Question

finding the mean absolute deviation
evelyns scores 125 137 138 145 145
distance from the mean 13 1 0 7 7
what is the mean absolute deviation of evelyns scores?
○ 5.1
○ 5.6
○ 5.8
○ 7

Explanation:

Step1: Recall the formula for MAD

The mean - absolute deviation (MAD) is the average of the absolute deviations from the mean. The formula is $MAD=\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n}$, where $|x_{i}-\bar{x}|$ are the absolute deviations from the mean and $n$ is the number of data - points. Here, the absolute deviations from the mean are already given as 13, 1, 0, 7, 7 and $n = 5$.

Step2: Calculate the sum of the absolute deviations

$\sum_{i=1}^{5}|x_{i}-\bar{x}|=13 + 1+0 + 7+7=28$.

Step3: Calculate the MAD

$MAD=\frac{28}{5}=5.6$.

Answer:

5.6