Range (Statistics) Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Range (Statistics).

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The statistical range is the difference between the maximum and minimum values in a data set: $\text{range} = \max - \min$ .

The range answers "how spread out is the data from end to end?" — it captures the total span but ignores everything in between.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The range is just the biggest value minus the smallest — the total width of the data.

Common stuck point: The procedure for range (statistics) is the easy part; the trap is subtracting in the wrong order and getting a negative. Asking "Am I just subtracting the smallest value from the largest?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I just subtracting the smallest value from the largest?

Worked Examples

Example 1

easy

Find the range of the data set:

\{3, 7, 2, 9, 5, 1, 8\}

Answer

\text{Range} = 8

First step

Identify the maximum value:

\max = 9

Full solution

2
Identify the minimum value: $\min = 1$
3
Apply the range formula: $\text{Range} = \max - \min = 9 - 1 = 8$

The range measures the total spread of a data set by subtracting the smallest value from the largest value. A larger range indicates greater variability in the data.

Example 2

medium

Two classes took the same test. Class A scores:

\{55, 70, 85, 90, 95\}

. Class B scores:

\{72, 74, 76, 78, 80\}

. Compare the ranges and explain what the difference tells you.

Example 3

medium

Compare the ranges of

A=\{10,10,11,11,30\}

and

B=\{2, 8, 12, 16, 22\}

Example 4

hard

Why might range be a poor summary of spread for the data

\{50, 52, 51, 53, 49, 100\}

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Find the range of the monthly temperatures (°F):

\{32, 45, 58, 72, 85, 90, 88, 75, 62, 48, 36, 30\}

Example 2

hard

A data set has a range of 24. If the maximum value is

3x + 5

and the minimum value is

x - 3

, find the value of

x

Example 3

easy

Find the range of

\{3, 7, 2, 9, 5\}

Example 4

easy

Range of

\{10, 10, 10\}

Example 5

easy

Range of

\{-4, 0, 6\}

Example 6

easy

The max of a data set is 50 and range is 20. Find the min.

Example 7

easy

Range of test scores

\{88, 92, 79, 95, 84\}

Example 8

easy

Which measures spread: range or mean?

Example 9

easy

Range of

\{2.5, 4.0, 1.5, 3.0\}

Example 10

easy

Two sets both have range 5. Do they have the same spread shape?

Example 11

medium

Add the value 100 to

\{3, 5, 7, 9\}

. How does the range change?

Example 12

medium

Data

\{x, 4, 9, 2\}

has range 12 with

x

the max. Find

x

Example 13

medium

A set has min 12, and after adding 3 to every value the range is 20. Original range?

Example 14

medium

Multiply every value of a set with range 8 by 3. New range?

Example 15

medium

Five distinct integers from 1 to 10 are chosen. What is the maximum possible range?

Example 16

medium

A class has range 30 for ages 10 to 40. A new student age 45 joins. New range?

Example 17

medium

Set A:

\{1,2,3,4,5\}

. Set B:

\{1,3,3,3,5\}

. Compare ranges.

Example 18

medium

The range of

\{a, a+2, a+5, a+9\}

is what (in terms of

a

Example 19

medium

The range of

\{12, 7, 19, 7, 15\}

is what?

Example 20

challenge

A set of 6 values has range 10, min 4. If the mean is 9, what is the sum of the four middle values?

Example 21

challenge

Two sets are merged: A has range 6 (values 2 to 8), B has range 9 (values 5 to 14). Range of the union?

Example 22

challenge

A data set of positive integers has range 7 and exactly 8 values with mean 10. Can all values be distinct? Explain by min/max bound.

Example 23

easy

Find the range of

\{8, 15, 4, 23, 11\}

Example 24

easy

Find the range of

\{6, 6, 6, 6\}

Example 25

easy

A data set has range 25 and minimum 12. Find the maximum.

Example 26

easy

Find the range of

\{1.2, 3.4, 5.6, 7.8\}

Example 27

easy

Find the range of heights (cm):

\{145, 152, 160, 138, 170\}

Example 28

easy

Find the range of

\{0, 0, 0, 10\}

Example 29

medium

A set of test scores has range 35. If the lowest score is 58, what is the highest?

Example 30

medium

Add the value 30 to the set

\{2, 5, 7, 10\}

. How does the range change?

Example 31

medium

Add a constant 5 to every value of a set with range 12. What is the new range?

Example 32

medium

Multiply every value of a set with range 4 by

-3

. What is the new range?

Example 33

medium

\{3, 7, x, 11, 4\}

, the range is 12 and

x

is the minimum. Find

x

Example 34

medium

A data set has values from 14 to 50. After removing the maximum, the new range is 22. What was the new max?

Example 35

medium

Two sets each have range 10. Does this mean their distributions look alike?

Example 36

medium

\{6, 9, 11, 14, 17\}

, what happens to the range if you replace 17 with 100?

Example 37

medium

Range of

\{a, a+3, a+8, a+11\}

Example 38

medium

Find the range of

\{42, 15, 67, 31, 22, 58\}

Example 39

hard

A set of 5 integers has range 10 and sum 35. If the minimum is 2 and the maximum is 12, find the sum of the three middle values.

Example 40

hard

A data set

\{x, x+2, x+5, x+9, 2x\}

has range 15 and

2x

is the max. Find

x

Example 41

hard

Set

A

has range 8 (values 3 to 11), set

B

has range 6 (values 9 to 15). Range of

A\cup B

Example 42

hard

After multiplying each value of a data set by 2 and adding 3, the new range is 18. What was the original range?

Example 43

hard

In a set of 7 distinct positive integers with range 6 and minimum 4, what must be the maximum?

Example 44

challenge

Six positive integers have mean 8, range 7, and minimum 5. What is the largest possible value of the second-largest entry?

← Back to Range (Statistics) Formula Explained Practice Mode

Related Concepts

Subtraction Standard Deviation Interquartile Range

Background Knowledge

These ideas may be useful before you work through the harder examples.

subtraction