Outliers (Deep) Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
A data set has Q1=50Q_1 = 50, Q3=70Q_3 = 70. Determine if each value is an outlier: (a) 85, (b) 15, (c) 105.

Solution

  1. 1
    IQR =70−50=20= 70 - 50 = 20; Lower fence =50−30=20= 50 - 30 = 20; Upper fence =70+30=100= 70 + 30 = 100
  2. 2
    (a) 85: between 20 and 100, NOT an outlier
  3. 3
    (b) 15: less than 20, IS an outlier
  4. 4
    (c) 105: greater than 100, IS an outlier

Answer

(a) 85: not an outlier. (b) 15: outlier. (c) 105: outlier.
Once fences are calculated, outlier identification is straightforward: values outside [lower fence, upper fence] are outliers. Always calculate both fences — outliers can be in either tail.

About Outliers (Deep)

An outlier is a data value that lies unusually far from most other values, potentially indicating measurement error, a rare event, or an important exception.

Learn more about Outliers (Deep) →

More Outliers (Deep) Examples

Example 1 medium

Data: [formula]. Use the [formula] rule to determine if 85 is an outlier, and discuss whether it sho

Example 2 hard

Calculate the effect of an outlier (value 200) on the mean and median for [formula], comparing to th

Example 4 hard

A researcher finds that removing one outlier changes the correlation from 0.45 to 0.82. Discuss whet

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