Median of grouped data
The median of grouped data is the middle value that divides the frequency distribution into two equal parts.
In one line: Median means the middle position, not the biggest frequency.
Practice This ConceptUnderstand it
For grouped data, we first find the median class using cumulative frequency. Then we apply the median formula with lower boundary, total frequency, cumulative frequency before the median class, and class width. This gives the central value of the distribution.
Example
Formula and rule
Median = l + [(N/2 - cf) / f] x h, where l is lower boundary, cf is cumulative frequency before median class, f is frequency of median class, and h is class width.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
If N = 40, N/2 = 20.
- 1Suppose cumulative frequencies are 5, 13, 22, 30.
- 2The median class is the class where cumulative frequency first crosses 20, that is the third class.
- 3If l = 20, cf = 13, f = 9, and h = 10, then median = 20 + [(20 - 13)/9] x 10 = 27.78.
Method you can reuse
- 1Find total frequency N.
- 2Compute N/2.
- 3Locate the median class using cumulative frequency.
- 4Note l, cf, f, and h.
- 5Substitute into the median formula.
Sketch it in your answer
Use a cumulative frequency table to mark N/2 and identify the median class clearly.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
How do you identify the median class in grouped data?
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Common wrong answer
A common wrong answer is to use the modal class or the largest frequency class instead of the median class.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
The median of grouped data is the middle value that divides the frequency distribution into two equal parts.
- 2
Add for 2 marks
Example: If the total frequency is 50, the median is located around the 25th observation and then calculated using the median class.
- 3
Add for 3 marks
For grouped data, we first find the median class using cumulative frequency.
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