Practice Interquartile Range in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The interquartile range (IQR) is $Q3 - Q1$ — the spread of the middle 50% of the data, resistant to outliers.

The IQR ignores the extreme 25% on each end, capturing only the spread of the central bulk of data — making it robust when outliers inflate the regular range.

Showing a random 20 of 50 problems.

Example 1

medium

Find the lower outlier fence for

Q1=20

Q3=40

using the

1.5\times\text{IQR}

rule.

Example 2

easy

A box plot shows the box from

40

70

. What is the IQR?

Example 3

medium

Multiplying every value of a data set by

4

changes the IQR by what factor?

Example 4

medium

IQR

=12

and

Q_3 = 50

. Find

Q_1

Example 5

easy

If every value in a data set is the same, the IQR is ___.

Example 6

challenge

A data set of 200 values has

Q_1=30, Q_3=60

. Approximately how many values lie in

[30,60]

Example 7

medium

Find the IQR of test scores:

55,60,62,68,72,75,78,80,85,90

Example 8

easy

Is the IQR resistant to a single extreme outlier? Answer yes or no.

Example 9

hard

For the data

3,7,8,5,12,15,9,11,2,10

, find the IQR after sorting.

Example 10

easy

A box plot shows the box edges at

30

and

48

. What is the IQR?

Example 11

medium

For the data

2, 5, 7, 8, 10, 13, 14, 16, 20

, find the IQR. (9 values; median

=10

; lower half

2,5,7,8

; upper half

13,14,16,20

Example 12

easy

For the data

\{4,6,8,10,12,14,16,18\}

find the IQR. (Lower half:

4,6,8,10

; upper half:

12,14,16,18

Example 13

hard

A box plot has whisker endpoints at

5

and

95

, box from

30

70

. Identify the IQR and check if

95

is an outlier under the

1.5\times

IQR rule.

Example 14

easy

For the ordered data with

Q1 = 12

and

Q3 = 20

, find the interquartile range.

Example 15

hard

Test scores

\{60,70,75,80,82,85,88,92,95,100\}

. After replacing

100

with

200

, does the IQR change?

Example 16

easy

Given

Q1 = 100

and

Q3 = 100

, what is the IQR, and what does it tell you?

Example 17

medium

A five-number summary is min

=4

Q1=10

, median

=15

Q3=22

, max

=40

. Compare the IQR with the range.

Example 18

hard

A symmetric data set has

Q_1=40, Q_3=60

. Give the interval of values NOT flagged as outliers.

Example 19

challenge

Set A:

1,2,3,4,5,6,7,8

. Multiply every value by

3

to get Set B. By what factor does the IQR change?

Example 20

hard

Two data sets have the same median but Class X has IQR

=2

and Class Y has IQR

=14

. Which class has scores more spread out around the median?

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