Question 1

Given the exam scores: 82, 77, 90, 71, 62, 68, 74, 84, 94, 88, what is the range of the scores?

Accepted Answer

$$R = 94 - 62 = 32$$

Question 2

Which of the following best describes the interpretation of standard deviation in a data set?

Accepted Answer

It is the typical distance of a data value from the mean.

Question 3

For the sample data: 62, 88, 77, 68, what is the sample standard deviation (rounded to one decimal place)?

Accepted Answer

$$s = 11.3$$

Question 4

If the sample standard deviation for the data set 20, 13, 4, 8, 10 is $$s = 6$$, what is the sample variance?

Accepted Answer

$$s^2 = 36$

Question 5

Which city has greater variability in temperature based on the standard deviation: Des Moines, Iowa ($$\sigma = 11.05) or $$San Francisco, California ($$\sigma = 3.15$$)?

Accepted Answer

Des Moines, Iowa

Question 6

What is the formula for the population standard deviation $$\sigma$$?

Accepted Answer

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

Question 7

What is the formula for the sample standard deviation $$s$$?

Accepted Answer

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

Question 8

Why is $$n-1$$ used in the denominator when calculating the sample variance?

Accepted Answer

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

Question 9

If a data set has a mean of 54 and a standard deviation of 12, which value is most likely to be considered an outlier?

Accepted Answer

30

Question 10

Which measure of dispersion is most affected by extreme values in a data set?

Accepted Answer

Range

Question 11

A hospital tracks the recovery times (in days) for patients after surgery: 5, 7, 8, 6, 10, 12, 9. What is the range of recovery times?

Accepted Answer

$$R = 12 - 5 = 7$$

Question 12

If the sample variance for a data set is $$s^2 = 49$, what is the sample standard deviation?

Accepted Answer

$$s = 7$$

Question 13

Which of the following statements is TRUE regarding the relationship between variance and standard deviation?

Accepted Answer

Variance is the square of the standard deviation.

Question 14

A pharmaceutical company measures the effectiveness of a drug in two groups. Group A has a standard deviation of 2.5, Group B has a standard deviation of 7.8. Which group shows more variability in effectiveness?

Accepted Answer

Group B

Question 15

If the mean temperature in Des Moines, Iowa is 53.95 and the standard deviation is 11.05, what does the standard deviation tell us about the temperature data?

Accepted Answer

Temperatures are typically about 11.05 degrees away from the mean.

Question 16

Which formula represents the sample variance $$s^2$$?

Accepted Answer

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

Question 17

A data set has values: 10, 12, 14, 16, 18. What is the range?

Accepted Answer

$$R = 18 - 10 = 8$$

Question 18

Which of the following is NOT a measure of dispersion?

Accepted Answer

Median

Question 19

A researcher collects the following data: 4, 8, 12, 16, 20. If the mean is 12, what is the sum of squared deviations from the mean?

Accepted Answer

$$(4-12)^2$$ + $$(8-12)^2$$ + $$(12-12)^2$$ + $$(16-12)^2$$ + $$(20-12)^2 = 64 + 16 + 0 + 16 + 64 = 160$

Question 20

A teacher wants to compare the spread of test scores between two classes. Class 1 has a standard deviation of 5, Class 2 has a standard deviation of 9. What can the teacher conclude?

Accepted Answer

Class 2's scores are more spread out than Class 1's.

Measures of Dispersion: Range, Standard Deviation, and Variance

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