Chapter 10.3, Problem 9IP

a.

To determine

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

Answer to Problem 9IP

The mean absolute deviation is 2

Explanation of Solution

Given information:Wood planks made by the carpenter.

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

  $\begin{array}{l}\overline{x}=\frac{4+8+7+3}{4}\\ \overline{x}=\frac{22}{4}\\ \therefore \overline{x}=5.5\end{array}$

Thus, mean is 5.5

Now, calculation of mean absolute deviation

$x_i$	$x_i-\overline{x}$	$\left|x_i-\overline{x}\right|$
4	$4-5.5=-1.5$	1.5
8	$8-5.5=2.5$	2.5
7	$7-5.5=1.5$	1.5
3	$3-5.5=-2.5$	2.5
Total	0	8

  $\begin{array}{l}MD=\frac{8}{4}\\ MD=2\end{array}$

Thus, mean absolute deviation is 2

Hence, the required mean absolute deviation is 2.

b.

To determine

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

Answer to Problem 9IP

Mean absolute deviation is 6

Explanation of Solution

Given information:Wood planks made by the carpenter.

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:

Taking 1 yard equal to 3 feet the new data became

12, 24, 21, 9

Calculation of Mean

  $\begin{array}{l}\overline{x}=\frac{12+24+21+9}{4}\\ \overline{x}=\frac{66}{4}\\ \therefore \overline{x}=16.5\end{array}$

Thus, mean is 16.5

Now, calculation of mean absolute deviation

$x_i$	$x_i-\overline{x}$	$\left|x_i-\overline{x}\right|$
12	$12-16.5=-4.5$	4.5
24	$24-16.5=7.5$	7.5
21	$21-16.5=4.5$	4.5
9	$9-16.5=-7.5$	7.5
Total	0	24

  $\begin{array}{l}MD=\frac{24}{4}\\ MD=6\end{array}$

Thus, mean absolute deviation is 6

Hence, the required mean absolute deviation is 6

c.

To determine

To Compare:To compare the difference in mean absolute deviation of the given data in both conditions.

Answer to Problem 9IP

The reason is multiple of 3.

Explanation of Solution

Given information:Mean absolute deviation in both cases.

In the first case when data is given in yards mean absolute deviation is 2 and mean is 5.5 while in the second case when data is given in feet mean absolute deviation is 6 and mean is 16.5.

Comparing this, it can be concluded that the values are affected by a multiple of 3 and this is happened because of one yard is equal to three feet. So, every observation in yard is changed to feet with a multiple of 3.

Hence, mean absolute deviation is changed by three times by converting the data yards into feet.