Q.Why is standard deviation known as root mean square deviation ?

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" income in a village of 10 families. You could list all 10 incomes, but that's too much information. You want one number that represents the whole group. The arithmetic mean gives you that: it's the income each family would have if the total income were shared equally.

The Formula

The arithmetic mean of a set of $n$ observations is:

Where:

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

For grouped data (when data is arranged in a frequency distribution), 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

The arithmetic mean is the backbone of many economic indicators you'll study:

Per capita income — the most famous example. If India's national income is ₹295 lakh crore and the population is 140 crore, the arithmetic mean gives you per capita income:

Average price level — when you study inflation, the Consumer Price Index (CPI) is essentially a weighted arithmetic mean of prices of thousands of goods.

Average product — in production theory, Average Product of Labour is total output divided by number of workers. Same formula, different context.

How to Calculate It — Step by Step

For ungrouped data (say, prices of 5 commodities: ₹10, ₹15, ₹20, ₹25, ₹30):

1. Add: $10 + 15 + 20 + 25 + 30 = 100$
2. Count: $n = 5$
3. Divide: $\bar{X} = \frac{100}{5} = ₹20$

For grouped data (say, monthly savings of 100 households):