Q13. - Algebra 1

Question

SALES Nate is keeping track of how much people spent at the school bookstore in one day. Find the mean absolute deviation for the data to the nearest tenth: $\mathbf{1}\mathbf{,}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{,}\mathbf{3}\mathbf{,}\mathbf{4}\mathbf{,}\mathbf{5}\mathbf{,}\mathbf{12}$

Step-by-Step Solution

Answer

The mean absolute deviation for the data is $\mathbf{2}\mathbf{.}\mathbf{57}$.

Step 1. Find the mean.

To find the mean, add the numbers and then divide by the number of values in the data set.

$\begin{array}{l}\overline{x}=\frac{1+1+2+3+4+5+12}{7}\\ =\frac{28}{7}\\ =4\end{array}$

Step 2. Find the sum.

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

$\begin{array}{r}|1-4|+|1-4|+|2-4|+|3-4|+|4-4|+|5-4|+|12-4|=3+3+2+1+0+1+8\\ =18\end{array}$

Step 3. Division.

Divide the sum by the number of values in the set of data.

$\frac{18}{7}=2.57$ 

Therefore, the mean absolute deviation for the data is $2.57$.