Finding Median from Grouped Data
An Interactive Mathematics Learning Tool
Mathematical Vocabulary
Median
The middle value in a dataset when arranged in ascending order.
Class Intervals
Ranges of values used to group data in a frequency distribution.
Frequency
The number of times a value or range of values occurs in the dataset.
Cumulative Frequency
The running total of frequencies up to a particular class interval.
Median Class
The class interval that contains the median value.
Class Width (h)
The difference between upper and lower boundaries of a class interval.
Problem Statement
Example: The median of the following data is 525. Find the values of x and y, if the total frequency is 100.
| Class Intervals | Frequency |
|---|---|
| 0 - 100 | 2 |
| 100 - 200 | 5 |
| 200 - 300 | x |
| 300 - 400 | 12 |
| 400 - 500 | 17 |
| 500 - 600 | 20 |
| 600 - 700 | y |
| 700 - 800 | 9 |
| 800 - 900 | 7 |
| 900 - 1000 | 4 |
Problem Analysis
What is Given?
- Median = 525
- Total frequency = 100
- Frequency distribution with unknowns x and y
What to Find?
- Value of x
- Value of y
How to Find?
- Use total frequency equation
- Apply median formula
- Solve simultaneous equations
Median Formula
$$Median = L + \frac{\frac{n}{2} - cf}{f} \times h$$
Where:
L = lower boundary of median class, n = total frequency,
cf = cumulative frequency before median class, f = frequency of median class, h = class width
Solution Steps
Final Answer
x = 9 and y = 15