The interquartile range (IQR) is the range of the middle 50% of data, calculated as Q3−Q1. It measures spread while ignoring the top and bottom 25% of values, making it resistant to outliers.
IQR focuses on where most of the data lives, ignoring the extremes. If regular range is how far the outliers stretched, IQR is how wide the main crowd is. More resistant to outliers than range.
Showing a random 20 of 50 problems.
Example 1
challenge
Show that IQR ≤ range for any data set.
Example 2
easy
A box plot's box stretches from 40 to 55. What is the IQR?The box spans from Q₁ to Q₃. What is the IQR (the width of the box)?
Example 3
challenge
Two sets have equal IQR =10 but ranges 12 and 60. What distinguishes them?
Example 4
medium
A box plot shows Q1=22, Q3=34. The largest value is 80. Does 80 qualify as a high outlier by the 1.5⋅IQR rule?Q₁ = 22, Q₃ = 34. Upper fence = Q₃ + 1.5·IQR = 52. Is 80 an outlier?
Example 5
medium
Add 7 to every value. If the IQR was 9, find the new IQR.
Example 6
hard
A new value 200 is added to a set with Q1=20, Q3=40, and many values. The IQR barely changes. Why?
Example 7
easy
Which is generally more resistant to outliers: range or IQR?
Example 8
easy
If Q1=20 and Q3=20, find the IQR.
Example 9
easy
For a set with Q1=100,Q3=140, find the IQR.Box spans Q₁ = 100 to Q₃ = 140. Find the IQR.
Example 10
medium
If Q1=30, IQR =10, find Q3.
Example 11
medium
Find the IQR of 2,3,5,7,7,8,10.
Example 12
easy
If Q1=0 and Q3=9, find the IQR.
Example 13
hard
Daily commute times (min): 20,22,25,28,30,35,38,40,95. Find the IQR and explain why it is a better spread measure than the range here.Commute times (min): 20, 22, 25, 28, 30, 35, 38, 40, 95. Q₁ = 23.5, Q₃ = 39, IQR = 15.5. The value 95 is an outlier.
Example 14
easy
Given the data set: 4, 7, 9, 12, 15, 18, 22, 25, 30, find the interquartile range (IQR).
Example 15
challenge
Two cities report median household incomes both equal to $60k. City A has IQR $10k; City B has IQR $60k. What do these tell you about income inequality?
Example 16
medium
Multiply all data by 4. If the original IQR was 5, find the new IQR.
Example 17
medium
If you add 5 to every value, what happens to the IQR?
Example 18
easy
Is IQR more or less affected by outliers than range?
Example 19
hard
Two data sets: A has IQR 4 and B has IQR 20. Both have median 50. Which set is more reliable?
Example 20
easy
If Q1=5 and Q3=12, find the IQR.The box spans Q₁ = 5 to Q₃ = 12. What is the width of the box (the IQR)?