Chapter 13.2, Problem 17E

To determine

To find: The mean and median of the given data.

Answer to Problem 17E

The mean is $67\cdot 14$ and median is $98\cdot 02$ .

Explanation of Solution

Given:

The given data is shown in table 1

Table 1

Months	Amount of electric bills( $X_i$ )
January	$\$67\cdot 92$
February	$\$59\cdot 84$
March	$\$52\cdot 00$
April	$\$52\cdot 50$
May	$\$57\cdot 99$
June	$\$65\cdot 35$
July	$\$81\cdot 76$
August	$\$74\cdot 98$
September	$\$87\cdot 82$
October	$\$83\cdot 18$
November	$\$65\cdot 35$
December	$\$57\cdot 00$

Concept used:

Mean is given as:

  $\overline{X}=\frac{1}{n}\left({\displaystyle \sum _{i=1}^n{X}_i}\right)$

Here, $n$ is total number of terms.

And median is given as:

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

Calculation:

Mean of given data is calculated as:

  $\begin{array}{c}\overline{X}=\frac{67\cdot 92+59\cdot 84+52+52\cdot 50+57\cdot 99+65\cdot 35+81\cdot 76+74\cdot 98+87\cdot 82+83\cdot 18+65\cdot 35+57}{12}\\ =\frac{805\cdot 69}{12}\\ =67\cdot 14\end{array}$

After arranging the given data in ascending order we get,

  $52$ , $52\cdot 5$ , $57$ , $57\cdot 99$ , $59\cdot 84$ , $65\cdot 35$ , $65\cdot 35$ , $67\cdot 92$ , $74\cdot 98$ , $81\cdot 76$ , $83\cdot 18$ , $87\cdot 82$

Median of the above data is calculated as:

  $\begin{array}{c}\text{Median}=\frac{1}{2}\left\{\frac{12}{2}\text{th term}+\left(\frac{12}{2}+1\right)\text{th term}\right\}\\ =\frac{1}{2}\left\{6\text{th term}+7\text{th term}\right\}\\ =\frac{1}{2}\left\{65\cdot 35+65\cdot 35\right\}\\ =98\cdot 02\end{array}$

Therefore, mean is $67\cdot 14$ and median is $98\cdot 02$ .