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

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

Q: A sample of 5 measurements has a mean of 10 and a standard deviation of 2. What is the coefficient of variation (CV) for this sample?

$$CV = \frac{2}{10} \times 100 = 20\%$$

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 and a standard deviation of 6 minutes. Department B has a mean wait time of 45 minutes and a standard deviation of 9 minutes. Which department has a higher coefficient of variation (CV)?

Accepted Answer

Both departments have the same coefficient of variation, $$20\%$$

Question 2

Which of the following statements about the range as a measure of variation is TRUE?

Accepted Answer

The range is very sensitive to extreme values.

Question 3

Given the following sample data: 8, 12, 15, 20, 25. What is the sample variance $$s^2$$?

Accepted Answer

$$s^2 = 42.5$

Question 4

A set of exam scores is approximately bell-shaped with a mean of 80 and a standard deviation of 5. According to the Empirical Rule, about what percentage of scores fall between 70 and 90?

Accepted Answer

About 95\%

Question 5

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

Accepted Answer

To make the sample variance an unbiased estimator of the population variance.

Question 6

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

Accepted Answer

The range

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

It is a resistant measure of variation.

Question 9

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

Accepted Answer

$$\sigma = 2.24$$

Question 10

According to Chebyshev’s Theorem, what is the minimum proportion of data values that must lie within 3 standard deviations of the mean for any data set?

Accepted Answer

At least 89\%

Question 11

A sample of 5 measurements has a mean of 10 and a standard deviation of 2. What is the coefficient of variation (CV) for this sample?

Accepted Answer

$$CV = \frac{2}{10} 	imes 100 = 20\%$$

Question 12

Which of the following is TRUE regarding the variance of a data set?

Accepted Answer

The variance is the square of the standard deviation.

Question 13

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

Accepted Answer

$$s = \frac{40}{4} = 10$$

Question 14

Which of the following best describes why the sample standard deviation $$s is $$considered a biased estimator of the population standard deviation $$\sigma$$?

Accepted Answer

Because $$s$$ does not tend to center around $$\sigma.$$

Question 15

A data set of test scores is approximately bell-shaped with a mean of 70 and a standard deviation of 10. According to the Empirical Rule, what percentage of scores are expected to fall between 50 and 90?

Accepted Answer

About 95\%

Question 16

Which of the following is a correct interpretation of Chebyshev’s Theorem for $$k=2$$?

Accepted Answer

At least 75\% of data values are within 2 standard deviations of the mean.

Question 17

A sample of 6 weights (in kg) is: 50, 52, 53, 54, 55, 100. Which measure of variation is most affected by the outlier 100?

Accepted Answer

The standard deviation

Question 18

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 19

Which of the following is NOT a reason to use the coefficient of variation (CV) when comparing two data sets?

Accepted Answer

CV is always measured in the same units as the data.

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

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