Q: Given the data set: 10, 12, 15, 18, 20, what is the range?

$$\text{Range} = 20 - 10 = 10$$

Q: A data set has a mean of 50 and a standard deviation of 8. According to the range rule of thumb, what values are considered significantly high?

Values greater than $$50 + 2 \times 8 = 66$$

Q: Which of the following is the correct formula for the coefficient of variation (CV) for a sample?

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

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 5 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

Department B, because its coefficient of variation is higher.

Question 2

Given the data set: 10, 12, 15, 18, 20, what is the range?

Accepted Answer

$$	ext{Range} = 20 - 10 = 10$$

Question 3

Which of the following statements about the sample standard deviation is TRUE?

Accepted Answer

The sample standard deviation is a biased estimator of the population standard deviation.

Question 4

A set of exam scores is approximately bell-shaped with a mean of 80 and a standard deviation of 6. According to the Empirical Rule, about what percentage of scores are between 68 and 92?

Accepted Answer

About 95%

Question 5

Which formula correctly calculates the sample variance $$s^2$$ for a data set with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ and sample mean $$\bar{x}$$?

Accepted Answer

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

Question 6

A researcher collects the following data: 5, 7, 7, 8, 10. What is the sample standard deviation? (Round your answer to one more decimal place than the data.)

Accepted Answer

$$s = 1.8$$

Question 7

Which of the following is NOT a property of the variance?

Accepted Answer

Variance is resistant to outliers.

Question 8

A sample of five weights (in kg) is: 60, 62, 65, 68, 70. Use the range rule of thumb to estimate the standard deviation.

Accepted Answer

$$s \approx \frac{70 - 60}{4} = 2.5$$

Question 9

Which of the following best describes why the range is not a resistant measure of variation?

Accepted Answer

It only uses the maximum and minimum values, making it sensitive to outliers.

Question 10

A data set has a mean of 50 and a standard deviation of 8. According to the range rule of thumb, what values are considered significantly high?

Accepted Answer

Values greater than $$50 + 2 	imes 8 = 66$$

Question 11

A population consists of the values 2, 4, 6, 8. What is the population standard deviation $$\sigma$$?

Accepted Answer

$$\sigma = 2.24$$

Question 12

Which of the following is the correct formula for the coefficient of variation (CV) for a sample?

Accepted Answer

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

Question 13

A set of data has a mean of 100 and a standard deviation of 20. Using Chebyshev’s Theorem, what is the minimum percentage of data values that must lie between 60 and 140?

Accepted Answer

At least 75%

Question 14

Why does the variance use squared differences from the mean rather than absolute differences?

Accepted Answer

Squaring differences gives more weight to values farther from the mean.

Question 15

A pharmaceutical company is comparing the effectiveness of two drugs. Drug A has a mean effectiveness score of 80 with a standard deviation of 4, and Drug B has a mean of 60 with a standard deviation of 6. Which drug shows more consistency in effectiveness?

Accepted Answer

Drug A, because it has a lower coefficient of variation.

Question 16

If all values in a data set are increased by 5, how does this affect the standard deviation?

Accepted Answer

The standard deviation remains unchanged.

Question 17

A sample of test scores has a mean of 70 and a standard deviation of 10. According to the Empirical Rule, what interval contains approximately 99.7% of the scores?

Accepted Answer

$$[40, 100]$$

Question 18

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

Accepted Answer

At least $$\frac{8}{9} ($$about 89%) of all values lie within 3 standard deviations of the mean.

Question 19

A data set consists of the values 4, 4, 4, 4, 4. What is the standard deviation?

Accepted Answer

$$s = 0$$

Chapter 3: Describing, Exploring, and Comparing Data – Measures of Variation

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