Question 1

The histogram above displays a data set. Based on its shape, which of the following statements is most accurate about the relationship between the mean and the median of this data set?

Accepted Answer

The mean is likely to be greater than the median.

Question 2

Which term best describes the skewness of the distribution shown in the histogram?

Accepted Answer

Skewed to the right (positively skewed)

Question 3

Suppose you want to summarize the center and spread of the data shown in the histogram. Which combination of statistics is most appropriate?

Accepted Answer

Median and interquartile range (IQR)

Question 4

If you were to create a boxplot for the data shown in the histogram, which of the following would you most likely observe?

Accepted Answer

The median would be closer to the upper quartile (Q3) than to the lower quartile (Q1).

Question 5

Which of the following is a likely consequence of using the mean to describe the center of the data in the histogram above?

Accepted Answer

The mean will be pulled in the direction of the skew, overestimating the typical value.

Question 6

Given the histogram above, which of the following statements about potential outliers is most accurate?

Accepted Answer

Potential outliers are more likely to be found on the right side of the distribution.

Question 7

If the data in the histogram represents home prices, which measure of center would be most appropriate to report to a potential home buyer?

Accepted Answer

Median, because it is resistant to outliers and skewness.

Question 8

Which of the following formulas would you use to calculate the interquartile range (IQR) for the data in the histogram?

Accepted Answer

$$IQR = Q3 - Q1$$

Question 9

Suppose the maximum value in the data set is much higher than the rest of the data. Which measure of spread would be most affected?

Accepted Answer

Standard deviation

Question 10

If you apply the 1.5 IQR rule to the data in the histogram, what are you trying to identify?

Accepted Answer

Potential outliers

Summarizing Quantitative Data: Numbers and Graphs

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