Spread, Range & Outliers

Range — the simplest spread

It uses only the two extremes, so a single unusual value can blow it up.

What an outlier does

An outlier is a value far from the rest. Its effect:

• Range: changes a lot (extremes define it).
• Mean: pulled toward the outlier.
• Median: barely moves (it ignores how far, only position).
• Mode: unaffected unless the outlier repeats.

Mean vs median for skewed data

If a data set has one very large value, expect mean $>$ median. If one very small value, mean $<$ median. The median is the "resistant" average.

Comparing two data sets

Two sets can share a mean but differ in spread. The one with values clustered tightly has a smaller range; the one with extremes has a larger range.