[Maths Class Notes] on How To Find Median? Pdf for Exam

The middle value of a set of numbers is called the median. It is an integral concept in analysing 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.

 

What is Median?

The Median represents one of the three important measures of central tendency of grouped or ungrouped data. These three most commonly used central tendency is known as Mean (Arithmetic mean), Median and Mode. In order to describe a set of data, the central position of the data set is identified which is just known as the measurement of central tendency. 

 

In an ascending or descending ordered series, Median is the positionally centre most value of a provided set of data (either grouped or ungrouped) or The median can be also be defined as the value present at the midpoint of a given set of data, not the midpoint of the values itself. It is the point from where half of the data entry is more and half of the data entry is less. For the calculation of the median, all the data is first written in ascending or descending order and then the centre most data point is identified and that will be our median.

How to find the Median of Ungrouped Data?

How to Find the Median with ODD Number of observations?

The formula of the median for a given set of numbers, having the odd number of observations can be expressed as such 

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

Let us understand with an Example

The age of seven participants of a golf tournament has been listed below. Find the median of this given set. {44, 39, 51, 63, 36, 57, 31}

Ordered set of data : {31, 36, 39, 44, 51, 57, 63}

As the count of all the observations is seven, i.e. n = 7

By the formula of Median = [(n+1)/2]th term

Median = [(7+1)/2] = 4th term = 44, hence the median is 44.

 

How to find the Median with an Even Number of Observations?

The formula of the median for a given set of numbers, having the even numbers of observations can be expressed as such 

Median = [n/2]th term

Let us understand with an example

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

 = 10

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

 

How to find the Median in Maths 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,

 

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]

[(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

      = 42.50

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

Answer: To find the solution:

 

n = 50

Median Class = n/2th value

= (50/2)th value

            = 25th value

            = 20 – 30

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

Median = L+

(n/2)−C

[(n/2)−C / F ]*W

= 30.6.