Question

(a) identify the shape of the distribution, and (b) determine the five - number summary. assume that each number in
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

In a box - plot, if the median is in the middle of the box and the whiskers are approximately the same length, the distribution is roughly symmetric. Here, the box - plot has the median in the middle of the box and the whiskers (the lines extending from the box) are not extremely different in length. So, the distribution is roughly symmetric.

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 value is the left - most end of the whisker. Let's assume from the scale (since each mark on the x - axis is 2 units, the left - most whisker end is at \(4\)).
• The first quartile (\(Q_1\)) is the left end of the box. From the scale, \(Q_1 = 8\).
• The median (\(Q_2\)) is the line inside the box. From the scale, \(Q_2=10\).
• The third quartile (\(Q_3\)) is the right end of the box. From the scale, \(Q_3 = 14\).
• The maximum value is the right - most end of the whisker. From the scale, the maximum is \(18\).

Answer:

a. C. The distribution is roughly symmetric.
b. \(4,8,10,14,18\)