Question

Find the mean average deviation of his run times

Answer 1

The mean average deviation (MAD) shows the average of the deviation of all the values from their average/mean.

It is calculated as follows;

`\begin{gathered} M=\frac{\Sigma\text{ of data}}{Number\text{ of data}} \\ M=(9.6+9.1+8.7+8.6+8.4+8.1+7.5)/(7) \\ M=(60)/(7) \\ M=8.57 \\ M\approx8.6 \end{gathered}`

Next step, we find the difference of each given value from the mean. The result is now divided by the number of data which is 7.

`\begin{gathered} \text{MAD}=(|8.6-9.6|+|8.6-9.1|+|8.6-8.7|+|8.6-8.6|+|8.6-8.4|+|8.6-8.1|+|8.6-7.5|)/(7) \\ \text{MAD}=(1+0.5+0.1+0+0.2+0.5+1.1)/(7) \\ \text{MAD}=(3.4)/(7) \\ \text{MAD}=0.4857\ldots \\ \text{MAD}\approx0.5 \end{gathered}`

The mean average deviation is 0.5 minutes

Please note that when computing the MAD (mean average deviation, we take absolute values only, that is no negative values. Rather all negative values would be taken as positive. That is why we insert the absolute sign into the formula.