What Is Range in Statistics? — STEMBridge Stats

🕐 6 min read | Class 9–12 | FBISE · CBSE · IGCSE · O-Levels · IB

You probably already use range in everyday language without realising it. When someone says "temperatures ranged from 18°C to 35°C this summer," they are describing the statistical range. It is the simplest measure of how spread out a set of data is — and for exactly that reason, it is taught first in every statistics curriculum. But simple does not mean always correct. This guide will show you exactly when range is a great tool, and when it can deceive you.

Definition and Formula

The range is the difference between the largest (maximum) and smallest (minimum) values in a data set.

Range = Maximum value − Minimum value

That is the entire formula. One subtraction. The result tells you how wide the data is spread from one extreme to the other.

Step-by-Step Examples

Example 1 — Simple Data Set

Data: 14, 3, 27, 9, 41, 6, 18

📋 Calculating Range

1

Identify the maximum and minimum (scanning the list).

Max = 41 Min = 3

2

Subtract:

Range = 41 − 3 = 38

Example 2 — Frequency Table

A class of 30 students scored the following marks out of 50:

Score	Frequency
22	2
28	5
35	9
41	8
47	6

📋 Range from a Frequency Table

1

The highest score listed is 47. The lowest is 22.

2

Range = 47 − 22 = 25

Note: For a frequency table, you still only look at the extreme values, not the frequencies.

Why Range Can Be Misleading

Consider two data sets:

Set A

10, 11, 11, 12, 12, 12, 13, 100

Set B

10, 40, 45, 50, 55, 60, 65, 100

Both have a range of 90. But Set A has almost all values bunched between 10 and 13, with a single outlier at 100. Set B's values are genuinely spread across the whole range. The range alone cannot distinguish these very different situations.

💡 This is why more advanced measures like IQR, variance, and standard deviation exist — they describe spread without being dominated by a single extreme value.

Range vs IQR vs Standard Deviation

Measure	Uses all data?	Affected by outliers?	Complexity
Range	Only max & min	Yes (severely)	Very easy
IQR	Middle 50%	No	Easy–Medium
Std Deviation	All values	Somewhat	Medium–Hard

Real-Life Applications of Range

🌡️
Weather forecasting: A climate report might say "temperatures ranged from 8°C to 42°C this year." That 34°C range tells you the city has extreme seasonal variation.
🏏
Cricket: If a batsman's scores in a series range from 4 to 112, you know they are inconsistent — even if their mean score is decent.
🏭
Manufacturing: A bolt should be between 9.8mm and 10.2mm. The acceptable range is 0.4mm. Any bolt outside this range is rejected.
💹
Finance: A stock's 52-week high and low define its range for that year, giving investors a quick feel for price volatility.

Common Mistakes Students Make

⚠️ Subtracting in the wrong order. Range = Max − Min, not Min − Max. Range is always a positive number.

⚠️ Forgetting to identify max and min from a grouped table correctly. For grouped data (class intervals), the range is (upper boundary of highest class) − (lower boundary of lowest class).

⚠️ Treating range as a complete description of spread. In exam questions that ask you to comment on spread, mentioning only range without acknowledging its weakness (sensitivity to outliers) may cost marks, especially at IGCSE/A-Level.

Frequently Asked Questions

Yes. If all values in a data set are identical, then Max = Min, so Range = 0. This means there is no spread whatsoever in the data.

No. Range is always zero or positive because you always subtract the smaller value from the larger one. If you get a negative answer, you have subtracted in the wrong order.

No — these are completely different uses of the word. In statistics, range is a measure of spread of a data set. In algebra/functions, range refers to the set of possible output values of a function. Context determines the meaning.

Try the Range Calculator

Paste in any data set and get the range (plus min, max, and count) in one click.

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