Averages

Story hook

Imagine it is Sunday and three friends — Riya, Aman and Sara — empty their pockets to buy a shared bag of chips. Riya has 10 rupees, Aman has 20 rupees, and Sara has 30 rupees.

Riya frowns. "It's not fair — Sara has more, I have less. How much does each of us really have if we just shared it all equally?"

So they pile all the money in the middle. Together it is 10 + 20 + 30 = 60 rupees. They split it three ways: 60 ÷ 3 = 20 rupees each.

That number — 20 — is the average. It is the fair, "even-out" amount each friend would have if the total were shared equally. Notice something nice: it sits in the middle — bigger than Riya's 10, smaller than Sara's 30. That is why an average is often called the middle value or the mean.

In this lesson we will learn exactly how to find an average, how to hunt for a missing number when the average is known, how to mix two groups together, and what happens when one new person joins or leaves the group. By the end you will read a cricketer's "batting average" and your own "average marks" and know exactly what they mean. Let's begin from zero.

Why this matters for UPSC

For your CSAT exam (UPSC Prelims Paper II):

• CSAT is a qualifying paper. You do not need a top score — you only need 33% (that is 66 marks out of 200) to pass. Averages is one of the simplest and most predictable topics, so it is a safe, quick place to grab those qualifying marks.
• The whole topic rests on one tiny formula. Once you know it, most questions are just "add up and divide" — among the fastest sums in the whole paper. Averages also hide inside data-interpretation charts and statistics questions, so learning it once helps in several places.

For real life (this is the fun part):

• Your report card says "average marks: 72". Now you will know exactly how that single number was made.
• A cricket commentator says "his batting average is 50." You will understand what that tells you about the batsman.
• Tracking your monthly pocket money spending ("I spend about 150 rupees a week on average") helps you plan and save.
• Knowing the average temperature, average rainfall, or average travel time helps you decide what to wear, carry, or when to leave.

So this is not just an exam topic — it is the everyday habit of turning a messy list of numbers into one fair number you can actually use. Stay relaxed; it begins as simply as sharing pocket money.