Chapter 12, Problem 13PT

To determine

To find: the mean absolute deviation.

Answer to Problem 13PT

The mean absolute deviation is $\text{1}\text{.4,}\text{.6,}\text{.4,1}\text{.6,}\text{.4}$ .

Explanation of Solution

Given information:

The shovels each dayis : $\text{3,3,2,1,0,1,8}$

Calculation: to find the mean absolute deviation, find the mean and subtract mean from the data and find absolute value,

  $\begin{array}{l}\text{mean}=\frac{1+1+2+3+4+5+12}{7}\\ \text{mean}=\frac{28}{7}\text{ [add]}\\ \text{mean}=4\text{ [divide]}\end{array}$

Mean absolute deviation:

  $\begin{array}{l}|1-4|=3\text{ [subtract and absoulte value]}\\ |1-4|=3\text{ [subtract and absoulte value]}\\ |2-4|=2\text{ [subtract and absoulte value]}\\ |3-4|=1\text{ [subtract and absoulte value]}\\ |4-4|=0\text{ [subtract and absoulte value]}\\ |5-4|=1\text{ [subtract and absoulte value]}\\ |12-4|=8\text{ [subtract and absoulte value]}\end{array}$

Thus, the mean absolute deviation is $\text{3,3,2,1,0,1,8}$ .