Question

(a) identify the shape of the distribution, and (b) determine the five - number summary. assume that each number in the five - number summary is an integer.
a. choose the correct answer below for the shape of the distribution.
a. the distribution is skewed left.
b. the distribution is skewed right.
c. the distribution is roughly symmetric.
d. the shape of the distribution cannot be determined from the boxplot.
b. the five - number summary is □,□,□,□,□.

Explanation:

Step1: Identify the shape of the distribution

A box - plot is skewed right if the right whisker is longer than the left whisker. In the given box - plot, the right whisker is longer. So, the distribution is skewed right.

Step2: Determine the five - number summary

The five - number summary consists of the minimum, first quartile (\(Q_1\)), median (\(Q_2\)), third quartile (\(Q_3\)), and maximum.

• The minimum is the left - most value on the scale. From the box - plot, the minimum \(= 2\).
• The first quartile (\(Q_1\)) is the left - hand side of the box. \(Q_1 = 5\).
• The median (\(Q_2\)) is the line inside the box. \(Q_2=7\).
• The third quartile (\(Q_3\)) is the right - hand side of the box. \(Q_3 = 9\).
• The maximum is the end of the right whisker. Maximum \(= 20\).

Answer:

a. B. The distribution is skewed right.
b. The five - number summary is \(2,5,7,9,20\)