Question 1

Which of the following statements about the mean, median, and mode is TRUE?

Accepted Answer

The median is not affected by extreme values.

Question 2

A sample of exam scores is: 70, 75, 80, 85, 90. What is the standard deviation of this sample? Use the formula $$s = \sqrt{\frac{\sum (x_i - \bar{x})^2$}{n-1}}.$$

Accepted Answer

$$s = 7.91$$

Question 3

Given the following frequency distribution for test scores, estimate the mean.

Class Intervals: 10-19 (f=2), 20-29 (f=5), 30-39 (f=2)

Use midpoints and the formula $$\bar{x} = \frac{\sum f x}{\sum f}.$$

Accepted Answer

$$\bar{x} = 24.5$$

Question 4

Which measure of central tendency is most appropriate for describing the typical value in a highly skewed distribution?

Accepted Answer

Median

Question 5

A student’s test score is 90. The class mean is 80 with a standard deviation of 5. What is the student’s z-score? Use $$z = \frac{x - \mu}{\sigma}.$$

Accepted Answer

$$z = 2$$

Question 6

Which of the following best describes the Empirical Rule for a bell-shaped distribution?

Accepted Answer

All of the above.

Question 7

If a data set has a minimum value of 12 and a maximum value of 47, what is the range?

Accepted Answer

$$35$$

Question 8

A company’s employee ages are: 22, 25, 25, 28, 30, 60. Which measure is most affected by the outlier (age 60)?

Accepted Answer

Mean

Question 9

Given Q1 = 20 and Q3 = 40, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = 20$$

Question 10

A student’s GPA is calculated as a weighted average. If the student has grades: A (4.0) in 2 units, B (3.0) in 5 units, and C (2.0) in 2 units, what is the GPA? Use $$GPA = \frac{\sum (grade 	imes units)}{\sum units}.$$

Accepted Answer

$$GPA = 3.0$$

Question 11

Which of the following is NOT a measure of dispersion?

Accepted Answer

Median

Question 12

If a data set is symmetric and bell-shaped, which measure(s) of central tendency will be approximately equal?

Accepted Answer

Mean, median, and mode

Question 13

A data set has Q1 = 15, Q3 = 35, and IQR = 20. What is the lower fence for detecting outliers? Use $$Lower\ Fence = Q1 - 1.5 	imes IQR.$$

Accepted Answer

$$-15$$

Question 14

Which of the following is TRUE about Chebyshev’s Inequality?

Accepted Answer

It applies to all distributions, regardless of shape.

Question 15

A boxplot shows a long tail to the right. Which of the following best describes the distribution?

Accepted Answer

Skewed right

Question 16

If the mean of a population is $$\mu = 50$$ and the standard deviation is $$\sigma = 10$$, what value corresponds to a z-score of $$z = -1.5$$? Use $$x = \mu + z \sigma.$$

Accepted Answer

$$x = 35$$

Question 17

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

Accepted Answer

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

Question 18

A researcher wants to check for outliers in a data set. If Q1 = 25, Q3 = 45, and IQR = 20, what is the upper fence? Use $$Upper\ Fence = Q3 + 1.5 	imes IQR.$$

Accepted Answer

$$75$$

Question 19

A data set has the following five-number summary: Min = 10, Q1 = 20, Median = 30, Q3 = 40, Max = 100. Which value is most likely an outlier?

Accepted Answer

100

Question 20

Which of the following best describes the purpose of a boxplot?

Accepted Answer

To display the five-number summary and identify outliers

Numerically Summarizing Data: Measures of Central Tendency and Dispersion

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