How to find Median: Overview, Questions, Preparation

A median is a number in the middle of a list or set of numbers. For example, if a set comprises 12, 13, 15, 17, 19, 23, and 41, its median will be the middle number, i.e., 17. 

Finding the Median

Follow this process to find the value of a median. 

Step 1: Sort the given list of numbers if it is not in order. For example, if a set contains numbers 4, 8, and 6, it is not in order. The correct order would be 4, 6, 8. 

Step 2: Once the list is sorted, find the middle number. For instance, if there are 9 numbers in the list, then the middle number would be the 5th one. 

Step 3: Sometimes, you will find two numbers in the middle. For example, list 3, 5, 7, 9, 11, 13, 15, 17 contains two middle numbers, viz. 9 and 11. In such cases, we add the middle numbers and divide the result by 2 to find the median.

The Formula for Finding the Median

When observations are even

Median = average of [(n/2)th term + {(n/2)+1}^th] value 

When observations are odd 

Median = {(n + 1) ÷ 2}^th value 

Median for Grouped Data 

To find the median of ungrouped data, we need different formulas and procedures. 

First, we need to create a table consisting of 3 columns for the interval of class, frequency, and the last column for the cumulative frequency.

Finally, you can use the below formula for computing median:

Median = l + [(n/2 - cf)/f] x h.

Here, l is the median class’s lower limit, n is the total number of observations obtained by adding all the frequencies, f is the median class’s frequency, and h is the size of each class.

The concept of the median is covered in detail in Class X in chapter Statistics, which has a weightage of 8 marks. You can easily score up to 4 marks in the exam if you know how to compute the median perfectly. 

1. Find the median of 12, 24, 14. 

Solution.

The correct order is 12, 14, 24, and the median is the middle value, i.e., 14.

Therefore, the median of the given set = 14. 

2. The below table shows the electric consumption in units and the number of houses consuming those units. Find the median of this data.

Now, let’s find the cumulative frequency for this given data: 

Here, N/2 = 50/2 = 25 

l = 50

h = 40 and f = 20

Median = l + [(n/2 - cf)/f] x h

Therefore, median = 50 + [(25 - 5)/20] x 40 = 90

3.Find the median of 3, 4, 6, 12. 

Solution.

The below formula gives the median of the ungrouped data for even observations:

Median = average of [(n/2)th term + {(n/2)+1}th] value.

Here, n/2 th term is 4 and n/2 + 1 term is 6 and the average of 4 and 6 is 4 + 6/2 = 5.

Therefore, median = 5.

Q: How to calculate the median of 6 observations?

Q: What is the difference between mean and median?

Q: State a real-life application of median?

Q: Who discovered the median?