Finding the Range of a Data Set

When you're looking at a set of numbers, two different questions are worth asking. First: what's a typical value? That's what the mean, median, and mode are for. Second: how spread out are the numbers? That's where the range comes in.

How to Find the Range

The range is the simplest measure of spread there is:

$$\text{range} = \text{maximum} - \text{minimum}$$

Find the biggest number, find the smallest number, subtract. Done.

Example: Find the range of 12, 7, 24, 5, 19.

The largest value is 24. The smallest is 5.

$$\text{range} = 24 - 5 = 19$$

Example: A teacher records these test scores: 88, 95, 72, 91, 84, 78. What's the range?

Biggest score is 95, smallest is 72.

$$\text{range} = 95 - 72 = 23$$

So the scores were spread across a 23-point window. That's a pretty useful thing to know — it tells you right away whether students were all performing similarly or all over the map.

Small Range vs. Large Range

A small range means everyone's bunched together. A large range means the values are scattered. Compare these two classes on the same test:

  • Class A scores: 78, 80, 82, 79, 81 → range = \(82 - 78 = 4\)
  • Class B scores: 55, 70, 82, 91, 97 → range = \(97 - 55 = 42\)

Those two classes might actually have similar averages, but Class A is remarkably consistent while Class B is all over the place. One number — the range — captures that whole story.

Watch Out for Outliers

Here's the thing about range: it only pays attention to two values, the very top and the very bottom. Everything in the middle gets completely ignored. That makes it vulnerable to outliers — values that are unusually far from the rest of the data.

Say seven students ran a mile and here are their times (in minutes): 7, 8, 8, 9, 9, 10, 24.

The range is \(24 - 7 = 17\) minutes. But look at that 24 — that's way out there. Maybe that student stopped to chat with a friend. The other six all finished between 7 and 10 minutes, which is a range of just 3.

One unusual value turned a tight range of 3 into a sprawling range of 17. If someone just told you "the range was 17 minutes," you'd picture a wildly inconsistent group — but that's not really what happened.

This is why the range is great for a quick first look at data, but it can mislead you when outliers are involved. More advanced measures of spread (like standard deviation) handle this better, but range is still worth knowing and easy to calculate.

Negative Numbers

The same formula works with negatives — just be careful with the subtraction.

Example: Find the range of: −8, 3, −1, 7, −4

Largest value: 7. Smallest value: −8.

$$\text{range} = 7 - (-8) = 7 + 8 = 15$$

Subtracting a negative is the same as adding, so don't let the signs trip you up.

Give These a Shot

  1. Find the range: 14, 6, 23, 9, 17 Show answer17 — \(23 - 6 = 17\)

  2. Find the range of these test scores: 100, 85, 92, 78, 96, 88 Show answer22 — \(100 - 78 = 22\)

  3. Find the range: −5, 2, −11, 8, 0 Show answer19 — \(8 - (-11) = 19\)

  4. A data set has a range of 30 and a minimum value of 15. What is the maximum? Show answer45 — range = max − min, so \(30 = \text{max} - 15\), which gives max = 45

  5. Two data sets each have 5 values. Set A has a range of 4. Set B has a range of 40. What does that tell you about the two sets? Show answerSet A's values are clustered close together; Set B's are much more spread out. The range doesn't tell you the actual values or the average — just how wide the spread is from end to end.

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