Descriptive Statistics
Computes mean, median, mode, variance, standard deviation, quartiles and outliers from pasted numbers.
Paste a column of numbers and get the summary: mean, median, mode, quartiles, standard deviation and the outliers. It shows the sample and population standard deviations side by side rather than choosing for you, because which one is right is a question about what the numbers are for.
Numbers
Paste a column from a spreadsheet, or type them separated by commas, spaces or newlines. On this page the comma also groups digits, so 1,234 is read as one number and 1,23 as two.
Summary
count
8
sum
40
mean
5
median
4.5
min
2
max
9
range
7
mode
4
Spread
Sample (n − 1)
Use this when these numbers are a sample and you want to describe the population they came from. Excel calls it STDEV.S.
- variance
- 4.5714
- std deviation
- 2.1381
- standard error
- 0.7559
Population (n)
Use this when these numbers are the whole population. Excel calls it STDEV.P.
- variance
- 4
- std deviation
- 2
- coefficient of variation
- 0.4276
Quartiles and outliers
Q1
4
Q2 (median)
4.5
Q3
5.5
IQR
1.5
lower fence
1.75
Q1 − 1.5 × IQR
upper fence
7.75
Q3 + 1.5 × IQR
outliers
9
median abs deviation
0.5
There is no single definition of a quartile. The two methods here disagree whenever the data does not divide evenly — which is why two people can plot the same numbers and get different boxes.
Shape and intervals
95% CI of the mean
3.2122 – 6.7878
Student t = 2.365 at 7 df
skewness
0.8185
0 is symmetric
excess kurtosis
0.9406
0 is normal-tailed
geometric mean
4.6032
Distribution
- 2 – 3.751
- 3.75 – 5.55
- 5.5 – 7.251
- 7.25 – 91
Bin count from Sturges’ rule: ⌈log₂ n⌉ + 1.
How to use it
Paste the numbers
A column out of a spreadsheet works as it is. Commas, spaces and newlines all separate, and since a comma also groups digits on an English page, its shape settles which job it is doing: 1,234 is read as one number and 1,23 as two. On the pages whose language writes the decimal with a comma — Italian, German, French, Spanish, Portuguese — that reading is the other way round, and values are separated with semicolons, the way those spreadsheets do it.
Check what was ignored
Non-numeric tokens are listed rather than silently dropped. A header row you pasted along with the data shows up there.
Read the spread, not just the middle
Mean and median together tell you about skew; the standard deviation and the coefficient of variation tell you whether the mean means anything.
Common questions
Sample or population standard deviation?
Sample, dividing by n − 1, when these numbers are a sample and you want to describe the population they came from — Excel’s STDEV.S. Population, dividing by n, when these numbers are everything there is. Both are shown along with how far apart they are on your data.
How are outliers decided?
By the 1.5 × IQR rule — anything more than one and a half interquartile ranges below the first quartile or above the third. It is a convention, not a verdict: an outlier by this rule can be a perfectly real value.
My quartiles differ from Excel’s
There are nine accepted ways to interpolate a quartile and different tools pick different ones. The difference is small and only appears with few data points. Neither is wrong; they answer slightly different questions about the same numbers.
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