Question

(a) identify the shape of the distribution, and (b) determine the five - number sum 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 roughly symmetric.
c. the distribution is skewed right.
d. the shape of the distribution cannot be determined from the boxplot
b. the five - number summary is 1, 3, 4, 7, 17

Explanation:

Step1: Identify the shape of the distribution

For a box - plot:

• If the whisker on the right - hand side is longer than the left - hand side whisker and the median is closer to the first quartile (\(Q_1\)) than the third quartile (\(Q_3\)), the distribution is skewed right.
• In the given box - plot, the right - hand side whisker is longer. So, the distribution is skewed right.

Step2: Determine the five - number summary

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

• From the box - plot, we can read the values:
• The minimum value (\(Min\)) is \(1\).
• The first quartile (\(Q_1\)) is \(3\).
• The median (\(M\)) is \(4\).
• The third quartile (\(Q_3\)) is \(7\).
• The maximum value (\(Max\)) is \(17\).

Answer:

a. C. The distribution is skewed right.
b. The five - number summary is \(1\), \(3\), \(4\), \(7\), \(17\).