Mean, Median and Mode
Quick Summary
Mean = Average of all numbers.
Median = Middle number when sorted.
Mode = Most frequently occurring number.
How to Find the Median for Ranges (Grouped Data)
When given grouped data (data in ranges or intervals), we estimate the median using a formula rather than finding the exact middle number.
Steps to Find the Median for Grouped Data (Ranges):
1) Find the Cumulative Frequency (CF) for each class interval.
2) Find the Median Class:
- Use N/2 to locate the median position (N = total frequency).
- The median class is the group where this position falls.
3) Use the Median Formula:
Where:
- L = Lower boundary of the median class
- N = Total frequency
- CF = Cumulative frequency before the median class
- f = Frequency of the median class
- h = Class width (difference between upper and lower boundaries)
Example: Find the Median for Grouped Data
Data Table
| Class Interval | Frequency (f) | Cumulative Frequency (CF) |
|---|---|---|
| 0 – 10 | 4 | 4 |
| 10 – 20 | 6 | 10 |
| 20 – 30 | 10 | 20 |
| 30 – 40 | 8 | 28 |
| 40 – 50 | 5 | 33 |
Step 1: Find N/2
Total frequency N = 33, so:
N/2=33/2=16.5
The median class is the class where CF just exceeds 16.5, which is 20 – 30.
Step 2: Apply the Formula
- L = 20 (Lower boundary of median class)
- CF = 10 (Cumulative frequency before median class)
- f = 10 (Frequency of median class)
- h = 10 (Class width)
Median ≈ 26.5
