Q.Find the range of the marks obtained by 12 students in a unit test: $45, 52, 38, 61, 47, 55, 42, 58, 33, 49, 63, 40$.

Range: The Simplest Measure of Spread

When you first look at a set of numbers, the most natural question is: how far apart are they? Not the average, not the middle value — just the sheer distance from the smallest to the largest. That distance is the range.

The Intuition

Imagine you and your friends are comparing heights. The shortest person is 150 cm, the tallest is 185 cm. Without doing any calculation, you can see that the heights span 35 cm. That span — the gap between the extremes — is the range. It tells you, in one number, the total spread of the data.

If the range is small, the data is tightly clustered. If it's large, the data is spread out. That's all.

The Precise Definition

That's it. No division, no squaring, no complicated formula. You find the largest number in your data set, subtract the smallest number, and you have the range.

A Worked Example

Consider the marks of 10 students in a test:

$45, 67, 72, 38, 91, 55, 83, 60, 49, 78$

1. Find the maximum: $91$
2. Find the minimum: $38$
3. Subtract: $91 - 38 = 53$

So the range is $53$ marks. The scores are spread across a 53-mark interval.

What the Range Tells You (and What It Doesn't)

The range is useful because it's fast and intuitive. In one glance, you know the total spread of the data. But it has a serious limitation: it depends only on the two extreme values. The middle 80% of the data could be packed tightly or spread out — the range won't show that.

When to Use It

Use the range when you need a quick, rough sense of spread — for example, checking daily temperature extremes, or comparing the spread of two small data sets. For deeper analysis, you'll later learn about quartiles, variance, and standard deviation, which are more robust. But the range is where every student starts, and it's perfectly fine for that purpose.