BIZNIQUE / LINEAR ALGEBRA / 12
Choose a scale that survives an outlier
Choose a scale that survives an outlier
Compare what one extreme observation does to the centre and spread.
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THE IDEA
Read the example.
Read the example.
The mean and standard deviation respond to extreme values. A median and interquartile range can provide a more resistant centre and scale. The example moves one observation and recomputes both summaries. Here the quartiles are the linearly interpolated 25th and 75th percentiles: the second and fourth values in this five-point sample.
Robust scale: (x − median) / IQR
Use it well
Use it well
Robust scaling does not remove an outlier or decide whether it is an error. Investigate the source and the model’s intended behaviour. A zero IQR needs separate handling.
TRY IT YOURSELF
A quick check.
A quick check.
Why can an extreme value compress most points after min–max scaling?
Check your reasoning
Check your reasoning
The extreme value widens the range used in the denominator, so ordinary differences occupy a smaller fraction of the scaled interval.
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