Median

In statistics and probability theory, the median is the value that separates the higher half from the lower half of a data sample. In a data set of values that are sorted, the median can be a middle value.


The basic feature of the median, in comparison to the mean (or the "average"), is that it is not skewed by a small proportion of extremely large or small values. 

 

For an odd number of observations, the median can be calculated as:

Step 1: Sort the data from the smallest number to the highest number.

Step 2: Find the number where there are an equal number of data points above and below the number.

Median= Central Observation or (N+1)/2th observation

 

For even number of observation,

Step 1: Sort the data from the smallest number to the highest number.

Step 2: Find the central two numbers.

Step 3: Add these two numbers and then divide by two.

Median = Average of the two middle number or { (N/2)th + ((N/2)+ 1)th } /2 observation

 

For example: Consider this set of numbers: 5, 6, 13, 2, 22, 7, 17, 18, 11

 

To find the median, arrange the numbers in ascending order: 2, 5, 6, 7, 11, 13, 17, 18, 22

 

Now, the total number of observations is 9 hence N = 9 which is an odd number and median observation will be calculated as follows:

 

Hence, the median value will be the  5th observation, i.e. 11

 

Now consider the series to be : 5, 6, 13, 2, 22, 7, 17, 11. Arranging in ascending order the series will be: 2, 5, 6, 7, 11, 13, 17, 22. Here, the number of observations is 8 which is an even number. Therefore, the median will be the average of (8/2)th =4th and (8/2 + 1)th = 5th observations.

Hence, the median will be 9.