Q: A basketball team has a mean height of 78 inches with a standard deviation of 3.5 inches. What is the coefficient of variation (CV) for the heights?

$$CV = \frac{3.5}{78} \times 100 \approx 4.5\%$$

Q: If the sample mean of a data set is 20 and the sample standard deviation is 4, what is the coefficient of variation?

$$CV = \frac{4}{20} \times 100 = 20\%$$

Question 1

Which of the following best describes the range of a data set?

Accepted Answer

The difference between the maximum and minimum data entries in the set.

Question 2

A sample of recovery times (in days) for 12 athletes after a concussion is: 8, 10, 4, 6, 7, 7, 9, 10, 7, 6, 5, 11. What is the formula for the sample variance $$s^2$$?

Accepted Answer

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

Question 3

Which statement about standard deviation is TRUE?

Accepted Answer

The standard deviation is always greater than or equal to 0.

Question 4

A population has data values: 2, 4, 4, 4, 5, 5, 7, 9. What is the population mean $$\mu$$?

Accepted Answer

$$\mu = 5$$

Question 5

If a data set has a mean of 50 and a standard deviation of 5, what percentage of data falls within the interval [40, 60] according to the Empirical Rule?

Accepted Answer

About 95%

Question 6

Which formula would you use to estimate the sample standard deviation for grouped data?

Accepted Answer

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

Question 7

A basketball team has a mean height of 78 inches with a standard deviation of 3.5 inches. What is the coefficient of variation (CV) for the heights?

Accepted Answer

$$CV = \frac{3.5}{78} 	imes 100 \approx 4.5\%$$

Question 8

According to Chebychev’s Theorem, at least what percentage of data values lie within 3 standard deviations of the mean for any data set?

Accepted Answer

About 88.9%

Question 9

A data set has all entries equal to 10. What is the standard deviation?

Accepted Answer

0

Question 10

A sample of home prices (in thousands of dollars) is grouped into classes. To estimate the sample mean, which value should you use for each class?

Accepted Answer

The midpoint of each class

Question 11

If the sample mean of a data set is 20 and the sample standard deviation is 4, what is the coefficient of variation?

Accepted Answer

$$CV = \frac{4}{20} 	imes 100 = 20\%$$

Question 12

A data set has a mean of 100 and a standard deviation of 15. According to the Empirical Rule, what is the approximate range that contains 68% of the data?

Accepted Answer

$$[85, 115]$$

Question 13

Which of the following is NOT a correct interpretation of standard deviation?

Accepted Answer

It is a measure of central tendency.

Question 14

A researcher finds that the sample standard deviation of recovery times is 2.2 days. What does this value represent?

Accepted Answer

The typical amount a recovery time deviates from the mean recovery time.

Question 15

If a data set is highly spread out, what can you say about its standard deviation?

Accepted Answer

The standard deviation will be large.

Question 16

A city’s home prices are grouped into classes. The class $$500,000+ is $$open-ended. What should you do to estimate the mean and standard deviation?

Accepted Answer

Choose a reasonable value to represent the midpoint of the open-ended class.

Question 17

Which of the following is a correct formula for the population variance $$\$$sigma^2$$?

Accepted Answer

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

Question 18

A data set has a mean of 70 and a standard deviation of 10. According to Chebychev’s Theorem, at least what percentage of data values lie between 50 and 90?

Accepted Answer

At least 75%

Question 19

Which of the following scenarios best illustrates the use of the coefficient of variation?

Accepted Answer

Comparing the variability of heights (in inches) and weights (in pounds) of basketball players.

Measures of Variation in Descriptive Statistics

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