Question

in the data set below, what is the mean absolute deviation? 65.3 95.4 96.8 15.7 66.4 13.7 90.9 87.1 50.1 if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad):

Explanation:

Step1: Calculate the mean

First, sum the data values: $65.3 + 95.4+96.8 + 15.7+66.4 + 13.7+90.9+87.1+50.1=581.4$. There are $n = 9$ data - points. The mean $\bar{x}=\frac{581.4}{9}=64.6$.

Step2: Calculate the absolute deviations

Find the absolute deviation of each data - point from the mean:
$|65.3 - 64.6|=0.7$; $|95.4 - 64.6| = 30.8$; $|96.8 - 64.6|=32.2$; $|15.7 - 64.6| = 48.9$; $|66.4 - 64.6|=1.8$; $|13.7 - 64.6| = 50.9$; $|90.9 - 64.6|=26.3$; $|87.1 - 64.6| = 22.5$; $|50.1 - 64.6|=14.5$.

Step3: Calculate the mean of the absolute deviations

Sum the absolute deviations: $0.7+30.8+32.2+48.9+1.8+50.9+26.3+22.5+14.5 = 228.6$.
The mean absolute deviation $MAD=\frac{228.6}{9}\approx25.4$.

Answer:

$25.4$