Median

After mean, the most important term is median. As I discussed in the previous blog, "Meaning of Mean" that mean, median and mode are important concepts, thus I am going to explain Median.

In this blog, I will explain in detail the meaning of median, its application and how to find the median from data. I will give real life example to understand the actual application of median.

Median is basically the middle point of any data. This tell, how the data is distributed. If we select 8 people randomly and want to find their median age.

If the ages are:

22, 24, 42, 48, 55, 30, 20, 22

STEP 1:

If you rearrange this ages from younger age people to older people, we will get:

20, 22, 22, 24, 30, 42, 48, 55

STEP 2:

I have just arranged the ages in ascending order and now I will count the number of samples in the list. In this list we have 8 numbers (ages).

STEP 3:

Now, if the number of samples (n) are Even, then middle value will be at (n+1)/2 th place. Here we have 8 people, so n=8.

Now, if we put in the above formula (n+1)/2 we will get 4.5. That means the median value is at 4.5 place. So, in step 1 if we go 4 places from left to right, we get 24. And on 5th place we have 30. So, 24 is on 4th place and 30 is on 5th place.

We have to calculate the mean of these two ages as they are at center of the data. If we find the mean of 24 and 30, we get 27, which is the Median of the data.

So the median age of the people is 27.

Why median is important:

Managers and Statisticians use Median to describe the mid-point of the data. We can study if the midpoint is exactly in the middle of the data or if it is skewed on one side. Median gives us the estimate of how much balanced the data is. You can think of a scale where you have lot of big values on one side and other side has very small values. Thus, we can get to know that if the data values are balanced or not. Also, the extreme values can be ignored if they are far from Median.

The 50 % values are above the median and 50% values are below the median.