Range Examples in Statistics

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

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

Concept Recap

The range is the difference between the maximum and minimum values in a data set, giving the simplest measure of overall spread. It tells you the total span of the data from lowest to highest in a single number.

Range tells you how spread out your data is from end to end. If the tallest kid is 5 feet and the shortest is 4 feet, the range is 1 foot - that's the 'stretch' of heights.

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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: Range asks how tightly or loosely the values sit around the data set, not just where the middle is.

Common stuck point: Students often know a procedure related to range but skip the recognition step: Do I need to describe how far the data values extend or vary, rather than where the middle is? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Do I need to describe how far the data values extend or vary, rather than where the middle is?

Worked Examples

Example 1

medium
Data set {5,9,x,14,20}\{5, 9, x, 14, 20\} has range 1818. Find all possible values of xx.

Answer

x=2 or x≤2 (if max stays 20)x=2 \text{ or } x\le 2 \text{ (if max stays } 20\text{)}

First step

1
Range == max −- min =18= 18.

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Example 2

hard
A class has 55 test scores with mean 8080 and range 2020. What are the possible values of the maximum if all five scores are distinct integers?

Example 3

challenge
Six positive integers have mean 1010 and range 1414. If the smallest is 44, can all six be distinct? Justify with an example or counterexample.

Example 4

easy
Find the range of the data set: 15, 8, 22, 3, 17.

Example 5

medium
Two basketball players' points per game — Player A: 10, 12, 11, 13, 9. Player B: 5, 20, 8, 18, 4. Who is more consistent?

Practice Problems

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

Example 1

easy
Find the range of 3,7,103, 7, 10.

Example 2

easy
Find the range of 12,4,8,2012, 4, 8, 20.

Example 3

easy
Find the range of 5,5,55, 5, 5.

Example 4

easy
Find the range of −3,0,4-3, 0, 4.

Example 5

easy
Find the range of 100,50,75100, 50, 75.

Example 6

easy
Find the range of 2.5,1.5,4.02.5, 1.5, 4.0.

Example 7

easy
Find the range of 9,9,1,99, 9, 1, 9.

Example 8

easy
Find the range of 14,2214, 22.

Example 9

medium
Two classes have test ranges: A spans 6060 to 9595, B spans 7070 to 8080. Which is more spread out?

Example 10

medium
A data set has range 1515 and minimum 88. Find the maximum.

Example 11

medium
Daily highs were 68,72,65,80,7068, 72, 65, 80, 70. Find the range.

Example 12

medium
A set {4,9,x,2}\{4, 9, x, 2\} has range 1010. Find the possible values of xx.

Example 13

medium
Set A has range 1212. Adding 55 to every value, find the new range.

Example 14

medium
Multiply every value of a set with range 66 by 33. Find the new range.

Example 15

medium
A set of 55 integers has minimum 33 and range 88. What is the largest the mean can be?

Example 16

challenge
A set of 44 distinct positive integers has range 55 and the smallest value 22. What is the maximum possible median?

Example 17

challenge
Prove that for any data set, range ≥0\ge 0, with equality iff all values are equal.

Example 18

challenge
Set {a,b,c}\{a, b, c\} has range rr. If aa is the min and cc the max, express the IQR-like middle gap c−bc-b plus b−ab-a in terms of rr.

Example 19

medium
Daily lows were −2,3,−5,1,4-2, 3, -5, 1, 4. Find the range.

Example 20

medium
A set has maximum 3030 and range 1818. Find the minimum.

Example 21

easy
Find the range of 4,9,11,154, 9, 11, 15.

Example 22

easy
Find the range of 25,10,18,3225, 10, 18, 32.

Example 23

easy
Find the range of 7,7,7,77, 7, 7, 7.

Example 24

easy
Find the range of −5,−2,0,3-5, -2, 0, 3.

Example 25

easy
Find the range of 1.2,3.4,2.1,0.81.2, 3.4, 2.1, 0.8.

Example 26

easy
Find the range of 99,99,99,10099, 99, 99, 100.

Example 27

easy
A week's high temperatures (°F): 72,75,68,80,77,70,7472, 75, 68, 80, 77, 70, 74. Find the range.

Example 28

medium
A data set has range 2525 and maximum 4040. Find the minimum.

Example 29

medium
Class A range =30= 30; Class B range =60= 60. Which class has more spread test scores?

Example 30

medium
Add the value 5050 to {10,12,15,18}\{10, 12, 15, 18\}. By how much does the range increase?

Example 31

medium
Why is range a weak measure of spread for data with one extreme outlier?

Example 32

medium
Monthly rainfall (in): 2.1,3.4,0.9,5.2,1.7,4.82.1, 3.4, 0.9, 5.2, 1.7, 4.8. Find the range.

Example 33

medium
If every value in a data set is increased by 1010, what happens to the range?

Example 34

medium
Two friends' bowling scores: Aiko {120,140,130,135}\{120, 140, 130, 135\}; Ben {90,180,100,175}\{90, 180, 100, 175\}. Whose performance is more consistent (smaller range)?

Example 35

medium
A data set {a,2a,3a,4a}\{a, 2a, 3a, 4a\} has range 3030. Find aa (assume a>0a>0).

Example 36

hard
A data set has minimum −12-12 and range 5050. What is the maximum?

Example 37

hard
Find the range of {x,x+5,x+12,x+20}\{x, x+5, x+12, x+20\}.

Example 38

hard
Why does range, unlike standard deviation, use only TWO values from the data set?

Example 39

hard
Removing the largest value from {8,12,15,22,50}\{8, 12, 15, 22, 50\}, what is the new range?

Example 40

hard
Daily steps last week: 5000,6200,4800,7500,8100,4500,90005000, 6200, 4800, 7500, 8100, 4500, 9000. Find the range and interpret it.

Example 41

easy
The ages of children at a party are: 6, 9, 7, 11, 8, 10. What is the range of ages?

Example 42

easy
Morning temperatures for five days are 12, 13, 12, 14, and 25. What is the range, and what does the day with 25 tell you about the data?
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Background Knowledge

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

spread vs center