Questions: The five-number summary for a distribution of final exam scores is 66, 78, 82, 86, 96, is it possible to draw a boxplot based on this information? Why or why not? Select the correct answer below. A. it isn't possible to draw a boxplot based on the five-number summary because the five-number summary doesn't contain the interquartile range (IQR), which is necessary to draw the boxplot if the IQR is found using other summary statistics, then the boxplot can be drawn. B. It isn't possible to draw a boxplot based on the five-number summary because the five-number summary is used to summarize symmetric distributions, not asymmetric distributions. The boxplot cannot be constructed with the information in the five-number summary. C. It is possible to draw a boxplot based on this information. The five-number summary contains all information necessary to construct the boxplot. D. It is possible to draw a boxplot based on this information. Both the minimum and maximum are within the bounds of the left limit and right limit, which means that all potential outliers can be displayed. This is necessary to construct the boxplot.

Solution Steps

To determine if it is possible to draw a boxplot based on the five-number summary, we need to understand what a boxplot requires. A boxplot is constructed using the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. The given five-number summary provides all these values: minimum (66), Q1 (78), median (82), Q3 (86), and maximum (96). Therefore, it is possible to draw a boxplot with this information.

The correct answer is C. The five-number summary contains all information necessary to construct the boxplot.### Step 1: Understanding the Five-Number Summary The five-number summary for a distribution consists of the following:

• Minimum value
• First quartile (Q1)
• Median (Q2)
• Third quartile (Q3)
• Maximum value

Given the five-number summary for the final exam scores:

• Minimum: 66
• Q1: 78
• Median (Q2): 82
• Q3: 86
• Maximum: 96

A boxplot (or box-and-whisker plot) is a graphical representation of the five-number summary. It includes:

• A box from Q1 to Q3
• A line inside the box at the median (Q2)
• Whiskers extending from the minimum to Q1 and from Q3 to the maximum
• Potential outliers, if any, are plotted as individual points

Let's evaluate each option based on the information provided:

• Option A: This option states that the five-number summary does not contain the interquartile range (IQR). However, the IQR can be calculated as \( \text{IQR} = Q3 - Q1 \). The five-number summary does provide all necessary information to draw a boxplot, including the IQR.

• Option B: This option claims that the five-number summary is only for symmetric distributions. This is incorrect; the five-number summary can summarize both symmetric and asymmetric distributions.

• Option C: This option correctly states that the five-number summary contains all the necessary information to construct a boxplot.

• Option D: This option introduces the concept of outliers and their bounds. While it is true that outliers can be displayed, the primary requirement for constructing a boxplot is the five-number summary.

Final Answer