Question

the credit card purchases (rounded to the nearest dollar) over the last three months for you and a friend are listed below. use technology to draw side-by-side box-and-whisker plots that represent the data sets. then describe the shapes of the distributions.

click the icon to view the data table.

identify the correct box-and-whisker plot below.

○ a. ○ b. ○ c. ○ d.
(box plots for you and friend with x-axis 0, 60, 120, 180, 240)

the shape of the distribution of your purchases is skewed right.
the shape of the distribution of your friend’s purchases is skewed left.

Explanation:

To solve this, we analyze the box - and - whisker plots and distribution shapes:

Step 1: Analyze the box - and - whisker plot selection

A box - and - whisker plot shows the five - number summary (minimum, first quartile \(Q_1\), median, third quartile \(Q_3\), maximum) of a data set. For the data of "you" and "your friend" related to credit card purchases, we need to match the plot with the correct five - number summary and the skewness of the distribution.

• A right - skewed distribution has a longer tail on the right (higher values), which means that the median is closer to the first quartile and the whisker on the right (maximum side) is longer.
• A left - skewed distribution has a longer tail on the left (lower values), so the median is closer to the third quartile and the whisker on the left (minimum side) is longer.

Looking at the plots, we need to find the one where the box for "you" (right - skewed) has the median closer to \(Q_1\) and a long right whisker, and the box for "friend" (left - skewed) has the median closer to \(Q_3\) and a long left whisker. After analyzing the given options (the visual cues like the position of the median in the box and the length of the whiskers), we can identify the correct plot.

Step 2: Analyze the distribution shapes

• For a right - skewed (positively skewed) distribution, the mean is greater than the median, and the tail of the distribution extends to the right (towards higher values). In the context of credit card purchases, if your purchases are right - skewed, it means that there are a few relatively large purchase amounts that pull the tail to the right.
• For a left - skewed (negatively skewed) distribution, the mean is less than the median, and the tail of the distribution extends to the left (towards lower values). For your friend's purchases, a left - skewed distribution implies that there are a few relatively small purchase amounts that pull the tail to the left.

Answer:

The correct box - and - whisker plot is the one (among A, B, C, D) that matches the right - skewed distribution for "you" (longer right whisker, median closer to \(Q_1\) in the box) and left - skewed distribution for "friend" (longer left whisker, median closer to \(Q_3\) in the box). The shape of your purchases' distribution is skewed right, and the shape of your friend's purchases' distribution is skewed left. If we assume that option B is the correct plot (based on the visual analysis of the box positions and whisker lengths), then:

The correct box - and - whisker plot is B. The shape of the distribution of your purchases is skewed right. The shape of the distribution of your friend's purchases is skewed left.