Q.Following table gives the marks obtained by 100 students in statistics subject. Marks : 20 10 50 40 30
No. of students : 10 5 25 20 40 Find the average and median marks of students. Or Compute mean deviation from mean of the following data : Marks : 0–10 10–20 20–30 30–40 40–50
No. of students : 5 10 20 5 10

Arithmetic Mean in Economics — A First Look

You already use the arithmetic mean every day without thinking about it. If your marks in five tests are 72, 85, 68, 91, and 79, and someone asks "what did you average?", you add them up and divide by 5. That's the arithmetic mean. In economics, we do exactly the same thing — but with data that matters for the whole economy.

The Intuition

Imagine a small village with 10 households. Their monthly incomes (in ₹) are: 5000, 6000, 7000, 8000, 9000, 10000, 11000, 12000, 13000, 14000. If you had to pick one number that represents the "typical" income in that village, what would it be? You'd add all ten incomes and divide by 10. That single number — ₹9500 — is the arithmetic mean. It's the value you'd get if every household had exactly the same income.

The arithmetic mean answers the question: "If we redistributed the total equally among all units, what would each one get?"

The Precise Meaning

The arithmetic mean (often just called the mean or average) of a set of $n$ observations is the sum of all observations divided by $n$.

Where:

• $\bar{X}$ (read "X-bar") = the arithmetic mean
• $X_i$ = each individual observation (the $i$-th value)
• $\sum$ (sigma) = "sum of"
• $n$ = total number of observations

For grouped data (where values are arranged in a frequency distribution), the formula becomes:

Where:

• $f_i$ = frequency of the $i$-th class or value
• $X_i$ = the midpoint of the $i$-th class (for continuous data) or the actual value (for discrete data)
• $N = \sum f_i$ = total frequency (total number of observations)

Why It Matters in Economics

Economics deals with aggregates — total income, total consumption, total output. But a single total tells you nothing about the typical experience. The arithmetic mean lets you compare across groups, across time, and across countries.

Consider: India's per capita income is the arithmetic mean of all individual incomes. If the mean rises from one year to the next, it suggests the average person is better off. But here's the catch — and this is crucial for an economics student — the mean is sensitive to extreme values. If one billionaire moves into that village of 10 households, the mean income jumps dramatically, even though 9 out of 10 families saw no change. That's why economists also use the median (the middle value) alongside the mean.

A Worked Example (Discrete Data)

A shopkeeper records daily sales (in ₹) for a week: 1200, 1500, 1100, 1800, 1300, 1600, 1400.

The mean daily sale is ₹1414.29.

A Worked Example (Continuous Data)

Consider the following distribution of monthly wages of 50 workers:

The mean monthly wage is ₹3160. …