Why does an outlier cause the extra class decision to reverse?
The decision rule is based on comparing the class average to a fixed threshold. An outlier artificially inflates the average above the threshold, preventing the class from receiving help. Removing the outlier lowers the average below the threshold, triggering the decision to hold extra classes.
Conditions
- The decision rule is: hold extra classes only if the average score is below 35.
- The dataset contains an outlier.
- The threshold is fixed at 35.
Reasoning, step by step
- Calculate the mean with the outlier and compare it to 35.
- Calculate the mean without the outlier and compare it to 35.
- Observe how the presence of the outlier changes the inequality relative to the threshold.
- Conclude that the outlier reverses the downstream decision.
Example
With the outlier 100, the mean is 36, which is greater than 35, so no extra classes are scheduled. After replacing 100 with 20, the mean is 20, which is less than 35, so extra classes are justified.
Common misconceptions
- Assuming outliers only affect descriptive statistics and not practical decisions.
- Believing that a single extreme value is harmless in a small sample.
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