Chapter 11, Problem 36E

Solution

To find: The mean, median and mode for the provided data set.

The mean and medianare 9.5 and 9.5 respectively.

Given information:

The data set is:

11
6
9
4
19
10
15
2

Formula used:

Formula to compute the mean and median are:

  $\text{Mean = }\frac{\text{Sum of observations}}{\text{Number of observations}}$

Median when numbers of observations are evenare:

  $\begin{array}{l}\text{Median = }\frac{{\left(\frac{n}{2}\right)}^{th}term+{\left(\frac{n}{2}+1\right)}^{th}term}{2}\\ \end{array}$

Concept used:

Mode is a value that happens maximum number of times in a set of data.

Calculation:

The mean is:

  $\begin{array}{c}\text{Mean = }\frac{\text{Sum of observations}}{\text{Number of observations}}\\ =\frac{11+6+\mathrm{..........}+2}{8}\\ =\frac{76}{8}\\ =9.5\end{array}$

To find the Median, data is required in ordered manner. So, the data is arranged in ascending order as follows:

2
4
6
9
10
11
15
19

Median is computed as:

  $\begin{array}{c}\text{Median =}\frac{{\left(\frac{n}{2}\right)}^{th}term+{\left(\frac{n}{2}+1\right)}^{th}term}{2}\\ =\frac{{\left(\frac{8}{2}\right)}^{th}term+{\left(\frac{8}{2}+1\right)}^{th}term}{2}\\ =\frac{4^{th}term+5^{th}term}{2}\\ =\frac{9+10}{2}\\ =9.5\end{array}$

Here, no value is occurring maximum number of times. So, no modes exist here.

Hence, mean and median and mode are 9.5 and 9.5 respectively.