-immigrant respondents spent at least 30% of their income on shelter in 2021. Approximately 1 in 7 recent immigrants (14.3%) were deemed in core housing need, compared with around 1 in 16 (6.4%) for those born in Canada.

Other possible factors for the shift in settlement patterns of immigrants include changes in regional economic conditions, immigration programs and source countries of immigrants.

Almost one-third of all children in Canada have a least one parent born abroad

Canadian-born children of immigrants, also called the "second generation," have at least one foreign-born parent. The second generation may adopt a dual cultural background, combining the values and culture of their parents' country of origin with the values, social norms and official languages of the host country, and act as a bridge between their immigrant parents and the rest of the population.

According to 2021 Census data, almost 1.9 million children younger than 15 years had at least one parent born abroad, accounting for almost one-third (31.5%) of all children in Canada. This proportion was up from 26.7% in 2011 and 29.2% in 2016.

When added to the children of immigrants who are now adults, the share of second-generation Canadians has remained relatively stable in the last decade. Just under 6.4 million people born in Canada had at least one foreign-born parent in 2021, representing 17.6% of the total population, compared with just over 5.7 million in 2011, or 17.4% of the total population.

Children of immigrant s—b oth young and ol d—c ontribute to the population renewal, economic growth and diversity of Canada.

Looking ahead

Public decision makers, employers and providers of health care, education, justice and other services use census data to better meet the needs of immigrants.

Immigrants who have settled in Canada for a certain number of years can apply for and obtain Canadian citizenship. Read more about Canadian citizenship in the Census in Brief article coming soon.

For more census results on the diversity of the population, consult the Daily article on ethnocultural diversity and religion, also released today.

Look out for the next census release on education and the labour force, coming out on November 30, 2022. The release of these data will allow for more in-depth analysis of socioeconomic outcomes for immigrants.

More census information on non-permanent residents in Canada will be released in 2023.

  Note to readers

Canadians are invited to download the StatsCAN app to view the census results.

Definitions, concepts and geography

The 2021 Census collected information on place of birth , place of birth of parents and citizenship .

Generation status can be derived when the place of birth and place of birth of parents are combined to establish whether the respondent is in the first, second, or third generation or more.

A change in the 2021 Census consisted of getting information on immigrant status and year of immigration from Immigration, Refugees and Citizenship Canada administrative data rather than from census questions, as was done in previous censuses. This helped to improve data quality and reduce the burden on respondents to recall information, such as the year they were granted the right to live in Canada permanently. Data integration is a secure process in which all information remains confidential.

Immigrant refers to a person who is or has been a landed immigrant or permanent resident. Such a person has been granted the right to live in Canada permanently by immigration authorities. Immigrants who obtained Canadian citizenship by naturalization are included in this group.

Period of immigration refers to a specific time frame in which an immigrant first obtained permanent resident or landed immigrant status. Period of immigration allows recent immigrants to be identified.

Recent immigrant (or new immigrant or newcomer) refers to a person who has been admitted to the country permanently in the five years preceding a census. In the 2021 Census, this period is January 1, 2016, to May 11, 2021.

Admission category and applicant type provide information on the conditions under which immigrants were granted the right to live in Canada (e.g., economic immigrants, immigrants sponsored by family, refugees). Applicant type is most often used in combination with admission category, particularly for the economic immigrant categories, in which principal applicants are selected based on their ability to contribute to the Canadian economy. These variables are available for immigrants who have been admitted since 1980.

Pre-admission experience indicates whether the immigrant held a work or study permit or claimed refugee status (asylum claimant) before admission as a permanent resident. This helps to further understand the socioeconomic outcomes of immigrants with pre-admission experience in Canada and how they compare with those of immigrants without pre-admission experience.

Non-permanent resident refers to a person from another country with a usual place of residence in Canada and who has a work or study permit or who has claimed refugee status (asylum claimant). Family members living with work or study permit holders are also included, unless these family members are already Canadian citizens, landed immigrants or permanent residents. Other concepts that are sometimes used interchangeably with non-permanent residents include "temporary residents" or "temporary immigrants."

Immigrant status provides information on the number of non-immigrants, immigrants and non-permanent residents with a usual place of residence in Canada at the time of the census.

For more information on census questions and derived variables related to immigration, citizenship, place of birth and generation status since Confederation, please refer to Appendix 2.1 of the Dictionary, Census of Population 2021 , Statistics Canada Catalogue no. Catalogue number 98-301-X .

To better understand the relationship between the concepts of immigration, place of birth and generation status, please refer to Figure 2.5 in the Dictionary, Census of Population 2021 , Statistics Canada Catalogue no. Catalogue number 98-301-X .

To better understand the relationship between the concepts of immigration, citizenship and place of birth, please refer to Figure 2.6 in the Dictionary, Census of Population 2021 , Statistics Canada Catalogue no. Catalogue number 98-301-X .

All findings in this document are based on the 2021 geographic boundaries.

The 2021 Census uses Statistics Canada's standard classifications for all place of birth, generation status, citizenship and immigration variables. Data from responses to the census questions or from administrative records are used to produce summary and detailed variables that provide a portrait of the population living in Canada.

New for 2021, additional immigration variables on year of arrival, pre-admission experience and province or territory of intended destination were included in the census.

For more information, please see the Place of Birth, Generation Status, Citizenship and Immigration Reference Guide, Census of Population, 2021 .

2021 Census of Population products and releases

Today, Statistics Canada is releasing the sixth set of results from the 2021 Census of Population.

Several 2021 Census products are also available today on the 2021  Census Program web module. The web module has been designed to provide easy access to census data, free of charge.

Analytical products include two releases in The Daily and one infographic on citizenship in Canada.

Data products on immigration, place of birth, and citizenship, ethnocultural and religious diversity, as well as mobility and migration for a wide range of standardized geographical areas are available through the Census Profile and data tables .

The Focus on Geography series provides data and highlights on key topics found in this Daily release and in the Census in Brief articles at various levels of geography.

Reference materials are designed to help users make the most of census data. They include the Guide to the Census of Population, 2021 , the Dictionary, Census of Population, 2021 , and the 2021 Census of Population questionnaires . Both the dictionary and the guide are updated with additional information throughout the release cycle. Five reference guides for place of birth, generation status, citizenship and immigration ; visible minority and population group ; religion ; ethnic or cultural origin ; and mobility and migration are also available.

Geography-related 2021 Census Program products and services can be found under Geography . This includes GeoSearch , an interactive mapping tool that provides data for various standard geographic areas, along with the Focus on Geography Series and the Census Program Data Viewer , both data visualization tools.

Videos on census concepts can be found in the Census learning centre .

An infographic, Overview of Canadian citizenship in 2021 , is also available.

Over the coming months, Statistics Canada will continue to release results from the 2021 Census of Population, providing an even more comprehensive picture of the population of Canada. Please see the 2021 Census release schedule to learn the topics and date for the next census release.

Contact information

For more information, or to enquire about the concepts, methods or data quality of this release, contact us (toll-free 1-800-263-1136 ; 514-283-8300 ; [email protected] ) or Media Relations ( [email protected] ).

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