Question

Arithmetic mean is best among all averages why or why not

Answer 1

Answer:

No, it is not the best one.

Explanation:

Average gives us the middle value in simple meaning.

There are many ways to find the average of a data set.

Arithmetic mean is not the best among all the averages due to some reason. It is greatly affected by outliers.

Example:

Consider the data

            1 , 2 , 3 , 5 , 9

⇒ Arithmetic mean = ( 1+ 2 + 3 + 5 + 9) / 5 = 4

But if I change only One value of the same data, then

          1 , 2 , 3 , 5 , 59

⇒ Arithmetic mean = ( 1+ 2 + 3 + 5 + 59) / 5 = 14

So the average changes suddenly. It is not the real image of the data in 2nd case.

But if we consider the Median, then it is the same in both the case which is the middle value "3". And the outlier 59 didn't change it.

I hope it will help you.