Chapter 10.3, Problem 15STP

To determine

To find:Which option describes the mean absolute deviation of the given data.

Answer to Problem 15STP

The average distance between the mean distances and the actual distances is $10$ , option B is the right answer.

Explanation of Solution

Given information:

Distance (miles)
60	40	15	25	30	35	40

Calculation:

Finding the mean absolute deviation,

  $\begin{array}{l}\text{mean}=\frac{60+40+15+25+30+35+40}{7}\\ \text{mean}=35\end{array}$

Absolute values of the differences between each value in the data set and the mean,

  $\begin{array}{c}\left|60-35\right|=25\\ \left|40-35\right|=5\\ \left|15-35\right|=20\\ \left|25-35\right|=10\\ \left|30-35\right|=5\\ \left|35-35\right|=0\\ \text{mean}\text{absolute}\text{deviation}=\frac{25+5+20+10+5+0+5}{7}\\ \text{mean}\text{absolute}\text{deviation}=10\end{array}$

Therefore we can conclude that the average distance between the mean distances and the actual distances is $10$ .