Median of Numbers

Median Value

The median is the "middle" value of a list of data that is sorted. The data or observations can be arranged either in ascending order or descending order. 

Example: The median of 2,5,5,6,8,8,9 is 3. 

Apart from the median, mean and mode are the other two central tendencies. The mean is the cumulative ratio of all observations and the total number of observations. The mode is the value repeated most of the time in the specified data set.

How to Find the Median of Numbers?

The data should be sorted in order to find the median. Either in the order of the least to the greatest or the greatest to the least value. A median is a number that is divided from the lower half by the higher half of a data set, a population, or a distribution of probability. For different kinds of distribution, the median is different. Read further to find step by step procedure to find the median. 

Steps to Find Median:

Step 1: Put the numbers from the smallest to the largest in numerical order. 

Step 2:  Find the middle number if there is an odd number of observations, so that there is an equal number of left and right numbers. If there is an even number of observations, find the two middle numbers, such that the left and right of these two numbers have an equal number of values. 

Step 3: The middle number is the median if there is an odd number of numbers. Add the two intermediates and divide by 2 if there is an even number of numbers. The median would be the result.

Median of Numbers Formula: 

The median formula for even and odd numbers of observations is different. Therefore, if we have an odd number of values or even a number of values in a given data set, it needs to be recognized first.

a. Median of Odd Numbers Formula

If the total number of observations given is odd, then the median formula is as follows:

Median = {(n+1)/2}th term

Here, n will be the number of observations

b. Median of Even Numbers Formula

If the total number of observations is even, the median formula is as follows:

Median  = [(n/2)th term + {(n/2)+1}th term]/2

Here, n will be the number of observations

Let’s look at a few solved examples to find the median of a set of numbers

Example 1:

Find the median of three numbers i.e., 15, 50, and 85.

Ans: Let’s first keep them in order: 15, 50, 85

Here, the middle number is 50. So, clearly, the median is 50.

Example 2:

Find the median of stream of numbers of the following:

4, 15, 71, 26, 23, 24, 93, 81, 88.

Ans: Let’s first keep them in order: 4,15,23,24,26,71,81,88,93

Here, there are 9 numbers and our middle is the fifth number.

Hence, 26 is in 5th place and it’ll be the median of the data.

Where to Use Median: 

• The median and the mean difference in a number of ways. In certain cases, the mean is a better measure, since many of the statistical studies will use the mean and standard deviation of two observations to compare them, although the medians can not be used to make the same comparison. 

• Median is more useful, if the variance is not important, we just need a central measure of the values. If the maximum value of a number set changes when the other numbers of that number set remain the same, the mean of that number set changes, but the median does not change.

• Another benefit of the median is that when we analyze survival results, it can be measured sooner. For example, when half of the patients involved in the study die, a researcher can measure the median of survival of patients with a kidney transplant.  Calculating a mean of survival requires continuity of the study and follow up of all the patients till their death.