CREATE YOUR OWN FORM(Managing Data)
Grades 5-6
Skills and Objectives:
* Students will gather and organize data using a "mock" census form.
* Students will determine mean, mode, range, and median for sets of data.
Suggested Croupings-Small groups
Materials-Index cards or notebook paper
Getting Started:
1. Students may be familiar with finding the mean, range, and median; they may not understand the
ways in which these statistics are used to describe a set of data. Mean, median, and mode are
types of statistics known as measures of central tendency. Range is a measure of data
dispersion. The Census Bureau uses such measures to describe some of the data it collects
about the United States. Depending on what is being studied, different researchers may find one
measure more useful than another. Median income, for example, may provide economists with a
better picture of what a person "in the middle" earns than mean income, which can be distorted
by large ranges and unequal distribution.
2. The day before your class does this activity, explain to students that they will be conducting
a class census. To do this, they will be collecting information from their own households.
* Your class census will include two questions.
1. How many people live in your household?
2. What are their ages?
* Have students write each question on an index card or a sheet of paper, leaving room for
answers. Instruct students to take their "census form(s)" home, ask family members
(including themselves) each question, and record the answers on the cards or paper.
Using the Activity Worksheets:
1. Make copies of the Lesson 5 Activity Worksheets (pages 16 and 17).
2. Divide your class into small groups (no more than 6). Give each group one copy of each
worksheet and a pile of index cards.
* Groups will use their worksheets to develop their own household statistics.
Wrapping Up:
1. Compare group results to national figures (refer to the Census Facts box on page 16).
Statistics will vary, but students should be able to explain their work.
* Why might the mean household size for your group be higher than the national mean? (All
student households include at least one child and one adult. The national mean includes many
households made up of a single adult.)
* Make sure students understand that there can be more than one mode if two or more numbers
show up an equal number of times in a set.
* Why might the median age for your group be lower than the national median? (Again, all
student households include at least one child. The national median age includes a segment of
the population that doesn't have children.)
2. Photocopy the Selected Census 2000 Short Form Questions on page 21 and distribute them to your
class, explaining to students that these are some examples of the actual census questions.
Extension Activity:
Have students visit the U.S. Census Bureau Web site (www.census.gov) to get updated statistics
on mean household size and median age. How do those data compare with the class' statistics?
Have students choose other questions they could ask, then collect data and compile statistics based
upon the answers.
Chalkboard Definitions
mean: the average of a set of numbers.
median: the middle number (or the average of the two middle numbers) in a set of numbers.
mode: the number that appear's most often in a set of numbers.
range: the difference between the greatest number and the least number in a set of numbers.
addend: any number that is added to another to form a sum.
Lesson 5 Activity Worksheet
CREATE YOUR OWN FORM
* The U.S. Census Bureau will use the data gathered in Census 2000 to develop statistics that
tell us more about our country. Some of the statistics the U.S. Census Bureau might use are:
mean (or average), mode, range, and median.
The Census Facts box (right) gives you two of these statistics. Read the Census Facts box. Then
work with your group to develop your own census-style statistics. Follow the directions below.
Census Facts
* The mean (or average) number of people in a U.S. household was 2.63 in 1990.
* The median age of people in the United States in 1990 was 33.
MEAN
The mean is the average of all the numbers in a set of numbers. Follow these steps to find the
mean number of people in your group's households:
1. Write down the number of people in your household on a card. Have a group member collect the
cards and list all the numbers.
2. Add all the numbers, then divide the sum by the number of addends. (In this case, the total
number of households in your group.) If necessary, round your answer to the hundredths place.
This number is the mean number of people per household for your group.
3. Write the mean here: _______
4. Compare this mean to the national mean listed above. Is the mean for your group higher or
lower than the national mean from the 1990 Census?
MODE
The mode is the number that occurs most often in a group of numbers. There can be more than one
mode. Find the mode of the ages of household members in your group. Here's how:
1. Write down the age of each person in your household on a separate index card.
2. Have a group member collect the cards and sort them by age. Make a stack for each age.
3. Which stack (or stacks) has the most index cards? That age (or ages) is your group mode.
4. Write the mode here: ________
RANGE
Range is the difference between the greatest number and the least number in a set of numbers.
Find the range of age for household members in your group. Here's how:
1. Take the age index cards you used for finding the mode, and order them from least
to greatest.
2. What is the youngest age?
3. What is the oldest age?
4. Subtract answer 2 from answer 3. This is your range.
5. Write your range here.
MEDIAN
The median is the middle number in a set of numbers. If there is an even number of numbers, the
median is the mean of the two middle numbers. To figure out the median age of people in your
group's household, follow these steps:
1. Use the same index cards as above, still ordered from least to greatest.
2. Find the middle number or numbers. You might want to remove cards in pairs, one from each end,
until only one number is left. If two numbers are left, find the mean of the two.
Example:
3,8,9-Median = 8
3,9,11,15-Median = 10
3. What is the median age of your group's household members?
4. Compare your group's median age to the national median age in the Census Facts box.
Is yours higher or lower than the national median age? By how much?
* Compare the statistics your group gathered with those gathered by other groups.
GRAPH IT!(Managing Data)
Grades 7-8
Skills and Objectives:
* Students will practice calculating percentages.
* Students will determine measures of central angles.
* Students will display information in a circle graph.
Suggested Groupings-Small to medium sized groups
Materials-Protractors, calculators (optional)
Getting Started:
1. Begin this lesson by providing students with some information about the U.S. Census. Did
they know that the United States collects more varied and complete census information than
any other country? The Census Bureau gathers information from households about population
and housing, including questions about age, race, and education. Once census data are
collected, statistics are used to compile this information in a more meaningful way so it can
be shared with agencies, businesses, universities, and the public. Information such as age
distribution of a population is crucial because it impacts government programs and spending.
For example, if the percentage of U.S. citizens ages 65 and over increases between 1990 and
2000, this might affect the allocation of funds to social security and programs for the elderly.
2. Explain to students that they will be calculating percentages to complete a table and then use
the table to create a graph. To prepare for the activity, ask students to write the ages of
their household members on a piece of paper. If students completed Lesson 5, they will
already have this information.
Using the Activity Worksheets:
1. Divide class into groups (no less than 6 students each) and distribute one copy of the
Activity Worksheet on page 19 to each group. Introduce them to the activity and remind them
that they will need the information about the ages of their household members to complete it.
* After students have completed the table, review the answers so they can correct their data
before performing the graphing activity.
2. Distribute one copy of the worksheet on page 20 to each group and introduce them to this
activity.
* Guide students through the steps for creating sections of the circle graph. Make sure
students understand how to calculate central angles. If necessary, have a volunteer
demonstrate how to use a protractor.
Wrapping Up:
* Have students compare their completed tables and circle graphs.
* What if the number in each age group was doubled? Would its percentage of the total change?
(no) Would its angle in the circle graph change? (no)
* If the class requires additional practice, have them determine how many students have last names that start with A-H, I-Q, or R-Z.
that start with A-H, I-Q, or R-Z. Calculate each number as a percentage of the class. Have
students create circle graphs to display these percentages.
Extension Activities:
1. Have students visit the library or the U.S. Census Bureau Web site (www.census.gov) to research
a table of census information for their city or county. Have them create a circle graph to
display percentage data for one statistic.
2. Students can use household population data collected from Lesson 5 or from the Census Bureau Web
site to create computer spreadsheets, using graphing features in spreadsheet or database
software.
Chalkboard Definitions
circle graph (pie chart): a graph that is used to show the relationship of parts to a whole.
percent: the ratio of a number to 100. Like a fraction, a percent signifies a part of a whole.
Answers:
Worksheet answers will vary.
Lesson 6 Activity Worksheets
GRAPH IT!
Collecting data is a big part of the U.S. Census Bureau's work, but displaying that information
in a useful way is also important. The Census Bureau and other data users convert numbers into
percents and display those percents in tables and graphs. One graph that shows percents is a
circle graph, or pie chart. For example, the circle graph at right shows household age-group
percents for Mr. Stilwell's 7th Grade Class.
Example:
Household Population by Age Group of Mr. Stilwell's 7th Grade Class
Ages 65 and over: 17%
Ages 51-64: 15%
Ages 21-50: 35%
Ages 6-20: 21%
Ages 0-5: 12%
CALCULATINC PERCENT
* Using the information each member in your group wrote down about the ages of members of their
household, determine what part of your group's total household population each age group
represents. First, add up your group's totals in each age group, then follow these 3 steps:
Step 1: Divide the population for the age group by the total population. (Use a calculator.)
Example: 136 (population for age group)/1200 (total population) = .11333333333
Step 2: Round the decimal to the hundredth place. Example: .11333333333 becomes .11
Step 3: Multiply by 100. Add the % sign. Example: .11 becomes 11%
Now find the percent of the total population for each of your group's age groups.
Group Household Population Table
Age group 0-5, number, percent
Age group 6-20, number, percent
Age group 21-50, number, percent
Age group 51-64, number, percent
Age group 65 and over, number, percent
Total Population: _________
* Now you can display the percents you calculated about your group's household ages in a circle
graph. Here's how to do it:
1. Begin with the percent for each group. Use your percent figures from page 19 to fill in the
percent column in the table below.
2. Calculate the measure of the central angle for each age group. Remember, a circle has 360
degrees.
For example: If the percent for age group 0-5 is 11%, then 11% of 360 = 0.11 x 360 = 39.6
degrees.
If you are using a calculator, percent can be calculated by 360' x 11, followed by the %
sign.
3. Now complete the circle graph for your group. Place your protractor on the graph so that
the black dot in the middle of the circle lines up with the O degree indicator on the
protractor. For the 0-5 Age Group, use your protractor to indicate the angle measure on
the circle graph. For each succeeding group, reorient your protractor so that the endpoint
of the last line drawn is now the O degree line. Label each section and your circle graph
is complete.
Population by Age Group Circle Graph
Group Population by Age Group Table
Age group 6-20, percent, angle measure
Age group 21-50, percent, angle measure
Age group 51-64, percent, angle measure
Age group 65 and over, percent, angle measure
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 (wwwcensus.gov).