Use the image to answer the question.

Question

A number line ranges from 60 to 100 in increments of 5. A boxplot is placed above the number line. The box is divided into two sections. The first box extends from 65 to 70. The second box extends from 70 to 80. A line extends from each end of the box, terminating at 60 on the left and terminating at 100 on the right.

For the given box plot, which measure of center—mean or median—best represents the shape of the distribution? Enter 1 for median or 2 for mean.

(1 point)

Answer 1

To determine whether the mean or median best represents the distribution shape indicated by the boxplot, we need to consider the characteristics of the boxplot and its parts.

In this case, the boxplot shows two boxes: one from 65 to 70 and another from 70 to 80. There are also lines extending from the boxes to the minimum (60) and maximum (100) values. This shape suggests that there is a concentration of data points between 65 and 80, with more data points likely clustered toward the lower end.

The presence of a long line extending to 100 indicates that there may be some outliers or a long tail on the right side of the distribution. This can skew the mean higher than the median. In distributions with long tails or outliers, the median is often a better measure of center because it is less affected by extreme values.

Given this analysis, since the boxplot indicates a potential skew and the median would better reflect the center of the data:

The answer is 1 for median.