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 right.
b. the distribution is skewed left.
c. the distribution is roughly symmetric.
d. the shape of the distribution cannot be determined from the boxplot.

b. the five - number summary is (square), (square), (square), (square), (square).

Explanation:

Step1: Analyze boxplot skew

The left whisker is much longer than the right whisker, and the box is shifted toward the right side of the plot. This means the distribution is pulled toward the left (has a long left tail), so it is skewed left.

Step2: Identify minimum value

The left end of the left whisker aligns with 0 on the axis.
Minimum = $0$

Step3: Identify first quartile (Q1)

The left edge of the box aligns with 8 on the axis.
Q1 = $8$

Step4: Identify median (Q2)

The vertical line inside the box aligns with 12 on the axis.
Median = $12$

Step5: Identify third quartile (Q3)

The right edge of the box aligns with 16 on the axis.
Q3 = $16$

Step6: Identify maximum value

The right end of the right whisker aligns with 20 on the axis.
Maximum = $20$

Answer:

a. B. The distribution is skewed left
b. $0$, $8$, $12$, $16$, $20$