Q: A sample of female heights has a mean of 64.1 inches and a standard deviation of 2.6 inches. According to the Empirical Rule, what is the approximate range that contains 99.7% of the data?

$$64.1 \pm 3 \times 2.6 = [56.3, 71.9]$$

Q: Which formula gives the coefficient of variation (CV) for a sample data set with mean $$\bar{x}$$ and standard deviation $$s$$?

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

Q: A basketball team’s heights have a mean of 78 inches and a standard deviation of 3.5 inches. What is the coefficient of variation?

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

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 company has the following starting salaries for 10 employees (in thousands): 40, 42, 44, 46, 48, 50, 52, 54, 56, 58. What is the range of the salaries?

Accepted Answer

$$58 - 40 = 18$$

Question 3

Which formula correctly represents the population variance $$\$$sigma^2$$ for a data set with N$ entries and mean $$\mu$$?

Accepted Answer

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

Question 4

A sample of recovery times (in days) for 12 athletes is given. The mean is 7.5 days, and the sum of squared deviations from the mean is 50. What is the sample variance?

Accepted Answer

$$s^2$$ = \frac{50}{11} \approx 4.55$$

Question 5

Which of the following statements about standard deviation is TRUE?

Accepted Answer

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

Question 6

If a data set has all entries equal to 5, what is the standard deviation?

Accepted Answer

$$0$$

Question 7

The Empirical Rule states that for a bell-shaped distribution, approximately what percent of data falls within two standard deviations of the mean?

Accepted Answer

95%

Question 8

A sample of female heights has a mean of 64.1 inches and a standard deviation of 2.6 inches. According to the Empirical Rule, what is the approximate range that contains 99.7% of the data?

Accepted Answer

$$64.1 \pm 3 	imes 2.6 = [56.3, 71.9]$$

Question 9

Chebyshev’s Theorem guarantees that for any data set, at least what percent of the data lies within $$k = 2$$ standard deviations of the mean?

Accepted Answer

75%

Question 10

A city’s home prices are grouped into classes. To estimate the sample mean and standard deviation, which value should be used to represent each class?

Accepted Answer

The midpoint of each class

Question 11

Which formula gives the coefficient of variation (CV) for a sample data set with mean $$\bar{x}$$ and standard deviation $$s$$?

Accepted Answer

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

Question 12

A basketball team’s heights have a mean of 78 inches and a standard deviation of 3.5 inches. What is the coefficient of variation?

Accepted Answer

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

Question 13

Which scenario best illustrates the use of Chebyshev’s Theorem?

Accepted Answer

Analyzing the spread of ages in a population with a skewed distribution.

Question 14

A data set has a mean of 100 and a standard deviation of 15. According to Chebyshev’s Theorem, at least what percent of data falls between 70 and 130?

Accepted Answer

At least 75%

Question 15

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

Accepted Answer

It is always less than the mean.

Question 16

A frequency distribution for grouped data is given. Which formula estimates the sample standard deviation $$s$$?

Accepted Answer

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

Question 17

If two data sets have the same mean but different standard deviations, what does this indicate?

Accepted Answer

The data sets have different levels of variation.

Question 18

A sample of desk rental rates in Los Angeles has a mean of $$50 and a standard deviation of 8. $$What is the coefficient of variation?

Accepted Answer

$$CV = \frac{8}{50} 	imes 100\% = 16\%$$

Question 19

Which of the following is a correct application of the Empirical Rule?

Accepted Answer

Estimating that about 68% of data falls within one standard deviation of the mean in a bell-shaped distribution.

Measures of Variation in Descriptive Statistics

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