Question

calculate the mean absolute deviation for the data set shown below. {11, 13, 14, 16, 16, 19, 20, 21, 24, 24} provide an answer accurate to the nearest hundredth.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{11 + 13+14+16+16+19+20+21+24+24}{10}=\frac{178}{10} = 17.8$

Step2: Calculate the absolute - deviations

$|11 - 17.8|=6.8$, $|13 - 17.8| = 4.8$, $|14 - 17.8|=3.8$, $|16 - 17.8| = 1.8$, $|16 - 17.8|=1.8$, $|19 - 17.8| = 1.2$, $|20 - 17.8|=2.2$, $|21 - 17.8| = 3.2$, $|24 - 17.8|=6.2$, $|24 - 17.8| = 6.2$

Step3: Calculate the mean of the absolute - deviations

$MAD=\frac{6.8 + 4.8+3.8+1.8+1.8+1.2+2.2+3.2+6.2+6.2}{10}=\frac{38}{10}=3.80$

Answer:

$3.80$