Question

the data represent the age of world leaders on their day of inauguration. find the five - number summary, and construct a boxplot for the data. comment on the shape of the distribution.
the five - number summary is 41, 48, 54, 61, 69.
choose the correct boxplot of the data below.
choose the correct description of the shape of the distribution.
a. the distribution is skewed to the right.
b. the distribution is roughly symmetric.
c. the distribution is skewed to the left.
d. the shape of the distribution cannot be determined from the boxplot.

Explanation:

Step1: Understand the five - number summary

The five - number summary consists of the minimum value, first quartile ($Q_1$), median ($Q_2$), third quartile ($Q_3$), and maximum value. Here, the five - number summary is \(41\) (minimum), \(48\) ($Q_1$), \(54\) (median), \(61\) ($Q_3$), \(69\) (maximum).

Step2: Analyze the boxplot and distribution shape

For a symmetric distribution, the median is in the middle of the box (the distance from \(Q_1\) to the median is approximately equal to the distance from the median to \(Q_3\)), and the whiskers (the lines from the box to the minimum and maximum) are of similar lengths.
In this case, since the five - number summary has \(Q_2 - Q_1=54 - 48 = 6\) and \(Q_3 - Q_2=61 - 54 = 7\) (approximately equal), and if we assume a proper box - plot (like option A which is a candidate for a symmetric - looking plot based on the five - number summary), the distribution is roughly symmetric.

Answer:

B. The distribution is roughly symmetric.