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

 = 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.


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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,


Marks 

0-10

10-20

20-30

30-40

40-50

50-60

Number of Students

2

7

15

10

11

5


Answer: To find the solution:


Marks 

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

            = 25th value

            = 20 - 30

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

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

= 30.6.

FAQ (Frequently Asked Questions)

Q1. What is the Practical Application of the Median?

Ans: Most students know how to find out median but need to understand its necessity in the real world. Around us, we can find information which when collected into certain data sets, can be analyzed mathematically. Statistics formulates several basic techniques like mean, median, and mode to compare and contrast the data sets. For example, comparing the growth rate of two companies by analysis of the profits made by it in multiple years. Median is such a tool that measures the average of a group of data. Median refers to a point in the large group of data, where fifty percent of the data is above the median and fifty percent is below that value.

Q2. Is Median and Average the Same?

Answer: Median and average can sometimes be related, as the average is most commonly understood. However, the median is the middle value in a large set of data. A data set can have an equal number of values or repetitive numbers. This entire set needs to be first arranged from its lowest value to its highest value. From this, if we find that the majority of the data elements are clustered towards one extreme. Then merely finding the average or mean of the data does not give the middle point. In this case, the median needs to be found which is calculated depending on several factors of the set.