Question

what is the mean absolute deviation of the following set of data? 20 20 2 14 12 18 22 6 12 12

Explanation:

Step1: Calculate the mean

$\frac{20 + 20+2 + 14+12+18+22+6+12+12}{10}=\frac{138}{10} = 13.8$

Step2: Calculate absolute - deviations

$|20 - 13.8|=6.2$, $|20 - 13.8|=6.2$, $|2 - 13.8| = 11.8$, $|14 - 13.8|=0.2$, $|12 - 13.8| = 1.8$, $|18 - 13.8|=4.2$, $|22 - 13.8| = 8.2$, $|6 - 13.8|=7.8$, $|12 - 13.8| = 1.8$, $|12 - 13.8| = 1.8$

Step3: Calculate the mean of absolute - deviations

$\frac{6.2+6.2 + 11.8+0.2+1.8+4.2+8.2+7.8+1.8+1.8}{10}=\frac{48}{10}=4.8$

Answer:

4.8