Math 1 · Unit 12 · Lesson 4 · part 2 of 4
The 1.5 IQR rule
In middle school an outlier was a value that looked far from the rest.
The 1.5 IQR rule
In middle school an outlier was a value that looked far from the rest. Math 1 makes it a rule.
- 1Find the IQR.Q3 − Q1.
- 2Multiply it by 1.5.That is how far past the box a value is allowed to be.
- 3Build the fences.Lower fence: Q1 − 1.5 × IQR. Upper fence: Q3 + 1.5 × IQR.
- 4Judge.Any value below the lower fence or above the upper fence is an outlier.
The songs data: Q1 = 6.5 and Q3 = 18, so the IQR is 11.5. Then 1.5 × 11.5 = 17.25. Lower fence: 6.5 − 17.25 = −10.75. Upper fence: 18 + 17.25 = 35.25. No value is below −10.75 (nobody downloads a negative number of songs). The 88 is above 35.25: the 88 is an outlier.
A modified box plot shows outliers as separate dots, and its whisker stops at the last value inside the fences, here 32, instead of stretching out to 88.