Practice Quartiles in Statistics

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

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Quick Recap

Quartiles are values that divide ordered data into four equal parts: $Q_1$ (25th percentile) marks the boundary below which 25% of data falls, $Q_2$ (the median, 50th percentile) splits the data in half, and $Q_3$ (75th percentile) marks the boundary below which 75% falls.

If you line up 100 people by height and divide into 4 equal groups, quartiles mark the dividing points. $Q_1$ is where the shortest 25% ends, $Q_2$ is the middle, $Q_3$ is where the tallest 25% begins.

Showing a random 20 of 50 problems.

Example 1

medium

Ordered ages:

14, 15, 16, 17, 18, 19, 20

. Find

Q_3

Example 2

easy

For ordered

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

, find

Q_1

Example 3

medium

For

4,8,15,16,23,42

, find

Q_1

and

Q_3

Read Q₁ and Q₃ off the box plot.

Example 4

medium

Ordered ages:

14, 15, 16, 17, 18, 19, 20

. Find

Q_1

Example 5

medium

For ordered

6, 9, 11, 14, 17, 20

, find

Q_3

Example 6

hard

If a data set has

20

values, between which two ordered positions is

Q_1

found (inclusive method)?

Example 7

easy

For ordered

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

, find

Q_3

Example 8

easy

Find the median (

Q_2

) of

2, 4, 6, 8, 10

Example 9

medium

Test scores:

55, 62, 68, 75, 80, 88, 92, 95

. Find

Q_1, Q_2, Q_3

Find Q₁, Q₂, Q₃ from the test-score distribution.

Example 10

easy

For ordered

2,4,6,8

, find

Q_2

Example 11

medium

For ordered

6, 9, 11, 14, 17, 20

, find

Q_2

Example 12

easy

What percentile does

Q_3

represent?

Example 13

easy

Order

12, 5, 9, 3, 7

from least to greatest.

Example 14

easy

For ordered

3, 5, 7, 9, 11

, find

Q_1

Example 15

hard

For

\{3, 7, 8, 12, 14, 21, 22, 27, 30, 35\}

, find

Q_1, Q_2, Q_3

Find all three quartiles for this 10-value data set.

Example 16

medium

For

5,7,8,9,10,12,13,14,15

, find

Q_1

Find Q₁ — shown as ? on the box.

Example 17

hard

Annual rainfalls (in inches) over 9 years:

20, 22, 25, 28, 30, 32, 35, 40, 50

. Find all three quartiles.

Find Q₁, Q₂, Q₃ for the rainfall data.

Example 18

easy

Order

9, 3, 7, 1

before finding quartiles. Give the ordered list.

Example 19

medium

For

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

, find all three quartiles.

Find all three quartiles Q₁, Q₂, Q₃ — each shown as ? on the box.

Example 20

medium

Q_1=10

and

Q_3=22

, where do the middle 50% of values lie?

The shaded box shows where the middle 50% of values lie.

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Related Concepts

Median Box Plot Interquartile Range (IQR)