Q.The following series shows the daily pocket expenses of 7 boarders in a school boarding at Imphal : Rs. 40, Rs.25, Rs.50, Rs.30, Rs.38, Rs.45, Rs.24. Find the range.

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, say, 100 households. Some pay ₹8,000, some pay ₹25,000. The arithmetic mean gives you a single number that represents the whole group: if every household paid exactly the same rent, that common rent would be the mean.

The Formula

For a set of $n$ values $x_1, x_2, x_3, \dots, x_n$, the arithmetic mean $\bar{x}$ (read as "x-bar") is:

Where:

• $\bar{x}$ = arithmetic mean
• $x_i$ = each individual observation
• $\sum$ (sigma) = "sum of"
• $n$ = number of observations

For grouped data (when data is already in frequency tables), the formula becomes:

Where $f_i$ is the frequency of each value $x_i$, and $\sum f_i = N$ (total number of observations).

Why It Matters in Economics

Economics deals with aggregates — national income, average price levels, average wages, per capita consumption. The arithmetic mean lets us compress thousands or millions of individual numbers into one meaningful figure.

Example — Average Income: If a village has 5 families earning ₹2,000, ₹3,000, ₹4,000, ₹5,000, and ₹1,00,000 per month, the arithmetic mean is:

This ₹22,800 is the "average" income — but notice that four families earn far less than this. The single very high income pulls the mean upward. This is a critical limitation.

How It's Used in Your Syllabus

In Class 11 Statistics for Economics, you'll calculate the arithmetic mean for: …