How to Find the Median Class in Grouped Data (Statistics)

In Class 10 Mathematics (Statistics), when you are given a massive grouped frequency table (like 0-10, 10-20, 20-30), you cannot simply pick the middle number to find the Median. The very first, highly crucial step before applying the massive median formula is locating the exact 'Median Class'. Here is the simple step-by-step method.

Question (Click to Flip)

What if my N/2 value is exactly equal to a number in the CF column?

Answer

If $N/2 = 25$ and you have exactly '25' in your CF column, you do not pick 25. You must still look for the CF value that is just strictly greater than 25 (e.g., 26 or 30) to identify the true Median Class.

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Key Facts

Once you find the Median Class, you can easily find 'l' (the lower limit of the median class) and 'h' (the class size or height) to plug into the final massive Median formula.

The Median physically represents the exact mathematical 50th percentile of your massive data set.

Step 1: Create the Cumulative Frequency (CF) Column

A normal question paper will give you two columns: 'Class Interval' and 'Frequency (f)'.
You must create a third column called Cumulative Frequency (CF).
To find the CF, simply keep adding the frequencies diagonally.
Example: If frequencies are 4, 5, and 2. The CF column will be: 4, then (4+5)=9, then (9+2)=11.

Step 2: Find the Total Frequency (N)

Add up all the numbers in the basic Frequency (f) column to find the total sum.
This total sum is denoted by the capital letter N.
(Hint: The very last number at the bottom of your new CF column will always be exactly equal to N)..

Step 3: Calculate N/2

Simply take your total frequency (N) and divide it by exactly 2.
Formula: $N \div 2$
Example: If total frequency $N = 50$, then $N/2 = 25$.

Step 4: Locate the Median Class

Look at your Cumulative Frequency (CF) column.
Find the CF value that is just strictly greater than your N/2 value.
The Class Interval that sits directly next to this specific CF value is your official Median Class.
Example: If N/2 is 25. And your CF column has numbers 12, 22, 35, 48. The number just greater than 25 is 35. If '35' belongs to the row '20-30', then 20-30 is your Median Class.

Questions and Answers

What if my N/2 value is exactly equal to a number in the CF column?+

If $N/2 = 25$ and you have exactly '25' in your CF column, you do not pick 25. You must still look for the CF value that is *just strictly greater* than 25 (e.g., 26 or 30) to identify the true Median Class.

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