Outliers (Deep) Math Example 2

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

Example 2

hard
Calculate the effect of an outlier (value 200) on the mean and median for {10,12,11,13,12,200}\{10, 12, 11, 13, 12, 200\}, comparing to the data without the outlier {10,12,11,13,12}\{10, 12, 11, 13, 12\}.

Solution

  1. 1
    Without outlier: mean =10+12+11+13+125=585=11.6= \frac{10+12+11+13+12}{5} = \frac{58}{5} = 11.6; median =12= 12
  2. 2
    With outlier: mean =58+2006=2586=43= \frac{58+200}{6} = \frac{258}{6} = 43; median =12+122=12= \frac{12+12}{2} = 12
  3. 3
    Effect on mean: increased from 11.6 to 43 — massive distortion (280% increase!)
  4. 4
    Effect on median: unchanged at 12 — completely resistant to the outlier

Answer

Outlier changes mean from 11.6 to 43 (massive) but leaves median unchanged at 12.
The mean is non-resistant to outliers — one extreme value can dramatically distort it. The median is resistant — it only depends on middle ranks, not actual values. This is why median is preferred for skewed data or when outliers are suspected.

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 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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