Chapter 10.3, Problem 18STP

a.

To determine

To find:Which fund should M choose and the mean absolute deviation for that fund.

Answer to Problem 18STP

M should not choose fund A and the mean absolute deviation of fund A is approximately $3$ which is greater than fund B.

Explanation of Solution

Given:

M should invest in smaller mean absolute deviation of profits.

Fund A	5%	11%	8%	2%	10%
Fund B	9%	7%	5%	3%	7%

Calculation:

Mean for Fund A,

  $\begin{array}{l}\text{mean}=\frac{5+11+8+2+10}{5}\\ \text{mean}=7.2\end{array}$

To find mean absolute deviation of Fund A,

  $\begin{array}{c}\left|5-7.2\right|=2.2\\ \left|11-7.2\right|=3.8\\ \left|8-7.2\right|=0.8\\ \left|2-7.2\right|=5.2\\ \left|10-7.2\right|=2.8\\ \text{Mean}\text{absolute}\text{deviation}=\frac{2.2+3.8+0.8+5.2+2.8}{5}\\ \text{Mean}\text{absolute}\text{deviation}\approx \text{3}\end{array}$

The mean absolute deviation is approximately $3$ for fund A and it is greater than fund B.

b.

To determine

To find: Which fund should M choose? What is the mean absolute deviation for that fund?

Answer to Problem 18STP

M should choose fund B and the mean absolute deviation of fund B is approximately $1.8$ which is lesser than fund A.

Explanation of Solution

Given:

M should invest in smaller mean absolute deviation of profits.

Fund A	5%	11%	8%	2%	10%
Fund B	9%	7%	5%	3%	7%

Calculation:

Mean for Fund B,

  $\begin{array}{l}\text{mean}=\frac{9+7+5+3+7}{5}\\ \text{mean}=6.2\end{array}$

To find mean absolute deviation of Fund B,

  $\begin{array}{c}\left|9-6.2\right|=2.8\\ \left|7-6.2\right|=0.8\\ \left|5-6.2\right|=1.2\\ \left|3-6.2\right|=3.2\\ \left|7-6.2\right|=0.8\\ \text{Mean}\text{absolute}\text{deviation}=\frac{2.8+0.8+1.2+3.2+0.8}{5}\\ \text{Mean}\text{absolute}\text{deviation}\approx 1.8\end{array}$

The mean absolute deviation is approximately $1.8$ for fund B and it is lesser than fund A.