Chapter 11, Problem 35E

Solution

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

The mean, median and mode are 15, 15 and 18 respectively.

Given information:

The data set is:

8
9
11
12
13
15
16
18
18
18
27

Formula used:

Formula to compute the mean and median are:

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

Median when number of observations are odd are:

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

Concept used:

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

Calculation:

The mean is:

  $\begin{array}{c}\text{Mean = }\frac{\text{Sum of observations}}{\text{Number of observations}}\\ =\frac{8+9+\mathrm{..........}+27}{11}\\ =\frac{165}{11}\\ =15\end{array}$

Median is computed as:

  $\begin{array}{c}\text{Median = }{\left(\frac{n+1}{2}\right)}^{th}term\\ ={\left(\frac{11+1}{2}\right)}^{th}term\\ =\frac{{12}^{th}term}{2}\\ =6^{th}term\\ =15\end{array}$

Here, 18 is occurring maximum number of times in comparison of other values of the data set.

Hence, mean, median and mode are 15, 15 and 18 respectively.