Step by Step
1
Find the IQR
IQR (interquartile range) = Q3 − Q1, the range spanned by the middle 50% of the data.
2
Calculate the lower fence
Lower fence = Q1 − 1.5×IQR. Any value below this fence is considered an outlier.
3
Calculate the upper fence
Upper fence = Q3 + 1.5×IQR. Any value above this fence is considered an outlier.
4
Why 1.5×IQR is the standard
The 1.5×IQR rule is the conventional, widely-used standard for identifying outliers in box plots and statistical reports — it provides an objective, consistent method rather than relying on subjective judgment.
Applied Walkthrough
1
A dataset has Q1 = 20 and Q3 = 35. Find the IQR: IQR = 35 − 20 = 15.
2
Calculate the lower fence: 20 − 1.5(15) = 20 − 22.5 = −2.5.
3
Calculate the upper fence: 35 + 1.5(15) = 35 + 22.5 = 57.5.
4
Any data value below −2.5 or above 57.5 would be flagged as an outlier using this rule — for example, a value of 60 in this dataset would be classified as an outlier, since it exceeds the upper fence of 57.5.
Exam Application
Exams test whether you can correctly calculate the IQR, lower fence, and upper fence, and whether you can correctly classify specific data values as outliers or not based on these fences.
⚠ Common Trap
The most common trap is confusing the multiplier direction — remember the lower fence SUBTRACTS 1.5×IQR from Q1, while the upper fence ADDS 1.5×IQR to Q3.
✓ Quick Self-Check
1. What is the formula for IQR?
IQR = Q3 − Q1.
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2. What is the formula for the lower fence?
Lower fence = Q1 − 1.5×IQR.
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3. What is the formula for the upper fence?
Upper fence = Q3 + 1.5×IQR.
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4. If Q1 = 20 and Q3 = 35, what are the lower and upper fences?
Lower fence = −2.5; upper fence = 57.5.
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5. What multiplier is used in the standard outlier fence rule?
1.5 (times the IQR).
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