Outliers (Deep) Math Example 1

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

Example 1

medium
Data: {12,15,14,13,16,14,15,85}\{12, 15, 14, 13, 16, 14, 15, 85\}. Use the 1.5×IQR1.5 \times IQR rule to determine if 85 is an outlier, and discuss whether it should be removed.

Solution

  1. 1
    Sort data: {12,13,14,14,15,15,16,85}\{12, 13, 14, 14, 15, 15, 16, 85\}; n=8n=8
  2. 2
    Q1=13+142=13.5Q_1 = \frac{13+14}{2} = 13.5; Q3=15+162=15.5Q_3 = \frac{15+16}{2} = 15.5
  3. 3
    IQR=15.5−13.5=2IQR = 15.5 - 13.5 = 2; Upper fence =15.5+1.5(2)=18.5= 15.5 + 1.5(2) = 18.5
  4. 4
    85 > 18.5, so 85 is flagged as an outlier
  5. 5
    Decision: investigate before removing — 85 could be a data entry error (e.g., 15 mis-typed as 85) or a genuine extreme value (e.g., a special event)

Answer

85 is an outlier (exceeds fence of 18.5). Investigate cause before removing.
The 1.5×IQR rule identifies potential outliers but does not determine whether to remove them. Outliers might be data errors (should remove), legitimate rare events (keep), or indicators of a different subgroup (analyze separately).

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 2 hard

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

Example 3 easy

A data set has [formula], [formula]. Determine if each value is an outlier: (a) 85, (b) 15, (c) 105.

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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