Chapter 10.4, Problem 4GP

To determine

To calculate five number summary.

Answer to Problem 4GP

The five number summary is 5, 25, 35, 45, 95

Explanation of Solution

Given information:

Data set

Formula used:

Lower quartile is,

  $Q1=(n+1)\frac{1}{4}term$

Upper quartile is,

  $Q3=(n+1)\frac{3}{4}term$

Median is,

  $M=\frac{(\frac{n}{2})+(\frac{n}{2}+1)}{2}term$

Graph:

  

Calculation:

Re-arranging the data in ascending order,

5, 8, 15, 16, 18, 20, 21, 25, 28, 27, 27, 31, 32, 33, 34, 36, 38, 38, 49, 41, 42, 42, 45, 50, 52, 57, 58, 62, 65, 95.

For median, substituting the values,

  $\begin{array}{l}M=\frac{(\frac{30}{2})+(\frac{30}{2}+1)}{2}term\\ M=\frac{{15}^{th}+{16}^{th}}{2}term\\ M=\frac{34+36}{2}\\ M=35\end{array}$

Hence, median and Q2 is 35

For lower quartile, substituting the values,

  $\begin{array}{l}Q1=(30+1)\frac{1}{4}\\ Q1=31\times \frac{1}{4}\\ Q1=7.75\\ Q1\approx 8\end{array}$

Hence, lower quartile is 25

For upper quartile, substituting the values,

  $\begin{array}{l}Q3=(30+1)\frac{3}{4}\\ Q3=(31)\times \frac{3}{4}\\ Q3=23.25\\ Q3\approx 23\end{array}$

Hence, upper quartile is 45

Minimum is the smallest value of the data set.

Hence, minimum is 5

Maximum is the biggest value of the data set.

Hence, maximum is 95