Question 1

Which of the following statements best describes why the mean is not considered a resistant measure of center?

Accepted Answer

Because a single extreme value (outlier) can substantially change the mean.

Question 2

Given the following data set representing the number of years to earn a degree: 4, 4, 4, 4, 4, 4, 4.5, 4.5, 4.5, 4.5, 4.5, 4.5, 6, 6, 8, 9, 9, 13, 13, 15, what is the mode?

Accepted Answer

4

Question 3

Which measure of center is most appropriate for describing the typical value of a data set with significant outliers?

Accepted Answer

Median

Question 4

A student’s grades and credits are as follows: A in a 3-credit course, B in a 4-credit course, C in a 2-credit course. Using the weighted mean formula $$\displaystyle \overline{x} = \frac{\sum (w \cdot x)}{\sum w}$$, what is the student’s GPA if A=4, B=3, C=2?

Accepted Answer

$$\displaystyle \frac{(3 \cdot 4) + (4 \cdot 3) + (2 \cdot 2)}{3 + 4 + 2} = \frac{12 + 12 + 4}{9} = \frac{28}{9} \approx 3.11$$

Question 5

Which of the following is the correct formula for estimating the mean from a frequency distribution?

Accepted Answer

$$\displaystyle \overline{x} = \frac{\sum (f \cdot x)}{\sum f}$$

Question 6

A data set has a mean of 100 and a standard deviation of 15. According to the empirical rule, approximately what percentage of data values fall between 85 and 115?

Accepted Answer

About 68%

Question 7

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

Accepted Answer

It is resistant to outliers.

Question 8

Given the data set: 6, 8, 10, 12, calculate the range.

Accepted Answer

$$12 - 6 = 6$$

Question 9

Which measure of center can be used with nominal (qualitative) data?

Accepted Answer

Mode

Question 10

If a data set is bell-shaped with mean $$\mu$$ and standard deviation $$\sigma$$, which interval contains approximately 95% of the data according to the empirical rule?

Accepted Answer

$$\mu \pm 2\sigma$$

Question 11

A frequency distribution has class midpoints of 10, 20, 30 with corresponding frequencies 2, 3, 5. What is the estimated mean?

Accepted Answer

$$\displaystyle \frac{(2 \cdot 10) + (3 \cdot 20) + (5 \cdot 30)}{2 + 3 + 5} = \frac{20 + 60 + 150}{10} = \frac{230}{10} = 23$$

Question 12

Which of the following best describes the midrange and its sensitivity to outliers?

Accepted Answer

The midrange is not resistant because it only uses the maximum and minimum values.

Question 13

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

Accepted Answer

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

Question 14

A data set has a mean of 80 and a standard deviation of 10. According to the range rule of thumb, what is the lowest value considered significantly high?

Accepted Answer

$$80 + 2 	imes 10 = 100$$

Question 15

Which of the following is NOT a property of the variance?

Accepted Answer

Variance is measured in the same units as the original data.

Question 16

Which scenario best illustrates when the mean and median are not meaningful statistics?

Accepted Answer

When analyzing the zip codes of various landmarks.

Question 17

If a data set has no repeated values, which statement is true about its mode?

Accepted Answer

There is no mode.

Question 18

A sample of four bowlers scored 6, 8, 10, and 12 strikes. What is the sample mean?

Accepted Answer

$$\displaystyle \frac{6 + 8 + 10 + 12}{4} = 9$$

Question 19

Which of the following best describes the empirical rule for a bell-shaped distribution?

Accepted Answer

About 68% of values fall within 1 standard deviation, 95% within 2, and 99.7% within 3 standard deviations of the mean.

Chapter 3: Describing, Exploring, and Comparing Data – Measures of Center and Variation

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