Chapter 12.5, Problem 44SR

To determine

To calculate: the mean absolute deviation to the nearest tenth.

Answer to Problem 44SR

The mean absolute value to the nearest tenth is 100.8

Explanation of Solution

Given information:

A group of 1000 randomly selected teens were asked if they believed there was global warming.

Yes, strongly agree $=$ 312

Yes, mildly agree $=$ 340

No, I don’t think so $=$ 109

No, absolutely not $=$ 116

Not sure $=$ 123

Calculation :

The mean of the of the data

  $\begin{array}{l}=\frac{312+340+109+116+123}{5}\\ =\frac{1000}{5}=200\end{array}$

Find the sum of the absolute values of the differences between each value and the mean.

  $\begin{array}{l}=\left|312-200\right|+\left|340-200\right|+\left|109-200\right|+\left|116-200\right|+\left|123-200\right|\\ =112+140+91+84+77\\ =504\end{array}$

Divide the sum by the number of values

  $\begin{array}{l}=\frac{504}{5}\\ =100.8\end{array}$

Therefore,

The mean absolute value to the nearest tenth is 100.8