Question

(a) find the five - number summary, and (b) draw a box - and - whisker plot of the data. 3 8 8 6 2 9 8 7 9 6 9 5 2 6 2 9 8 7 7 9 (a) min = 2 (simplify your answer.) q1 = (simplify your answer. do not round.)

Explanation:

Step1: Sort the data

First, sort the data set \(2,2,2,3,5,6,6,6,7,7,7,8,8,8,8,9,9,9,9,9\). There are \(n = 20\) data - points.

Step2: Calculate \(Q_1\)

The position of \(Q_1\) is \(i=\frac{n + 1}{4}=\frac{20+1}{4}=5.25\). This means \(Q_1\) is \(0.25\) of the way between the 5th and 6th ordered data - values. The 5th value is \(5\) and the 6th value is \(6\). So \(Q_1=5+(6 - 5)\times0.25 = 5.25\).

Answer:

\(5.25\)