Question

11 fill in the blank 6 points (a) find the five - number summary, and (b) draw a box - and - whisker plot of the data. 2 8 8 3 1 9 8 7 9 6 9 2 1 6 1 9 8 7 7 9 (a) min = 1 q1 = 2.5 q2 = 7 q3 = type your answer. max = 9 (b) choose the correct box - and - whisker plot below. b o a. o b. o c. o d.

Explanation:

Step1: Sort the data

The sorted data set is: 1, 1, 1, 1, 2, 2, 3, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9.

Step2: Find Q1

There are $n = 20$ data - points. The position of Q1 is $i=\frac{n + 1}{4}=\frac{20+1}{4}=5.25$. So, $Q1=2+(0.25)\times(3 - 2)=2.25$.

Step3: Find Q2 (Median)

The position of Q2 is $i=\frac{n + 1}{2}=\frac{20 + 1}{2}=10.5$. So, $Q2=\frac{7+7}{2}=7$.

Step4: Find Q3

The position of Q3 is $i=\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$. So, $Q3=8+(0.75)\times(9 - 8)=8.75$.

Answer:

(a) Min = 1, Q1 = 2.25, Q2 = 7, Q3 = 8.75, Max = 9
(b) Without seeing the actual box - and - whisker plots A, B, C, D in detail, we have calculated the five - number summary which can be used to correctly identify the plot. If the box - and - whisker plot has the left - most point at 1, the left side of the box at 2.25, the line in the box at 7, the right side of the box at 8.75 and the right - most point at 9, then it is the correct one.