Distribution Explorer

center, spread, shape, and the average that lies

Every dataset answers four questions: where is its center, how wide is its spread, what is its shape, and where does a value sit (its position). This tool lets you reshape a sample and watch the three centers move. The mean follows the tail; the median holds the middle. When they separate, the number you report stops being a matter of taste.

Built-in AI tutor. Ask what the shape is telling you, or which center to report, using the helper on this page. It coaches, it does not hand you the answer.
Drag from a symmetric bell toward a strong right-skew. As the tail grows, the mean pulls away from the median.
One giant account, a fraud loss, a mis-keyed entry. Watch the mean lurch while the median barely moves.
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Mean
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Median
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Mode (modal bin)
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Std. deviation
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IQR (middle 50%)
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Sample size

Distribution shape

Mean Median Mode (modal bin)

The same sample as a box-and-whisker plot

The box plot is the picture of spread. The box runs from the first quartile (Q1) to the third (Q3), so it holds the middle 50 percent (the IQR). The line in the box is the median. The whiskers reach the farthest points within 1.5 times the IQR, and any dots past them are outliers. Watch the median slide toward one end of the box as the skew grows, and a new dot appear past the whisker each time you inject an outlier.

All statistics are computed in your browser from a synthetic sample, seeded so every preset looks the same each time. The mean is the arithmetic average, the median is the middle value, the mode here is the midpoint of the tallest histogram bar, the IQR is the spread of the middle 50% (the third quartile minus the first). The empirical rule (68 / 95 / 99.7) holds for the bell and breaks for the skewed and long-tailed shapes that dominate accounting data.