Practice Quartiles in Math

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

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Quick Recap

Quartiles divide an ordered data set into four equal parts: Q1 is the 25th percentile, Q2 is the median (50th), and Q3 is the 75th percentile.

Q1 = 25th percentile, Q2 = median (50th), Q3 = 75th percentile.

Showing a random 20 of 50 problems.

Example 1

challenge
Find the IQR of 4, 8, 15, 16, 23, 42 (6 values) and identify any upper outliers.

Example 2

easy
Q2 is also known as which percentile?

Example 3

medium
Find Q1Q_1, Q2Q_2, and Q3Q_3 for the dataset: 4,7,8,12,15,18,21,25,304, 7, 8, 12, 15, 18, 21, 25, 30.

Example 4

medium
Data 10,20,30,40,50: find Q1, Q2, Q3.

Example 5

medium
Why must data be sorted before computing quartiles?

Example 6

medium
If Q3=50 and Q1=20, what is the IQR?

Example 7

hard
Given the sorted dataset 3,5,7,8,9,11,12,14,17,18,20,253, 5, 7, 8, 9, 11, 12, 14, 17, 18, 20, 25, find Q1Q_1, Q3Q_3, and the upper outlier (if any).

Example 8

easy
What fraction of the data lies between Q1Q_1 and Q3Q_3?

Example 9

hard
A dataset has Q1=35Q_1 = 35 and Q3=55Q_3 = 55. Determine whether 8080 is an outlier by Tukey's rule.

Example 10

medium
The five-number summary of a dataset is {10,18,25,35,50}\{10, 18, 25, 35, 50\}. State Q1Q_1, the median, Q3Q_3, and the IQR.

Example 11

easy
Q3 is the median of which half of the data?

Example 12

easy
Find Q1Q_1 and Q3Q_3 for: {10,20,30,40,50,60,70}\{10, 20, 30, 40, 50, 60, 70\}.

Example 13

challenge
For 100 sorted values, which positions estimate Q1 and Q3 using rank =p(n+1)=p(n+1)?

Example 14

hard
Compare two box plots: Plot A has Q1=20,Q3=40Q_1 = 20, Q_3 = 40; Plot B has Q1=25,Q3=50Q_1 = 25, Q_3 = 50. Which dataset has greater variability and by what margin (in IQR)?

Example 15

hard
For the dataset 2,4,4,5,6,7,7,8,9,102, 4, 4, 5, 6, 7, 7, 8, 9, 10, find Q1,Q2,Q3Q_1, Q_2, Q_3.

Example 16

hard
Quiz scores: 4,6,7,9,10,12,13,14,15,17,18,204, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 20. Find the IQR and identify any outliers.

Example 17

medium
A value is at the 25th percentile in a set of 80 values. About how many values are below it?

Example 18

medium
Find Q3 of 2, 4, 6, 8, 10, 12 (6 values).

Example 19

medium
If Q1=20 and IQR=15, find Q3.

Example 20

medium
For the dataset 11,13,14,16,18,19,21,23,25,2711, 13, 14, 16, 18, 19, 21, 23, 25, 27, find Q1Q_1, Q2Q_2, Q3Q_3, and the IQR.
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