Posted by Anjali Kaur on Jul 22, 2021

Median Under Less Than Cumulative Frequency Distribution

Median is the mid-value of any given series. To find median under less than cumulative frequency distribution, when continuous series is given to us. We need to correct the class intervals and find the frequencies related to that class interval.

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How to find median in case of less than cumulative frequency distribution?

The following steps are to be applied to find the median:

1. Re-write the given table by creating Class intervals.
2. Given the number of students is cumulative frequency. Find frequency by doing subtraction, but keeping the first frequency and cumulative frequency as same.
3. For frequency calculation; Present CF – Previous CF
4. Find the median class using N/2, where N is the sum of frequency. Locate the number obtained in the cumulative frequency and select the next number available in CF. Bold this, it is median class.
5. Apply the median formula.

Calculate median of the following series:

Marks	Number of Students
Less than 10	12
Less than 20	26
Less than 30	40
Less than 40	58
Less than 50	80
Less than 60	110
Less than 70	138
Less than 80	150

Step 1: Re-write the given table by creating Class intervals.

Marks	Number of Students
0 – 10	12
10 – 20	26
20 – 30	40
30 – 40	58
40 – 50	80
50 – 60	110
60 – 70	138
70 – 80	150

Step 2: Given the number of students is cumulative frequency. Find frequency by doing subtraction, but keeping the first frequency and cumulative frequency as same.

Marks	Cumulative Frequency	Frequency
0 – 10	12	12
10 – 20	26	26-12 = 14
20 – 30	40	40-26 = 14
30 – 40	58	58-40 = 18
40 – 50	80	80-58 = 22
50 – 60	110	110-80 = 30
60 – 70	138	138-110 = 28
70 – 80	150	150-138 = 12
		Sum of Frequency = 150

Step 3: Find the median class using N/2

Where N is the sum of frequency. Median Class = 150/2 = 75.

Locate 75 (N/2) in cumulative frequency and pick the next number available in cf after 75.

Marks	Cumulative Frequency	Frequency
0 – 10	12	12
10 – 20	26	14
20 – 30	40	14
30 – 40	58*	18
40 – 50*	80	22*
50 – 60	110	30
60 – 70	138	28
70 – 80	150	12
		Sum of Frequency = 150

Median = Lower limit of the median class + {(N/2) – Previous CF} * Class Interval/ Existing frequency

Median = 40 + {(75 – 58) * 10}/ 22

Median = 40 + 170/22

Median = 40 + 7.727

Median = 47.727 or 47.73 (Approx)

I hope it was helpful, you can refer to more posts related to the statistics.

1. Individual Series Arithmetic Mean
2. Discrete Series Arithmetic Mean
3. Continuous Series Arithmetic Mean
4. Inclusive and Exclusive Series – Arithmetic mean
5. Introduction to the statistics.
6. Functions and importance of statistics.
7. Calculating Correct Arithmetic mean

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