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2.7 Measures of the Spread of the Data

Standard deviation and variance computed from raw and grouped data, and using spread to judge how far one observation sits from typical.

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

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17 exercises

2.7 Exercise 2

Use the following data (first exam scores) from Professor Dean's spring pre-calculus class:

33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100

Create a chart containing the data, frequencies, relative frequencies, and cumulative relative frequencies to three decimal places.
Calculate the following to one decimal place:
1. T…

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2.7 Exercise 4

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 5

Two swimmers, Angie and Beth, from different teams, wanted to find out who had the fastest time for the 50 meter freestyle when compared to her team. Which swimmer had the fastest time when compared to her team?

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2.7 Exercise 6

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 8

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 10

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 11

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 13

The population standard deviation = _____

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2.7 Exercise 15

What is the IQR? What does the IQR represent?

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2.7 Exercise 17

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 18

Compare the IQR for the FTES 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 20

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 22

A selection of countries has poverty rates that range from 11.4% to 74.6%. This data is summarized in Table 14.

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’ poverty rate compa…

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2.7 Exercise 24

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 26

Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year.

177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 2…

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2.7 Exercise 30

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 32

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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