Free Interquartile Range Calculator
Compute the interquartile range (IQR) as the difference between the third and first quartiles.
Interquartile Range (IQR)
50.0000
Lower Fence (Q1 - 1.5*IQR)-50.0000
Upper Fence (Q3 + 1.5*IQR)150.0000
Interquartile Range (IQR) vs First Quartile (Q1)
How to Calculate the Interquartile Range
Formula
IQR = Q3 - Q1
Q1 is the value below which 25% of observations fall, and Q3 is the value below which 75% fall. The IQR captures the spread of the middle 50% of the data, ignoring extreme tails.
Outlier Fences
Values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR are considered potential outliers by the Tukey fence rule.
Example Calculation
A dataset has Q1 = 25 and Q3 = 75. Find the IQR and outlier fences.
- 01IQR = 75 - 25 = 50
- 02Lower Fence = 25 - 1.5 * 50 = 25 - 75 = -50
- 03Upper Fence = 75 + 1.5 * 50 = 75 + 75 = 150
- 04Any value below -50 or above 150 is a potential outlier
Frequently Asked Questions
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