Q: Which of the following statements about the range is TRUE?

The range is calculated as $(\text{maximum value}) - (\text{minimum value})$ and is very sensitive to extreme values.

Q: A sample has a mean of 50 and a standard deviation of 5. According to the range rule of thumb, what values would be considered significantly low?

Values less than $50 - 2 \times 5 = 40$

Question 1

A hospital administrator wants to compare the variation in patient wait times between two departments. Department A has a mean wait time of 30 minutes with a standard deviation of 6 minutes, and Department B has a mean wait time of 45 minutes with a standard deviation of 9 minutes. Which department has greater relative variation in wait times?

Accepted Answer

Both departments have the same relative variation, since both have a coefficient of variation of $20\%$.

Question 2

Which of the following statements about the range is TRUE?

Accepted Answer

The range is calculated as $(	ext{maximum value}) - (	ext{minimum value})$ and is very sensitive to extreme values.

Question 3

Given the following sample data: 8, 12, 15, 20, 25. What is the sample variance $s^2$? (Round your answer to one decimal place.)

Accepted Answer

$s^2 = 40.5$

Question 4

A researcher collects the following data set: 10, 12, 14, 16, 100. Which measure of variation will be most affected by the value 100?

Accepted Answer

Both the range and the standard deviation

Question 5

Why do we divide by $n-1$ instead of $n$ when calculating the sample variance?

Accepted Answer

Because dividing by $n-1$ makes the sample variance an unbiased estimator of the population variance.

Question 6

A set of exam scores is approximately bell-shaped with a mean of 70 and a standard deviation of 8. According to the Empirical Rule, about what percentage of scores are between 54 and 86?

Accepted Answer

About 95\%

Question 7

Which of the following is NOT a property of the standard deviation?

Accepted Answer

The standard deviation is a resistant measure of variation.

Question 8

Suppose the range of a data set is 40. Using the range rule of thumb, what is the estimated value of the standard deviation $s$?

Accepted Answer

$s = 10$

Question 9

A population has values 2, 4, 6, 8. What is the population standard deviation $\sigma$? (Round to one decimal place.)

Accepted Answer

$\sigma = 2.2$

Question 10

Which of the following best describes the coefficient of variation (CV)?

Accepted Answer

It is the ratio of the standard deviation to the mean, expressed as a percent.

Question 11

A sample has a mean of 50 and a standard deviation of 5. According to the range rule of thumb, what values would be considered significantly low?

Accepted Answer

Values less than $50 - 2 	imes 5 = 40$

Question 12

Which of the following statements about variance is FALSE?

Accepted Answer

Variance is measured in the same units as the original data.

Question 13

If a data set has a mean of 100 and a standard deviation of 15, what is the coefficient of variation (CV)?

Accepted Answer

$15\%$

Question 14

Chebyshev’s Theorem states that for any data set, at least what proportion of values lie within 3 standard deviations of the mean?

Accepted Answer

$\frac{8}{9}$

Question 15

A sample of 5 values has a mean of 10. Four of the values are 8, 10, 12, and 10. What is the fifth value?

Accepted Answer

10

Question 16

Which of the following is a correct interpretation of the empirical rule for a bell-shaped distribution?

Accepted Answer

About 99.7\% of values fall within 3 standard deviations of the mean.

Question 17

Which of the following is TRUE regarding biased and unbiased estimators?

Accepted Answer

The sample variance $s^2$ is an unbiased estimator of the population variance $\sigma^2$.

Question 18

A data set has a mean of 60 and a standard deviation of 8. According to the range rule of thumb, what is the approximate range of the data?

Accepted Answer

32

Question 19

Which formula is used to calculate the population standard deviation $\sigma$?

Accepted Answer

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

Chapter 3: Measures of Variation in Statistics – Range, Standard Deviation, and Variance

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