How does replacing an outlier with a typical value change the arithmetic mean?

Conditions

• The original dataset contains an outlier.
• The replacement value is consistent with the majority of the data.
• The sample size remains unchanged.

Reasoning, step by step

1. Identify the outlier in the dataset.
2. Replace the outlier with a typical value.
3. Recalculate the sum of the dataset.
4. Divide the new sum by the sample size to find the new mean.
5. Compare the new mean to the original mean.

Example

Replacing the outlier 100 with 20 in the set 15, 20, 25, 20, 100 changes the mean from $(15+20+25+20+100)/5 = 36$ to $(15+20+25+20+20)/5 = 20$.

Common misconceptions

• Believing that changing just one value in a small sample will not affect the overall conclusion.
• Assuming the mean is robust to extreme values.

Watch the explanation

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