2.7 Measures of the Spread of the Data

Sample and population standard deviation worked out by hand from squared deviations, and z-scores that compare values coming from different data sets.

Introductory Statistics 2e, 2.7 Measures of the Spread of the Data

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15 exercises

2.7 Exercise 1

Typically, you do the calculation for the standard deviation on your calculator or computer. The intermediate results are not rounded. This is done for accuracy.

For the following problems, recall that value = mean + (#ofSTDEVs)(standard deviation). Verify the mean and standard deviation or a calculator or computer.
For a sample: x = $\bar{x}$ + (#ofSTDEVs)(s)
For a population: x = μ + (#ofSTDEVs)(σ)
Fo…

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2.7 Exercise 5

Two students, John and Ali, from different high schools, wanted to find out who had the highest GPA when compared to his school. Which student had the highest GPA when compared to his school?

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2.7 Exercise 7

Use the following information to answer the next two exercises: The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150

Use a graphing calculator or computer to find the standard deviation and round to the nearest tenth.

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2.7 Exercise 9

Two baseball players, Fredo and Karl, on different teams wanted to find out who had the higher batting average when compared to h…

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2.7 Exercise 11

Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.

Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.

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2.7 Exercise 12

A sample of 11 years is taken. About how many are expected to have a FTES of 1014 or above? Explain how you determined your answer.

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2.7 Exercise 14

The population standard deviation = _____

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2.7 Exercise 16

What is the IQR? What does the IQR represent?

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2.7 Exercise 18

Calculate the mean, median, standard deviation, the first quartile, the third quartile and the IQR. Round to one decimal place.

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2.7 Exercise 20

Compare the IQR for the previous 29-year period with the IQR for the six-year period shown in the table. Why do you suppose the IQRs are so different?

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2.7 Exercise 22

A music school has budgeted to purchase three musical instruments. They plan to purchase a piano costing $3,000, a guitar costing $550, and a drum set costing $600. The mean cost for a piano is $4,000 with a standard deviation of $2,500. The mean cost for a guitar is $500 with a standard deviation of $200. The mean cost for drums is $700 with a standard deviation of $100. Which cost is the lowest,…

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2.7 Exercise 24

A selection of countries has poverty rates that range from 11.4% to 74.6%. This data is summarized in Table 2.76.

What is the best estimate of the average poverty percentage for these countries? What is the standard deviation for the listed poverty rates? The United States has an average poverty rate of 33.9%. Is this rate above average or below? How “unusual” is the United States’ rate compared t…

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2.7 Exercise 26

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:

Find the sample mean $\bar{x}$ .
Find the approximate sample standard deviation, s.

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2.7 Exercise 32

A survey of enrollment at 35 community colleges across the United States yielded the following figures:

6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622

Organize the data into a chart with six intervals of equal width from 0 t…

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2.7 Exercise 34

The number that is 1.5 standard deviations BELOW the mean is approximately _____

0.7
4.8
–2.8
Cannot be determined

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