SAMPLES AND STATS(Managing Data)
Grades 9-10
Skills and Objectives:
* Students will identify different sampling methods.
* Students will design and conduct surveys using
sampling methods.
Suggested Groupings-Partners, small groups
Getting Started:
* Have students share any prior knowledge of sampling they may have. Discuss the idea that
sampling makes it possible to gather information about a population when surveying every member
is impossible or impractical. Educators, advertisers, and policymakers all use information
gathered through sampling. The U.S. Census Bureau also develops and uses sampling techniques to
gather information about the U.S. population. For example, while the Census Bureau distributes
both a short and long census questionnaire, only one in six households will get a long form for
Census 2000. This sample is large enough to provide the data to accurately describe the U.S.
population.
* Explain to students that this activity will introduce them to a variety of sampling methods and
the multiple steps involved in the process of conducting a survey to gather statistical
information. Make sure they understand that the sampling process they will use to obtain data
is much simpler than the methods used by the U.S. Census Bureau and others.
Using the Activity Workshe0s:
* Distribute copies of pages 16 and 17 to students. Have them read and complete the activity on
page 16. Alternatively, you may wish to do this activity as a class.
* Then have students read and discuss the section on bias at the top of page 17. Ask: Can you
come up with your own example of a biased sample? (For example, if you conduct a survey of your
classmates by e-mail, you will automatically exclude all class members who do not have access
to e-mail.) What steps can researchers take to ensure that the studies they design are not
biased?
* Before students begin, discuss the difference between the type of survey the Census Bureau
conducts and a poll. The Census Bureau uses surveys to collect and analyze social, economic,
and geographic data. A poll is a survey that is used to measure attitudes and opinions. Go
over these steps with them. 1. Choose a survey question. Make sure students choose a question
that asks for factual information, like age or education level, rather than an attitude or
opinion. 2. Identify the target population and sample size. 3. Decide on the sample method.
4. Conduct the survey and interpret, tabulate, and graph or map results.
* To demonstrate, choose your own question and do a quick survey with your students.
Wrapping Up:
* Have each group present their surveys and results. Ask a spokesperson for each group to discuss
the target population, sample size, and sample method used in the survey. Have students share
their conclusions.
* Have students conduct further research about the sampling methods presented here. Have the
class agree on one survey question. Divide the class into three groups, and have each group use
a different sampling method. Be sure each group uses the same size sample. Then invite the
groups to compare results. Alternatively, student groups could use the same sampling method on
different sample sizes.
* Students can visit the U.S. Census Bureau Web site (www.census.gov) to get information from
surveys conducted on such subjects as computer use, crime, education, etc. Click on "Subjects
A-Z" and choose "S" then "Surveys.
Answers:
Page 16:
1. Cluster sampling.
2. Random sampling.
3. Systematic sampling.
Chalkboard Definitions
sampling: using a finite part of a statistical population for study, in order to gain information
about the whole
survey: a set of questions asked of a specific population to collect data for analysis.
poll: a survey that measures attitudes and opinions.
Lesson 5 Activity Worksheet
SAMPLES AND STATS
* Sampling is a scientific technique used to obtain as accurate a figure or measurement as
possible, when an exact count cannot be taken. By measuring a scientifically selected portion
of a population, it is possible to describe the characteristics of the entire population.
Below is a chart describing three different scientific sampling methods. The U.S. Census
Bureau's long form is an example of systematic sampling. For Census 2000, a systematic sampling
of approximately 1 in every 6 households will receive the long form, and an average of 5 out of
every 6 households will receive the short form. Although the long form doesn't go to every
household, information from these forms can be used to accurately describe the entire U.S.
population.
Here are three different sampling methods:
Random Sampling-Each individual in the population has an equal chance of being selected.
Example: To take a random sample of students in your school, you could write the name of each
student on a slip of paper, then choose slips at random.
Cluster Sampling-Groups, rather than individuals, are randomly selected. Example: You might
randomly select certain classes, then interview every student in only those classes.
Systematic Sampling-A rule, or pattern, that applies to a population is used to make selections.
Example: Using an alphabetical list of students, count off by 6, and select every 6th student on
the list.
* Test your understanding of different sampling techniques. Draw lines to match the sampling
methods with their types.
1. Choose any three pages from the telephone book at random, and call everyone on those pages.
2. Choose 100 telephone numbers at random from the entire book.
3. Choose every 100th listing in the telephone book.
a. Random Sampling
b. Systematic Sampling
c. Cluster Sampling
* When choosing a sampling method, you need to beware of hidden biases. For example, imagine that
you want to know if teenagers today are taller than teenagers in the past. You've found
information about the average height of students in your school in 1940 and 1970. Now you need
to find out the average height of students in your school today. You probably don't want to get
the height data from a sample consisting of members of the school basketball team! Why not?
* Design your own sample survey.
1. Acting as your school's census bureau, identify a characteristic of interest or importance to
your school and choose a survey question. (Topic examples- transportation to and from
school, team sports or other extracurricular activities, foreign languages studied, etc.) For
some of these topics, you may be able to check the accuracy of your survey results against
actual tallies your school keeps. Be sure not to ask questions about attitudes or opinions.
Write your topic and survey question here:
2. Choose your target population. The target population is the group of people to whom you want the
sample survey to apply. For instance, a survey about a school-related question could apply to
the students in your grade or to the whole student body. Make sure you survey a good sample of
your target population. (For example, if your survey applies to a student body of 400, you might
want to talk to at least 10%, or 40 people.)
Write your target population and sample size here:
3. Based upon the steps above, which sampling method would you choose for your survey? Why?
4. Now conduct your sample survey and tabulate the results. Then organize your results into a
graph or table and add a narrative summary. Share your graph, or table and summary, with the
class.
FORECASTING THE FUTURE(Managing Data)
Grades 11-12
Skills and Objectives:
* Students will learn about population estimates and population projections.
* Students will compare population projections based on numerical (arithmetic) growth and on
percent (geometric) growth.
Getting Started:
* Introduce the lesson by discussing the following terms that are defined in the lesson as they
relate to population: enumerations, estimates, projections, components of population change,
births, deaths, and net migration. Help the students understand that information about the U.S.
population is important for a variety of purposes, including planning in both the public sector
(e.g., where to build schools and hospitals) and the private sector (e.g., store location and
marketing), and that population figures are used in determining federal and state fund
allocations.
Using the Activity Worksheets:
Distribute copies of pages 19 and 20 to students and discuss the problems with them. Have students
individually, or in pairs, calculate the answers to questions 1 through 11. Then with the entire
class, discuss answers to questions 12 through 16.
Population estimates and projections:
Discuss with students how U.S. Census Bureau population estimates and projections are actually
done, and explain that the methodology used by Census Bureau demographers is more complicated
than the hypothetical examples given here. There can be many assumptions and variables involving
the set of components (fertility, mortality, and net migration) that contribute to the population
growth estimates and projections the U.S. Census Bureau publishes.
For further information on population estimates:
www.census.gov/population/www/estimates/concepts.html
For further information on population projections:
www.census.gov/population/www/projections/aboutproj.html
Answers:
1. 32,621,613.
2. 254,899 and 8.4 percent.
3. 568,996 and 14.9 percent.
4. 895,990 and 34.6 percent.
5. 1,889,829 and 106.4 percent.
6. Answers will vary.
7. 3,542,015 and 3,563,234.
8. 4,944,095 and 5,026,989.
9. 4,382,693 and 4,693,102.
10. 5,555,057 and 7,565,031.
11. Answers will vary.
12. Because the percent increase is applied to a larger population in 1990 than in 1970.
13. Arizona. Because Arizona had the highest percent increase in population during the 1970-1990
period, it has the largest proportionate difference between a population projection for the
year 2010 based on numerical growth versus percent growth.
14. The population projection based on percent change would be larger because the percent decline
would be applied to the smaller 1990 population.
15. Calculate one-half the numerical growth of the 1970-1990 period and then add it to the 1990
population.
16. Calculate the ratio of the 1990 to the 1970 population (to six decimal places to minimize
rounding error), then take the square root of the ratio and convert it to a percent increase.
Multiply the percent increase by the 1990 population, then add the product to the 1990
population. You can't assume one-half of the percent growth for the 1970-1990 period because
of the compounding effect of a geometric rate of increase - an analogy would be compound
interest rates. Taking South Carolina as an example, the ratio of its 1990 to its 1970
population is 1.345847. The square root of 1.345847 is 1.160, yielding a 16 percent increase
in population in the 1990-2000 decade. The increase of 557,872 added to the 1990 population of
3,486,703 yields a population projection for the year 2000 of 4,044,575.
Chalkboard Definitions
rate: a standard amount used to calculate a total, as in a percentage change in population over
the course of a year.
population estimate: a conclusion about the past or present population based on existing data.
population projection: computation of future changes in population size based on assumptions about
births, deaths, and migration.
Lesson 6 Activity Worksheet
FORECASTING THE FUTURE
* Enumerations, estimates, and projections of population
The U.S. Census Bureau produces three basic types of information about the U.S. population:
enumerations, estimates, and projections. Enumerations are counts of the population such as in
the 1990 census of population. Estimates are calculations of the population for a recent date
and are usually based on the last census as well as on information about population change since
the last census. Projections are calculations of the population for a future date and are
usually based on the last census or estimate, and on assumptions about future population growth
or decline.
* Population Estimates
The three basic components of population change between two dates are births, deaths, and net
migration. For population estimates for states, net migration may be divided into net
international migration (immigration to the United States minus emigration from the United
States) and net domestic migration (in-migration from other states minus out-migration to
other states).
For California, the population in 1990 was 29,785,857. For the 1990-1998 period, data on the
components of population change show the following:
births (B) = 4,708,894, deaths (D) = 1,810,698, net international migration (NIM) +2,019,488,
and net domestic migration (NDM) = -2,081,928. Calculate the 1998 population estimate for
California using the following formula:
1. P(1998)=P(1990) + B - D + NIM + NDM
* Population Projections
To make population projections for the United States or for individual states, demographers make
assumptions about future trends in the components of population change. These assumptions,
which reflect professional judgment and take into account past trends, are made in terms of
rates for births and deaths, and in terms of rates or numbers for migration.
For simplicity, the population projections discussed below are based on assumptions about past
trends in total population, not on assumptions about each component of population change. Table
1 shows the 1970 and 1990 census populations for four states, all with populations that
increased between 1970 and 1990. Calculate numerical growth (1990 population minus 1970
population) and percent growth (population growth as a percent of 1970 population, with percent
change rounded to one decimal place).
Table 1. Population of Selected States: 1970 and 1990
2. Connecticut in 1970 had 3,032,217, and had 3,287,116 people in 1990.
3. Minnesota had 3,806,103 in 1970, and had 4,375,099 people in 1990.
4. South Carolina had 2,590,713 in 1970, and had 3,486,703 in 1990.
5. Arizona had 1,775,399 in 1970, and in 1990 had 3,665,228.
6. Your State
(Also pictured: two empty columns; "Population growth, 1970-1990", "Numerical", "Percent")
Calculate population projections for each state for the year 2010 assuming a continuation of trends
for the 1970-1990 period: first based on numerical change (an arithmetic rate of change), then
based on percent change (a geometric rate of change) with the results rounded to the nearest
integer.
Table 2. Population Projections for Selected States: 2010
7. Conneticut(based on numerical, based on percent change)
8. Minnesota(based on numerical, based on percent change)
9. South Carolina(based on numerical, based on percent change)
10. Arizona(based on numerical, based on percent change)
11. Your State(based on numerical, based on percent change)
Questions about population projections
12. Why are the population projections for the year 2010 larger when based on percent change
than when based on numerical change for the 1970-1990 period?
13. For which of the first four states is the proportionate difference between the two projections
the largest and why?
14. If the population of a state had declined between 1970 and 1990, which population
projection-numerical change or percent change - would be larger for the year 2010 and why?
15. How would you use the data in Table 1 to project population for states for the year 2000
assuming past trends in numerical population change?
16. How would you use the data in Table 1 to project population for states for the year 2000
assuming past trends in percent population change?
Selected Census 2000 Short Form Questions
1. What is this person's sex? Male/Female
2. What is this person's age and date of birth? (Print numbers in boxes)
Age on April 1, 2000 __
Month of Birth __
Day of Birth __
Year of Birth ____
Note: Please answer BOTH questions 3 and 4.
3. Is this person Spanish/Hispanic/Latino?
* No, not Spanish/Hispanic/Latino
* Yes, Mexican, Mexican American, Chicano
* Yes, Puerto Rican
* Yes, Cuban
* Yes, other Spanish/Hispanic/Latino-Print group below.
4. What is this person's race? Mark one or more races to indicate what this person considers
himself/herself to be.
* White
* Black, African American, or Negro
* American Indian or Alaska Native-Print name of enrolled or principal tribe below.
* Asian Indian
* Japanese
* Chinese
* Korean
* Filipino
* Vietnamese
* Other Asian-Print race below.
* Native Hawaiian
* Guamanian or Chamorro
* Samoan
* Other Pacific Islander-Print race below.
* Some other race-Print race below.
View the Census 2000 questionnaire on the U.S. Census Bureau Web site (www.census.gov).