Concept 13.3
Median of Grouped Data
Source: NCERT Mathematics, Class 1012 minute lesson
Formal statement
Find the cumulative frequencies and n/2. The median class is the first class whose cumulative frequency is greater than n/2. Median = l + ((n/2 − cf) / f) × h, where cf is the cumulative frequency of the class before the median class.
The intuition
The median is the middle value when everything is lined up. With n = 40 values, it's around the 20th. The running totals, the cumulative frequencies, tell you which class the 20th value falls in.
The middle row of the table is irrelevant. A class can sit in the middle of the list and contain hardly anyone.
The attention
Look at the running totals: find where they pass n/2.
n = 40, n/2 = 20. Running totals: 10, 22, 27, 35, 40. The middle row: class 3
Look hereNot here
- Look here
- The first running total above n/2. 22 is the first running total above 20, so the 20th value sits in the second class. That's the median class.
- Not here
- The middle row of the table. The middle row is a position on the page, not in the data. Class 3 holds only 5 values.
- What it teaches
- The middle of a list of categories isn't the middle of the data inside them.