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.

Check this out:-

Feel free to join our Facebook group.

A quick note: Subscribe to our website to get answers to your curriculum questions. You can also subscribe to our YouTube channel.

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:

MarksNumber of Students
Less than 1012
Less than 2026
Less than 3040
Less than 4058
Less than 5080
Less than 60110
Less than 70138
Less than 80150

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

MarksNumber of Students
0 – 1012
10 – 2026
20 – 3040
30 – 4058
40 – 5080
50 – 60110
60 – 70138
70 – 80150

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.

MarksCumulative FrequencyFrequency
0 – 101212
10 – 202626-12 = 14
20 – 304040-26 = 14
30 – 405858-40 = 18
40 – 508080-58 = 22
50 – 60110110-80 = 30
60 – 70138138-110 = 28
70 – 80150150-138 = 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.

MarksCumulative FrequencyFrequency
0 – 101212
10 – 202614
20 – 304014
30 – 4058*18
40 – 50*8022*
50 – 6011030
60 – 7013828
70 – 8015012
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

Thank You!

Feel free to join our Facebook group and subscribe to this website to get daily educational content in your mailbox.

Happy Learning!


Disclosure: Some of the links on the website are ads, meaning at no additional cost to you, I will earn a commission if you click through or make a purchase.

Learn with Anjali started because there wasn't an easy-to-consume resource to help students with their studies. Anjali is on single-minded mission to make you successful!

If you would like to suggest topics, leave feedback or share your story, please leave a message.

Leave a message