Question 1

Which of the following best describes the purpose of standard deviation in statistics?

Accepted Answer

It quantifies the spread or variability of data values around the mean.

Question 2

Given the sample data set: 5, 10, 12, 13, 14, 4, what is the mean ($$\bar{x}) of $$the sample?

Accepted Answer

$$\bar{x} = 9.67$$

Question 3

Which formula is used to calculate the sample standard deviation ($$s) $$for a data set of $$n$$ values?

Accepted Answer

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

Question 4

A college class has ages: 24, 27, 34, 28, 30, 35, 28, 29. What is the first step in calculating the sample standard deviation?

Accepted Answer

Calculate the mean ($$\bar{x}) of $$the ages.

Question 5

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

Accepted Answer

To correct for bias in estimating the population variance from a sample.

Question 6

Given the sample data: 2, 4, 6, 8, 10, which calculation correctly finds $$\sum (x_i - \bar{x})^2$?

Accepted Answer

$$\sum (x_i - \bar{x})^2$ = 40$$

Question 7

If a data set has a standard deviation of $$s = 0$$, what does this indicate about the data?

Accepted Answer

All values are equal.

Question 8

Which sample has the greatest standard deviation based on the following histograms of quiz scores: (A) all scores are 4, (B) scores are evenly spread from 1 to 7, (C) most scores are 4 but some are 1 and 7?

Accepted Answer

Sample B

Question 9

A researcher collects the following data: 10, 12, 14, 16, 18. What is the sample standard deviation ($$s$$)?

Accepted Answer

$$s = 3.16$$

Question 10

Which of the following statements is TRUE regarding measures of center and measures of variation?

Accepted Answer

Mean is a measure of center; standard deviation is a measure of variation.

Question 11

If the ages in a class are tightly clustered around the mean, what can you say about the standard deviation?

Accepted Answer

The standard deviation will be small.

Question 12

Which shortcut formula can be used to calculate sample standard deviation more efficiently?

Accepted Answer

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

Question 13

A sample of exam scores is: 80, 85, 90, 95, 100. If one score (100) is replaced with 60, what happens to the standard deviation?

Accepted Answer

It increases.

Question 14

Which of the following is NOT a step in calculating sample standard deviation?

Accepted Answer

Multiply each data value by the mean.

Question 15

A sample has values: 3, 3, 3, 3, 3. What is the sample standard deviation?

Accepted Answer

$$s = 0$$

Question 16

If a sample has $$n = 6$$ and $$\sum (x_i - \bar{x})^2$ = 30$$, what is the sample standard deviation?

Accepted Answer

$$s = \sqrt{\frac{30}{5}} = \sqrt{6}$$

Question 17

Which scenario would result in a higher standard deviation?

Accepted Answer

Test scores: 40, 50, 60, 70, 80

Question 18

If the sample mean is $$\bar{x} = 20$$ and the sample values are 10, 20, 30, what is $$\sum (x_i - \bar{x})^2$?

Accepted Answer

$$\sum (x_i - \bar{x})^2$ = 200$$

Question 19

A sample of ages: 18, 22, 26, 30, 34. What is the mean age?

Accepted Answer

$$\bar{x} = 26$$

Question 20

Which of the following is a correct interpretation of a standard deviation of 0.5 years in the ages of students in a class?

Accepted Answer

Most students' ages are within 0.5 years of the mean age.

Standard Deviation: Calculating and Interpreting Sample Spread

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