Index / Maths
Statistics Summary
Paste a column of numbers and get the summary back: centre, spread, shape, quartiles and outliers. The four quartile conventions disagree with each other, so all four are printed rather than one being picked quietly.
The numbers
Spaces, commas, tabs, semicolons and newlines all
separate. Anything that is not a number is listed rather than
skipped silently.
Mean
--
Count
0
Median
--
Sample SD
--
Centre
Spread
sample and population bothQuartiles, all four conventions
Shape and outliers
1.5 × IQR fences
Which convention each number follows, and where they disagree
There is no single definition of a quartile. Nine are in common
use; four of them cover almost everything people actually run. For
1, 2, 3, 4 the first quartile is 1.75 by R-7,
1.5 by Tukey's hinges and by Moore and McCabe, and 1.25 by
R-6. That is not a rounding difference, it is four different questions,
so all four are printed and the one used for the fences is the one you
picked.
R-7 interpolates linearly between order statistics at position (n−1)p + 1. It is what NumPy, R's default,
The sample standard deviation divides by n − 1, the population one by n. Both are printed because which one is right depends on whether these numbers are all of the thing or a sample from it, and no page can know that. With n = 1 the sample figure does not exist at all, and it says so rather than showing zero.
Skewness and kurtosis are printed twice. g1 and g2 are the plain moment ratios; G1 and G2 are the bias-corrected versions that Excel's
Outliers are the 1.5 × IQR rule: anything below Q1 − 1.5 IQR or above Q3 + 1.5 IQR. That is Tukey's rule for drawing whiskers on a box plot, not a test for anything. A value outside the fences is worth looking at; it is not evidence that it is wrong, and this page will not remove it for you.
The geometric and harmonic means need every value to be positive, so they are shown only when they exist. The geometric mean is computed as the mean of the logarithms, which is what keeps a long list from overflowing on the way.
Everything is computed on the values as parsed. The sum and the mean are accumulated in a single pass in the order you pasted them; on a very long list of very different magnitudes that order is visible in the last digit or two, which is a property of floating point rather than of the data.
R-7 interpolates linearly between order statistics at position (n−1)p + 1. It is what NumPy, R's default,
PERCENTILE.INC and most spreadsheets do.
R-6 uses (n + 1)p, which is PERCENTILE.EXC
and Minitab. Tukey's hinges take the median of the lower half
including the overall median when n is odd; Moore and McCabe take
it excluding the median. The last two are the ones taught in schools,
and they are the two that never interpolate.
The sample standard deviation divides by n − 1, the population one by n. Both are printed because which one is right depends on whether these numbers are all of the thing or a sample from it, and no page can know that. With n = 1 the sample figure does not exist at all, and it says so rather than showing zero.
Skewness and kurtosis are printed twice. g1 and g2 are the plain moment ratios; G1 and G2 are the bias-corrected versions that Excel's
SKEW and KURT return. Kurtosis is given as
excess kurtosis, so a normal distribution reads zero rather than
three.
Outliers are the 1.5 × IQR rule: anything below Q1 − 1.5 IQR or above Q3 + 1.5 IQR. That is Tukey's rule for drawing whiskers on a box plot, not a test for anything. A value outside the fences is worth looking at; it is not evidence that it is wrong, and this page will not remove it for you.
The geometric and harmonic means need every value to be positive, so they are shown only when they exist. The geometric mean is computed as the mean of the logarithms, which is what keeps a long list from overflowing on the way.
Everything is computed on the values as parsed. The sum and the mean are accumulated in a single pass in the order you pasted them; on a very long list of very different magnitudes that order is visible in the last digit or two, which is a property of floating point rather than of the data.