Q: Which formula correctly calculates the range of a quantitative data set?

$$\text{Range} = (\text{Max. data entry}) - (\text{Min. data entry})$$

Q: Which formula is used to calculate the coefficient of variation (CV) for a sample data set?

$$CV = \frac{s}{\overline{x}} \times 100\%$$

Q: A basketball team has a mean height of 72.8 inches and a standard deviation of 3.3 inches. What is the coefficient of variation for the heights?

$$CV = \frac{3.3}{72.8} \times 100\% \approx 4.5\%$$

Question 1

Which formula correctly calculates the range of a quantitative data set?

Accepted Answer

$$	ext{Range} = (	ext{Max. data entry}) - (	ext{Min. data entry})$$

Question 2

A company has starting salaries for 10 employees: 41, 38, 39, 45, 47, 41, 41, 42, 44, 37 (in thousands). What is the range of the salaries?

Accepted Answer

$$47 - 37 = 10$$

Question 3

Which statement best describes the standard deviation of a data set?

Accepted Answer

It measures the variation of the data set about the mean and has the same units as the data.

Question 4

Given a population data set, which formula is used to calculate the population variance?

Accepted Answer

$$\$$sigma^2$$ = \frac{\sum (x - \mu)^2$}{N}$$

Question 5

A sample of recovery times (in days) for 12 football players is: 4, 7, 6, 7, 9, 5, 8, 10, 9, 8, 7, 10. The mean is 7.5 and $$\sum (x - \overline{x})^2$ = 39. $$What is the sample standard deviation?

Accepted Answer

$$s = \sqrt{\frac{39}{11}}$$

Question 6

Which of the following is true about the Empirical Rule for a bell-shaped distribution?

Accepted Answer

About 95% of the data lie within two standard deviations of the mean.

Question 7

Chebychev’s Theorem states that for any data set, at least what percent of the data lie within two standard deviations of the mean?

Accepted Answer

75%

Question 8

If a data set has all entries equal to the mean, what is the value of the standard deviation?

Accepted Answer

It is zero.

Question 9

Which formula is used to calculate the coefficient of variation (CV) for a sample data set?

Accepted Answer

$$CV = \frac{s}{\overline{x}} 	imes 100\%$$

Question 10

A basketball team has a mean height of 72.8 inches and a standard deviation of 3.3 inches. What is the coefficient of variation for the heights?

Accepted Answer

$$CV = \frac{3.3}{72.8} 	imes 100\% \approx 4.5\%$$

Question 11

Which step is NOT part of the process for finding the sample standard deviation?

Accepted Answer

Multiply each deviation by the mean.

Question 12

A sample of office rental rates in Los Angeles has a mean of $$36.9 and a sample standard deviation of 17.4. $$What does the standard deviation represent in this context?

Accepted Answer

The typical amount a rental rate deviates from the mean.

Question 13

For a frequency distribution with classes, how do you estimate the sample mean and standard deviation?

Accepted Answer

Use the midpoint of each class.

Question 14

If a data set is more spread out, what happens to the value of the standard deviation?

Accepted Answer

It increases.

Question 15

A survey finds the mean height of women (ages 20-29) is 64.2 inches with a standard deviation of 2.9 inches. Using the Empirical Rule, what percent of women are expected to have heights between 58.4 and 64.2 inches?

Accepted Answer

47.72%

Question 16

Which formula is used to calculate the sample variance?

Accepted Answer

$$s^2$$ = \frac{\sum (x - \overline{x}$$)^2$$}{n - 1}$$

Question 17

If a data set has a mean of 4 and all entries are 4, what is the population standard deviation?

Accepted Answer

$$\sigma = 0$$

Question 18

Which of the following is a correct interpretation of Chebychev’s Theorem for $$k = 3$$?

Accepted Answer

At least 88.9% of the data lie within three standard deviations of the mean.

Descriptive Statistics: Measures of Variation (Chapter 2, Section 2.4)

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