Median Calculation in Economics
You already know the median from everyday life. When your teacher says "half the class scored above 70% and half below," that 70% is the median. It's the middle point — the value that splits a group into two equal halves. In economics, this simple idea becomes a powerful tool for understanding income, wages, prices, and inequality.
The Intuition: Why Not Just Average?
Imagine five villages with annual incomes (in ₹ lakhs): 2, 3, 4, 5, 100. The average (mean) is ₹22.8 lakhs. Does that sound like a typical village? No — one rich village pulls the average up. The median, however, is the middle value when you arrange them in order: 2, 3, 4, 5, 100. The median is ₹4 lakhs. That tells you what a "typical" village actually earns. Half the villages earn less than ₹4 lakhs, half earn more.
This is why economists prefer the median for income, housing prices, and consumption data — it resists distortion by extreme values.
The Precise Definition
The median is the value that divides a data set into two equal halves when arranged in ascending or descending order.
For ungrouped data (raw numbers), the process is:
- Arrange all values in ascending order.
- Find the middle position: if there are n values, the median is the 2n+1th value when n is odd. When n is even, the median is the average of the 2nth and 2n+1th values.
Median=Value of (2n+1)th item (for odd n)
Median=2Value of 2nth item+Value of (2n+1)th item (for even n)
For Grouped Data (Frequency Distribution)
In economics, you rarely get raw numbers. You get data grouped into classes — like "income between ₹10,000–₹20,000: 50 families." Here, the median lies inside a class interval. The formula becomes:
Median=L+f2N−cf×h
Where:
- L = lower limit of the median class (the class where the cumulative frequency crosses 2N)
- N = total frequency (sum of all frequencies)
- cf = cumulative frequency of the class before the median class
- f = frequency of the median class
- h = class width (size of the interval)
Step-by-Step Example
Suppose you have this income data for 100 households:
| Income (₹) | Number of households |
|---|
| 0–5000 | 10 |
| 5000–10000 | 20 |
| 10000–15000 | 30 |
| 15000–20000 | 25 |
| 20000–25000 | 15 |
Step 1: Find N/2=100/2=50.
Step 2: Build cumulative frequencies: 10, 30, 60, 85, 100. The 50th household lies in the class 10000–15000 (since cumulative frequency 30 is below 50, and 60 crosses it). This is the median class.
Step 3: Identify values: …