Chapter 10, Problem 14CR

To determine

To find: The mean absolute deviation of each data set, and that data set has a greater mean absolute deviation.

Answer to Problem 14CR

The mean of absolute deviation of brown candies is $2.3$ and red candies is $1.9$ .

The mean of absolute deviation of brown candies is higher

Explanation of Solution

Given information: The given data of brown candies is $18,14,20,13,17$ and red candies is $10,8,5,12,8$ .

Calculation: The given data of brown candies is $18,14,20,13,17$ and red candies is $10,8,5,12,8$ .

Mean of the brown candies is:

  $\frac{18+14+20+13+17}{5}=\frac{82}{5}=16.4$

The absolute value of the difference between each value in the data and the mean is:

  $\left|18-16.4\right|=1.6,\left|14-16.4\right|=2.4,\left|20-16.4\right|=3.6,\left|13-16.4\right|=3.4,\left|17-16.4\right|=0.6$

The mean of absolute deviation is:

  $\frac{1.7+2.4+3.6+3.4+0.6}{5}=\frac{11.7}{5}=2.3$

Thus, the mean of absolute deviation of brown candies is $2.3$ .

Mean of the red candies is:

  $\frac{10+8+5+12+8}{5}=\frac{43}{5}=8.6$

The absolute value of the difference between each value in the data and the mean is:

  $\left|10-8.6\right|=1.4,\left|8-8.6\right|=0.6,\left|5-8.6\right|=3.6,\left|12-8.6\right|=3.4,\left|8-8.6\right|=0.6$

The mean of absolute deviation is:

  $\frac{1.4+0.6+3.6+3.4+0.6}{5}=\frac{9.6}{5}=1.9$

The mean absolute deviation of red candies is $1.9$ .

Thus, the mean of absolute deviation of brown candies is higher.