Question

The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 18, 16, 14, 22, 25, 18, 13 Send data to calculator Mean absolute deviation: 6 X 5 ?

Answer 1

We have the following equation for the mean absolute deviation:

$M_{ad}=\frac{\sum ^{}_{}|x_i-\mu|}{n}$

then, we have to find the mean first:

$\begin{gathered} n=7 \\ \mu=\frac{18+16+14+22+25+18+13}{7}=\frac{126}{7}=18 \\ \mu=18 \end{gathered}$

Now we can use the formula for the mean absolute deviation by calculating the difference between each value and the mean,and then adding all those and dividing by n. Then, we get the following:

$\begin{gathered} M_{ad}=\frac{|18-18|+|16-18|+|14-18|+|22-18|+|25-18|+|13-18|}{7} \\ =\frac{0+2+4+4+7+5}{7}=\frac{22}{7}=3.14 \\ M_{ad}=3.14 \end{gathered}$

therefore, the mean standard deviation is 3.14