Exercise
Suppose you want to find out what students at your school do for exercise, and then make a graph to display the results.
1. You construct this survey question: “What do you do for exercise?” Think about some possible responses. How many different responses do you think you would get if you asked 100 students?
2. Is “dance” a response you thought of for question 1? Is “skateboarding” or “martial arts” a response you thought of?
3. Is it possible that some students do more than one type of exercise? The answers to survey questions are data items, so collecting the answers is a form of collecting data. When constructing a survey question, it is often important to limit the number of possible responses so that you will be able to organize, display, analyze, and interpret the data you collect. Provide enough response choices so that there is a choice for everyone, and make sure the choices don’t overlap. That is, construct them so that there is clearly only one response. In the table below, the question about exercise is rephrased and answer choices are supplied, along with numbers of responses.
“Which of the following best describes your main type of exercise?”
Response Frequency
A. Competitive sports (team and individual) 24
B. Run, jog, or walk (not competitive) 16
C. Swim or bicycle (not competitive) 5
D. Strength training (weights and exercise
equipment) 15
E. Other 20
A bar graph and a circle graph are both appropriate ways to display this data. Copy and complete the bar graph and circle graph below.
4. Exercise 30 25 20 15 10 5 0 Number of Students Competitive Sports Run, Jog, or W alk Swim or Bicycle Str ength T raining Other 5. Exercise Competitive Sports 30% 6% % % % Exercise Competitive Sports 30% 6% % % % Online Connection www.SaxonMathResources.com Math Reasoning
Analyze Refer to the table. Which choice is needed so that everyone can choose at least one
response? What word(s) in the question allows everyone to be able to choose exactly one
response?
Hint
24 of 80 responses were
Competitive. To get the central angle measure for the Competitve sector in the circle graph, multiply 360° by the appropriate decimal.
24
_ 80 = 0.30 0.30 × 360° = 108°
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Investigation 7 503
Analyze and Write
A survey question is biased if there is a reasonable chance that it could influence a response because of the way it isconstructed. Determine whether each question below is biased. Explain your answer. If the question is biased, rewrite it so that it is not biased. 6. Do you agree with most high school students that parents give them
too little freedom to make their own decisions?
7. Do you support the unfair policy of requiring community service as a high school requirement?
8. Do you think energy conservation should be a high priority for state and national elected officials?
9. Write a biased survey question. Then rewrite it to remove the bias. A population is a group being studied. Populations are often too large to survey, so a subset of the population called a sample is surveyed. If a sample is not a fair representation of the population, it is biased. If a sample is a fair representation of the population, it is unbiased. When properly chosen in an appropriate situation, any of the following can be an unbiased sample.
• Random sample – Each member of the population has an equal chance of being selected.
• Systematic sample – Members are chosen based on a rule.
• Stratified sample – The population is divided into non-overlapping subgroups, and members are chosen at random from the subgroups. • Self-selected sample – Members volunteer to be in the sample.
Analyze and Write
Identify the type of sample and determine whether it is biased. Explain your answer.10. A manager asks every tenth customer who enters her store whether they like the recent remodeling of the store.
11. A candidate mails a survey about an upcoming election along with a request for campaign contributions, enclosing a return envelope for responses.
12. For a survey about school policies, a student randomly chooses 25 students from each grade. (There are approximately 200 students in each grade.)
13. There are 645 employees at a company. The president assigns the integers 1 through 645, one to each employee, and then randomly chooses 50 integers and surveys the corresponding employees.
14. Every voter in a town is registered as a Democrat, a Republican, or an Independent. For a survey of registered voters, 50 are randomly chosen from each group.
15. Multi-Step Complete parts a–d.
a. Construct a survey question with 4 or 5 response choices.
b. Identify a population. Describe 3 or 4 possible samples of different types. Identify each type and state whether it is biased or unbiased.
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c. Construct a frequency table. Show a reasonable distribution of responses.
d. Construct a bar graph and circle graph to show the data. It is useful to describe some data sets with measures of center such as
mode, median, and mean, and with measures of spread such as variance and standard deviation.
A teacher chose 2 students at random from each of the 10 sophomore homeroom classes in a school and asked “To the nearest half hour, what is the average number of hours per school night that you spend on homework?” The table below shows the data distribution.
Hours 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 or more
Frequency 0 1 4 5 5 3 1 1 0
16. Identify the population and the type of sample. Determine whether the sample is biased.
17. Find the mode(s) and median.
18. Supply the missing terms in the numerator, and then evaluate the expression to find the mean: x − = ___ 1(0.5) + 4(1.0) + 5(1.5) + … + 1(3.5)
20 .
19. The formula for variance is σ2= ___ (x1 - x − ) 2 + (x2 - x − )2 + … + 1(xn - x − )2
n , where
x1, x2, …, xn are the data values and x is the mean. Supply the missing − terms in the numerator, and then evaluate the expression to find the variance: σ2= ____ 1(0.5 - − x )2 + 4(1.0 - − x )2 + 5(1.5 - x − )2 + … + 1(3.5 - − x )2
20
20. The standard deviation is the square root of the variance: σ= √ σ2 .
Find the standard deviation to the nearest thousandth.