Question 1

Which of the following best explains why the range is considered an insensitive measure of variability for large data sets?

Accepted Answer

The range only considers the two most extreme values and ignores the distribution of the rest of the data.

Question 2

Given the following data set: 2, 4, 6, 8, 10. What is the range?

Accepted Answer

$$10 - 2 = 8$$

Question 3

Why do we square the deviations from the mean when calculating variance?

Accepted Answer

To prevent negative and positive deviations from canceling each other out.

Question 4

Which formula correctly represents the sample variance for a data set with $$n$$ measurements?

Accepted Answer

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

Question 5

A sample consists of the values 1, 2, 3, 4, 5. What is the sample mean?

Accepted Answer

$$\overline{x} = \frac{1+2+3+4+5}{5} = 3$$

Question 6

Which of the following is the correct formula for the sample standard deviation?

Accepted Answer

$$s = \sqrt{s^2$}$$

Question 7

Suppose two data sets have the same mean and range, but one has a much larger variance. What does this indicate about the data sets?

Accepted Answer

The data set with the larger variance is more spread out around the mean.

Question 8

Given the sample: 2, 3, 3, 3, 4, calculate the sample mean.

Accepted Answer

$$\overline{x} = \frac{2+3+3+3+4}{5} = 3$$

Question 9

Which symbol is used to represent the population standard deviation?

Accepted Answer

$$\sigma$$

Question 10

A researcher compares the response times to a stimulus for two drugs, A and B. Both have the same mean, median, and mode, but Drug A's response times are more spread out. Which drug has the higher standard deviation?

Accepted Answer

Drug A

Question 11

If the sum of squared deviations from the mean for a sample of 6 measurements is 24, what is the sample variance?

Accepted Answer

$$s^2$$ = \frac{24}{6-1} = \frac{24}{5} = 4.8$$

Question 12

Which of the following best describes the effect of outliers on the range and standard deviation?

Accepted Answer

Both the range and standard deviation are increased by outliers.

Question 13

Given the sample: 1, 2, 3, 4, 5, what is the sample variance?

Accepted Answer

$$s^2 = 2.5$

Question 14

Which shortcut formula can be used to calculate the sample variance?

Accepted Answer

$$s^2$$ = \frac{\sum x_$$i^2$$ - \frac{(\sum x_$$i)^2$$}{n}}{n-1}$$

Question 15

A sample of five measurements has a mean of 3 and the following values: 2, 3, 3, 3, 4. What is the sum of squared deviations from the mean?

Accepted Answer

$$(2-3)^2$$ + $$(3-3)^2$$ + $$(3-3)^2$$ + $$(3-3)^2$$ + $$(4-3)^2 = 1 + 0 + 0 + 0 + 1 = 2$

Question 16

Which of the following is NOT a reason for using $$n-1 in $$the denominator when calculating sample variance?

Accepted Answer

To make the variance smaller for larger samples.

Numerical Measures of Variability in Statistics

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