Question

why is the median less affected by the extreme values than the mean?

Answer 1

Solution:

It is correct that, median less affected by the extreme values than the mean.

Let's take an example for it,

The median is the middle score for a set of data that has been arranged in order of magnitude.

The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.

example 1:

65           55           89           56           35           14           56           55           87           45           92

We first need to rearrange that data into order of magnitude (smallest first):

14           35           45           55           55           56           56           65           87           89           92

Hence median is middle value = 56

and mean = 59.

This works fine when you have an odd number of scores, but what happens when you have an even number of scores? What if you had only 10 scores? Well, you simply have to take the middle two scores and average the result. So, if we look at the example below:

65           55           89           56           35           14           56           55           87           45

We first need to rearrange that data into order of magnitude (smallest first):

14           35           45           55           55           56           56           65           87           89

Median is average of middle two values = 55.5

and mean = 55.7

We can compare from first example and from second,

Median is still near about 56 but mean is highly decreased as compare to median.

Hence we can say, median less affected by the extreme values than the mean

Done