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.
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Mean
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Median
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Mode (modal bin)
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Std. deviation (STDEV.S)
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IQR (middle 50%)
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Skewness (SKEW)
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Excess kurtosis (KURT)
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Sample size

Distribution shape

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 seeded sample, so every preset looks the same each time. The conventions match Excel, so you can check any tile against a spreadsheet: the standard deviation is the sample standard deviation (n minus 1), which is STDEV.S and what Week 4 used; skewness is SKEW(); excess kurtosis is KURT(). Skewness near 0 is roughly symmetric, 0.5 to 1 is moderate, past 1 is strong. Excess kurtosis is 0 for a bell, and positive means the tails carry more weight than a bell does. The mode here is the midpoint of the tallest bar, and the IQR is 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, so the caption prints the measured percentage inside one standard deviation instead of asserting the rule. The receivables preset rebuilds the 2,500 Week 5 invoices from each segment's own measured percentiles, so its quartiles match the file you already hold to within a dollar or two. If you recompute from the CSVs you will get 463 pooled Tukey outliers and 12 split, against this page's 464 and 11: the rebuild is one invoice off at each fence, not a different dataset. The histogram's axis is set by the sample itself and never by an injected outlier, so anything you inject past the right edge stacks into the last bar and is counted in the caption rather than flattening the chart.