Q.Find out median and mode : Mid Value 1, 2, 3, 4, 5, 6, 7; Frequency 3, 10, 12, 20, 12, 10, 3.

Median Calculation in Economics

You already know the median from everyday life. If five friends earn ₹10, ₹15, ₹20, ₹25, and ₹100 per hour, the "middle" earner gets ₹20. That's the median. The average (mean) would be ₹34, which is pulled up by the one high earner and doesn't represent the group well. The median tells you what a typical person earns, not what the total divided equally gives.

The Precise Meaning

The median is the value that splits a sorted dataset into two equal halves. Half the observations lie below it, half above. For ungrouped data, you arrange all values in ascending order. If the number of observations ($n$) is odd, the median is the $\frac{n+1}{2}$th value. If $n$ is even, the median is the average of the $\frac{n}{2}$th and $\frac{n}{2}+1$th values.

For grouped data (like "income between ₹10,000–₹20,000: 50 people"), you cannot see individual values. You need a formula.

Why This Formula Works

Imagine a histogram of incomes. The total area under the bars represents all $N$ people. You want the vertical line that splits this area exactly in half. The median class is the bar that contains this halfway point. $L$ is where that bar starts. $\frac{N}{2} - cf$ tells you how many more people you need to count within this bar to reach the halfway mark. Dividing by $f$ gives the fraction of the bar's width you must go, and multiplying by $h$ converts that fraction into actual units of income.

Why It Matters in Economics

The median is crucial because income and wealth distributions are almost always skewed — a few people earn a lot, most earn less. The mean gets distorted by the very rich. When you read "the median household income in India is ₹X," that figure tells you what the person exactly in the middle earns. It is a better measure of the typical economic condition than the average.

A Worked Example (Grouped Data)

Consider this income distribution: