Descriptive statistics sandbox

Every value below is draggable. Move points, add them, delete them, and watch every summary statistic and the boxplot respond instantly.

n 10▲ mean 13.30| median 12.00SD 5.38IQR 2.00
boxplot of the same data (outliers plotted separately)051015202530
Presets:drag to move · click space to add · double-click to remove

28 is past the fence at 16, so the boxplot flags it. Notice the damage report: the mean got dragged 1.3 above the median, and the median barely noticed. That is resistance.

Try to:✓ create an outlier○ pull the mean 1.5 past the median○ get the SD under 2

Three experiments to run

  1. Resistance. Load the "with an outlier" preset and drag the far-right point further right. The mean follows it; the median barely moves. That is why the median is called resistant, and why one billionaire moving into town drags the average income but not the typical one.
  2. Skew. Build a long right tail and compare the mean and median markers. In right-skewed data the mean usually sits above the median; drag the tail to the left and watch them swap.
  3. Spread. Squeeze all the points together and watch the SD and IQR shrink; spread two clusters apart and watch the SD jump while the IQR can stay put.

The boxplot uses the 1.5 x IQR rule: points beyond the fences plot separately in red. For the arithmetic behind each readout, see standard deviation by hand, mean vs median, and the 1.5 x IQR rule.

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