Q.Find out the arithmetic mean of the following distribution : Items 0-2, 2-4, 4-6, 6-8, 8-10; Frequency 2, 4, 6, 8, 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 subjects 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 country.

The Intuition

Imagine you want to know the "typical" monthly rent in your city. You can't ask every single tenant, so you collect rents from a sample of 10 households. Some pay ₹8,000, some pay ₹15,000, one pays ₹25,000. The arithmetic mean gives you a single number that "balances" all these values — if every household paid the mean rent, the total rent collected would be exactly the same as what is actually paid.

That's the core idea: the mean is the value that, if repeated for every observation, would give the same total.

The Formula

Where:

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

For grouped data (when data is in class intervals with frequencies), the formula becomes:

Where $f_i$ is the frequency of the $i$-th class and $X_i$ is the midpoint of that class.

Why It Matters in Economics

Economics deals with aggregates — total income, total consumption, total output. The arithmetic mean lets us compare these across time or across groups.

Example — Per Capita Income: When you hear "India's per capita income is ₹1,70,000", that's an arithmetic mean. The government adds up the National Income (all the money earned in a year) and divides by the population. This single number lets you compare living standards across countries or across years.

Example — Average Price: If the price of wheat rises from ₹20/kg to ₹30/kg and rice from ₹30/kg to ₹40/kg, the arithmetic mean of the two price changes tells you the "average" price rise — but only if both goods are equally important. That's where weighted means come in, but that's for later.

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