Chapter 10.3, Problem 6IP

To determine

To calculate:The mean and the mean absolute deviation of the given information.

Answer to Problem 6IP

The Mean of the given set of values is $\overline{x}=6$ .

The Mean Absolute Deviation of the given set of values is $M.A.D=3.4$ .

Explanation of Solution

Given information:The table below shows the cost of different books in dollars.

Cost of book (in $)
1
1
3
4
4
6
7
8
11
15

Formula used:

The Mean of a given set of values is the average of the given set of values.

  $Mean=\frac{\text{sum}\text{of}\text{values}}{\text{number}\text{of}\text{values}}=\frac{{\displaystyle \sum x}}{n}$

The Mean Absolute Deviation of a given set of values is the average of deviation of each value from the mean value.

  $M.A.D=\frac{{\displaystyle \sum \left(|x-\overline{x}|\right)}}{n}$

Calculation:

The value of $x,\overline{x},\left(|x-\overline{x}|\right),\text{mean}\text{absolute}\text{deviation}\left(M.A.D\right)$ are shown below

$x$	$\left(|x-\overline{x}|\right)$
1	5
1	5
3	3
4	2
4	2
6	0
7	1
8	2
11	5
15	9
${\displaystyle \sum x}=60$	${\displaystyle \sum \left(|x-\overline{x}|\right)}=34$
$\overline{x}=\frac{{\displaystyle \sum x}}{n}=\frac{60}{10}=6$	$M.A.D=\frac{{\displaystyle \sum \left(|x-\overline{x}|\right)}}{n}=\frac{34}{10}=3.4$

The Mean of the given set of values is $\overline{x}=6$ .

The Mean Absolute Deviation of the given set of values is $M.A.D=3.4$ .

It shows that the average distance between actual cost of each book and the mean cost of each book is $3.4.