Question

(a) find the five - number summary, and (b) draw a box - and - whisker plot of the data. 4 8 8 6 2 9 8 7 9 6 9 5 1 6 2 9 8 7 7 9 (a) min = 1 (simplify your answer.) q₁ = (simplify your answer. do not round.)

Explanation:

Step1: Sort the data

First, sort the data set \(4,8,8,6,2,9,8,7,9,6,9,5,1,6,2,9,8,7,7,9\) in ascending - order: \(1,2,2,4,5,6,6,6,7,7,7,8,8,8,8,9,9,9,9,9\).

Step2: Find the minimum

The minimum value (Min) of the sorted data set is \(1\).

Step3: Calculate the position of \(Q_1\)

The formula to find the position of the first - quartile \(Q_1\) for a data set of size \(n\) is \(i=\frac{n + 1}{4}\). Here, \(n = 20\), so \(i=\frac{20+1}{4}=5.25\).

Step4: Determine \(Q_1\)

Since \(i = 5.25\), \(Q_1\) is the value that is \(0.25\) of the way between the \(5^{th}\) and \(6^{th}\) ordered data values. The \(5^{th}\) value is \(5\) and the \(6^{th}\) value is \(6\). So \(Q_1=5+(6 - 5)\times0.25 = 5.25\).

Answer:

\(Q_1 = 5.25\)