Q.Calculate the value of the lower quartile from the data of the marks obtained by ten students in an examination: 22, 26, 14, 30, 18, 11, 35, 41, 12, 32.

Median Calculation in Economics

You already know the median from everyday life. When your teacher says "half the class scored above 65 and half below," that 65 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 inequality, income distribution, and policy impact.

The Intuition First

Imagine five people in a room. Their monthly incomes (in ₹) are: 10,000, 12,000, 15,000, 18,000, and 2,00,000. The average (mean) income is ₹51,000. But does that number represent anyone in the room? Not really — four people earn far less, and one earns far more. The mean is pulled upward by that one high income.

Now find the median. Arrange the incomes in ascending order: 10,000, 12,000, 15,000, 18,000, 2,00,000. The middle value is ₹15,000. That's the income of the third person — the one exactly in the middle. Half the people earn less than ₹15,000, half earn more. This number tells you what a "typical" person in that room actually earns, without being distorted by the extreme outlier.

The Precise Definition

For a set of $n$ observations arranged in ascending order, the median is the value of the middle observation.

If $n$ is odd: The median is the $\left(\frac{n+1}{2}\right)^{\text{th}}$ observation.

If $n$ is even: The median is the average of the $\left(\frac{n}{2}\right)^{\text{th}}$ and $\left(\frac{n}{2}+1\right)^{\text{th}}$ observations.

Where $x_i$ denotes the $i^{\text{th}}$ observation when the data is sorted in ascending order.

Why Economics Uses the Median

Economics deals with distributions that are almost always skewed — income, wealth, land holdings, consumption expenditure. A handful of people at the top earn vastly more than the rest. The mean gets pulled toward that tail and stops being representative. The median stays anchored where most people actually are.

When the government reports "median household income," it's telling you what the middle household earns. When you hear "the median wage in this sector is ₹25,000," it means half the workers earn less and half earn more. This is far more useful for policy than the average wage, which could be ₹40,000 simply because a few executives earn crores.

The Median in Grouped Data

In real economic data, you rarely have individual incomes — you have frequency distributions like "number of households earning between ₹10,000 and ₹20,000." For grouped data, the median is found using interpolation.

Where:

• $L$ = lower limit of the median class (the class where the cumulative frequency crosses $N/2$)
• $N$ = total frequency
• $cf$ = cumulative frequency of the class preceding the median class
• $f$ = frequency of the median class
• $h$ = class width

The logic is simple: you locate the class that contains the middle observation, then proportionally move within that class to find the exact median value.

A Worked Example

Consider the distribution of monthly incomes for 100 workers:

Step 1: Find $N/2 = 100/2 = 50$. …