Question

in the data set below, what is the mean absolute deviation? 9.8 7.7 6.4 9.4 5.7 6.2 4.5 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: $9.8 + 7.7+6.4 + 9.4+5.7+6.2+4.5=49.7$. There are $n = 7$ data - points. The mean $\bar{x}=\frac{49.7}{7}=7.1$.

Step2: Calculate the absolute deviations

Find the absolute difference between each data - point and the mean:
$|9.8 - 7.1|=2.7$, $|7.7 - 7.1| = 0.6$, $|6.4 - 7.1|=0.7$, $|9.4 - 7.1| = 2.3$, $|5.7 - 7.1|=1.4$, $|6.2 - 7.1| = 0.9$, $|4.5 - 7.1|=2.6$.

Step3: Calculate the mean of the absolute deviations

Sum the absolute deviations: $2.7+0.6 + 0.7+2.3+1.4+0.9+2.6 = 11.2$.
The mean absolute deviation $MAD=\frac{11.2}{7}=1.6$.

Answer:

$1.6$