# How To Find Median?

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## How To Find The Median

The middle value of a set of numbers is called the median. It is an integral concept in analyzing statistical data. The calculation of the median value varies for an odd or even number of values. First of all, the list of numbers needs to be arranged in the order in an ascending sequence or a descending sequence. If there is an odd list of numbers, the midpoint of the list is the median. However, in the case of an even count of numbers, the two numbers in the middle of the list are considered. The process of calculating the median is a little complex. The examples will help the student to understand better.

### How to Find the Median with Even Numbers

Suppose the set has an even count of numbers for example, 8,1, 3, 5, 22,17,12,13. It is a set of 8 numbers. The list when sorted in ascending order 1, 3, 5, 8, 12, 13, 17, 22.

8 and 12 are the two middle numbers here.

Therefore, adding 8 and 12 and dividing the result by 2 = (8 + 12) / 2

Â = 10

Here, 10 is the median of the given list of numbers. 84 199.

### How to Find the Median in Math for Grouped Frequencies?

When we have grouped data, calculating the median becomes a little more complicated. Students must be careful during this calculation. Here we consider the following grouped data table for a set of balls,

 Balls 51-55 56-60 61-65 66-70 Frequency 2 7 8 4

Here, we find out the class interval that has the maximum frequency, 61 - 65.

Now, we need to find the midpoint of this interval. Using the formula,

Estimated Median = L+[ [( n/2 ) - C] / F ]*W

Where,

L is the lower class boundary of the group that contains the median.

n is the total number of values in the interval.

B is the cumulative frequency of all the groups before the median group.

F is the frequency of the group containing the median.

W is the width of each group.

### Solved Examples

1. How to find the median of the following set = {11, 22, 33, 55, 66, 99}

Answer: The given set {11, 22, 33, 55, 66, 99} is in ascending order.

The number of terms contained in the given list = 6 terms

Thus, the set contains an even number of elements.

The middle two terms of the list are 33 and 55.

Hence, the median of the set of numbers is = (33 + 55)/2

Â Â Â Â Â Â = 42.50

2. How to find the median of the marks scored by the students in an exam, as given below,

 MarksÂ 0-10 10-20 20-30 30-40 40-50 50-60 Number of Students 2 7 15 10 11 5

 MarksÂ 0-10 10-20 20-30 30-40 40-50 50-60 Number of Students 2 7 15 10 11 5 Cumulative Frequency (C) 2 9 24 34 45 50

n = 50

Median Class = n/2th value

= (50/2)th value

Â Â Â Â Â Â Â Â Â Â Â Â = 25th value

Â Â Â Â Â Â Â Â Â Â Â Â = 20 - 30

L = 20, n/2 = 25, C = 9, F = 15, W = 10

Median = L+[ [( n/2 ) - C] / F ]*W

= 30.6.