Question

3. How would an extreme outlier tend to distort the mean deviation of a data set?

Answer 1

we know that the mean deviation is defined as the sum of all differences between the individual data values and their mean value, divided by the total number of data values.

we can write mean deviation as

Suppose we have a data set which has maximum data values around 20 and its mean 20.

For example, we have the data set 10,15,25,30

Its mean = (10+15+25+30)/4 = 80/4 = 20

And its mean deviation is

Suppose we add an extreme outlier 90 in the data

then mean = (10+15+25+30+90)/5 = 170/5 = 34

And its mean deviation is

So, it is clear that an extreme value will increase the mean deviation because it increase the mean as well as increases the overall difference between individual values and mean.