Question

find the 5 number summary for the data shown
1 10
12 13
16 21
22 23
30 42
56 71
77 80
86
5 number summary:

use the locator/percentile method described in your book, not your calculator.
question help: video 1 video 2
calculator

Explanation:

Step1: Sort the data

First, we list out all the data points: \(1,10,12,13,16,21,22,23,30,42,56,71,77,80,86\)

Step2: Find the minimum

The minimum value is the first - value in the sorted list. So, \(Min = 1\)

Step3: Find the first quartile (\(Q_1\))

The formula for the locator of the first quartile \(L_{25}=\frac{25}{100}(n + 1)\), where \(n = 15\) (the number of data points).
\(L_{25}=\frac{25}{100}(15 + 1)=\frac{1}{4}\times16 = 4\)
The \(4^{th}\) value in the sorted list is \(Q_1=13\)

Step4: Find the median (\(Q_2\))

The formula for the locator of the median \(L_{50}=\frac{50}{100}(n + 1)\)
\(L_{50}=\frac{1}{2}(15 + 1)=8\)
The \(8^{th}\) value in the sorted list is \(Q_2 = 23\)

Step5: Find the third quartile (\(Q_3\))

The formula for the locator of the third quartile \(L_{75}=\frac{75}{100}(n + 1)\)
\(L_{75}=\frac{3}{4}(15 + 1)=12\)
The \(12^{th}\) value in the sorted list is \(Q_3=71\)

Step6: Find the maximum

The maximum value is the last value in the sorted list. So, \(Max=86\)

Answer:

\(1,13,23,71,86\)