Question 1

Which of the following statements about the range of a data set is TRUE?

Accepted Answer

The range is sensitive to extreme values because it only uses the maximum and minimum.

Question 2

Given the data set: 10, 15, 20, 25, 30, what is the sample standard deviation? (Round your answer to one decimal place.)

Question 3

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

Accepted Answer

Because there are only $n-1$ values that can be assigned freely when the mean is fixed.

Question 4

A set of IQ scores is approximately bell-shaped with a mean of 100 and a standard deviation of 15. According to the Empirical Rule, what percentage of scores fall between 85 and 115?

Accepted Answer

About 68%

Question 5

Which formula correctly estimates the standard deviation using the range rule of thumb?

Accepted Answer

$s = \frac{	ext{range}}{4}$

Question 6

If a sample has a mean of 50 and a standard deviation of 5, which value would be considered significantly high according to the range rule of thumb?

Accepted Answer

A value of 70

Question 7

Which of the following is a property of the sample standard deviation $s$?

Accepted Answer

$s$ is always zero if all data values are the same.

Question 8

A hospital is comparing the variation in patient wait times between two departments. Department A has a mean wait time of 20 minutes and a standard deviation of 5 minutes. Department B has a mean wait time of 40 minutes and a standard deviation of 8 minutes. Which department has greater relative variation?

Accepted Answer

Department A, because its coefficient of variation is higher.

Question 9

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

Accepted Answer

Variance is the square of the standard deviation.

Question 10

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

Accepted Answer

At least 89%

Question 11

A sample of exam scores has a mean of 80 and a standard deviation of 10. What is the coefficient of variation (CV) for this sample?

Accepted Answer

$CV = 12.5\%$

Question 12

Which of the following best describes why the sample variance $s^2$ is considered an unbiased estimator of the population variance $\sigma^2$?

Accepted Answer

Because the expected value of $s^2$ equals $\sigma^2$.

Question 13

A data set has a mean of 100 and a standard deviation of 20. According to the Empirical Rule, what interval contains approximately 99.7% of the data?

Accepted Answer

$[40, 160]$

Question 14

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

Accepted Answer

It is resistant to outliers.

Question 15

A researcher collects the following data: 2, 4, 4, 4, 5, 5, 7, 9. What is the range of this data set?

Accepted Answer

$7$

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

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

Accepted Answer

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

Question 18

A population consists of the values 3, 5, and 7. What is the population variance $\sigma^2$?

Accepted Answer

$\sigma^2 = 2.67$

Question 19

Which of the following best describes the coefficient of variation (CV)?

Accepted Answer

It is the ratio of the standard deviation to the mean, expressed as a percentage.

Question 20

A data set has a mean of 60 and a standard deviation of 8. According to Chebyshev’s Theorem, at least what percentage of data values must fall between 44 and 76?

Accepted Answer

At least 75%

Measures of Variation in Descriptive Statistics: Range, Standard Deviation, and Variance

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