Question

question 2
find the 5 number summary for the data shown
5 number summary:
use the locator/percentile method described in your book, not your calculator.
question help: video 1 video 2

Explanation:

Step1: Combine and sort data

Combine the data: \(5,7,8,13,17,28,33,34,43,63,64,74,79,91,99\). There are \(n = 15\) data points.

Step2: Find the minimum

The minimum value is the first - ordered data point. So, \(Min=5\).

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

The locator for \(Q_1\) is \(L_{25}=\frac{25}{100}(n + 1)=\frac{25}{100}(15+1)=4\). The \(4^{th}\) ordered data point is \(Q_1 = 13\).

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

The locator for the median is \(L_{50}=\frac{50}{100}(n + 1)=\frac{50}{100}(15 + 1)=8\). The \(8^{th}\) ordered data point is \(Q_2=34\).

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

The locator for \(Q_3\) is \(L_{75}=\frac{75}{100}(n + 1)=\frac{75}{100}(15+1)=12\). The \(12^{th}\) ordered data point is \(Q_3 = 74\).

Step6: Find the maximum

The maximum value is the last - ordered data point. So, \(Max=99\).

Answer:

\(5,13,34,74,99\)