Explanation
To get the mean absolute deviation, we will
Take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values.
Compute the mean absolute deviation by dividing the sum above by the total number of values in the data set.
For the given set
[tex]21,26,46,44,\text{ and 22}[/tex]
First, we have the mean as
[tex]\frac{21+26+46+44+22}{5}=31.8[/tex]
Next, we calculate the deviation and the absolute values
[tex]|21-31.8|+|26-31.8|+|46-31.8|+|44-31.8|+|22-31.8|[/tex]
From the above, we have the mean absolute deviation as
[tex]10.8+5.8+14.2+12.2+9.8=52.8[/tex]
Finally, we divide the answer above by 5 (mean)
The mean absolute deviation is:
[tex]\frac{52.8}{5}=10.56[/tex]
The answer is 10.56
