Median class

The median is the middle value once the data is in order. For grouped data, add up the frequencies to get n, and work out n/2. Then build the cumulative frequencies. The median class is the first class whose cumulative frequency is greater than n/2.

• Median = l + ((n/2 − cf) ÷ f) × h.
• l is the lower limit of the median class, f is its frequency and h is the class size.
• cf is the cumulative frequency of the class just before it.

A small example

Classes 0-10, 10-20 and 20-30 have frequencies 5, 10 and 5. So n = 20 and n/2 = 10. The cumulative frequencies are 5, 15 and 20. The first to reach 10 is 15, so the median class is 10-20. The median is 10 + ((10 − 5) ÷ 10) × 10 = 15.

Where marks go

Question 38(ii) of CBSE's 2026-27 Maths Standard sample paper asks for the class containing the median. It is worth 1 mark. The 2026-27 Maths Standard marking scheme shows a cumulative frequency column, then n/2 = 25, then the median class 30-40.

In the same question, the most common class is also 30-40. The two answers match only by chance. The median class comes from n/2, and the modal class comes from the largest frequency. Showing the n/2 line makes the method clear to the examiner. See how step marking works.

About the author

Mohit Sardana

Chief Architect

An engineer (B.Tech, Computer Science) with over 20 years of preparing students for entrance exams, including as Dean at FIITJEE and Vice-President at Aakash. He is the chief architect of the TRUpreBoards evaluation engine.

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