The average distance from the mean is:
$ 7.2
We are given data points as:
$7, $20 , $9 , $35 , $12 , $15 , $7 , $10 , $20 , $25 , $7 , $20 , $9 , $35 , $12 , $15 , $7 , $10 , $20 , $25
The mean of the data set is:
[tex]Mean=\dfrac{7+20+9+35+12+15+7+10+20+25+7+20+9+35+12+15+7+10+20+25}{20}\\\\\\Mean=\dfrac{320}{20}\\\\\\Mean=16[/tex]
Now we are asked to find the average distance from the mean or MAD of the data.
The absolute difference of each data point from mean is calculated as follows:
|7-16|=9
|20-16|=4
|9-16|=7
|35-16|=19
|12-16|=4
|15-16|=1
|7-16|=9
|10-16|=6
|20-16|=4
|25-16|=9
|7-16|=9
|20-16|=4
|9-16|=7
|35-16|=19
|12-16|=4
|15-16|=1
|7-16|=9
|10-16|=6
|20-16|=4
|25-16|=9
Hence, the mean of these absolute difference is calculated by:
[tex]MAD=\dfrac{9+4+7+19+4+1+9+6+4+9+9+4+7+19+4+1+9+6+4+9}{20}\\\\\\MAD=\dfrac{144}{20}\\\\\\MAD=7.2[/tex]
Hence, the answer is:
$ 7.2
