Chapter 10.3, Problem 10IP

a.

To determine

To Find: To find the mean and mean absolute deviation of the given data.

Answer to Problem 10IP

The mean is 5.65 and mean absolute deviation is 2.6.

Explanation of Solution

Given information: yards gained by football teams in each game

Formula used: For Mean: $\overline{x}=\frac{{\displaystyle \sum _{i=1}^n{x}_i}}{N}$ and for mean absolute deviation $MD=\frac{{\displaystyle \sum _{i=1}^n\left|x_i-\overline{x}\right|}}{N}$

Calculation:

Calculation of Mean

  $\begin{array}{l}\overline{x}=\frac{-9.5+12.5+17.5+-4+-6+12+8.5+-2.5+21.5+6.5}{10}\\ \overline{x}=\frac{56.5}{10}\\ \therefore \overline{x}=5.65\end{array}$

Thus, mean is 5.65

Now, calculation of mean absolute deviation

$x_i$	$x_i-\overline{x}$	$\left|x_i-\overline{x}\right|$
$-9.5$	$-9.5-5.65=-15.15$	15.15
12.5	$12.5-5.65=6.85$	6.85
17.5	$17.5-5.65=11.85$	11.85
$-4$	$-4-5.65=-9.65$	9.65
$-6$	$-6-5.65=-11.65$	11.65
12	$12-5.65=6.35$	6.35
8.5	$8.5-5.65=2.85$	2.85
$-2.5$	$-2.5-5.65=-8.15$	8.15
21.5	$21.5-5.65=15.85$	15.85
6.5	$6.5-5.65=0.85$	0.85

  $\begin{array}{l}MD=\frac{15.15+6.85+11.85+9.65+11.65+6.35+2.85+8.15+15.85+0.85}{10}\\ MD=\frac{89.2}{10}\\ MD=8.92\end{array}$

Thus, mean absolute deviation is 2.6

Hence, the required mean and mean absolute deviation is 5 and 2.6.

b.

To determine

To Explain:To explain the reasons of mean is less than from mean absolute deviation.

Answer to Problem 10IP

Because of negative information.

Explanation of Solution

Given information:Mean and mean absolute deviation.

In calculating mean some negative observations decrease the value of mean while in the mean absolute deviation, the negative symbols are ignored and absolute values are taken. So, it increases the value of mean absolute deviation.

Thus, because of negative observations the mean absolute deviation is greater then the mean.