One value, two centers

What this display answers

The mean assigns every value equal arithmetic weight, so one distant value can move it substantially. The median depends on order and usually changes only when the moving value crosses the middle positions.

The IQR flag is a descriptive rule, not a verdict that the point is wrong. An unusual observation may be an error, a rare valid case, or evidence that the model needs more than one summary.

What to notice

1. Begin near 12, where all ten observations occupy a narrow range.
2. Move the final value to 72 or 100. Compare the coral mean line with the dashed median line.
3. Check the upper fence in the value table before calling the moving observation an outlier.

The model behind it

Nine synthetic delivery-like values remain fixed and only the tenth changes. The quartiles use the quantile method implemented by the statistics library.

This setup isolates sensitivity. It is not a claim that either center is always preferable.

Where the result stops

A median can hide important changes in the tails, while a mean can be the estimand a real decision requires.

Do not remove observations solely because a rule labels them unusual; investigate generation and measurement first.