Question

the following data represent the dividend yields (in percent) of a random sample of 28 publicly traded stocks. complete parts (a) to (c). (b) draw a boxplot of the data. (c) determine the shape of the distribution from the boxplot. a. the distribution is skewed to the right. b. the distribution is skewed to the left. c. the distribution is roughly symmetric. d. the shape of the distribution cannot be determined from the boxplot.

Explanation:

To determine the shape of a distribution from a box - plot:

• If the median is in the middle of the box and the whiskers are approximately equal in length, the distribution is roughly symmetric.
• If the right whisker is longer than the left whisker, the distribution is skewed to the right.
• If the left whisker is longer than the right whisker, the distribution is skewed to the left.

In the given box - plot (assuming a standard box - plot where the box represents the inter - quartile range (IQR) from \(Q_1\) to \(Q_3\) and the line inside the box is the median), if the median is centered within the box and the whiskers are of similar length, we can make a judgment about symmetry.

Answer:

C. The distribution is roughly symmetric.