Tools / Descriptive statistics

Descriptive Statistics Calculator

Paste a list of numbers to get the mean, median, standard deviation, quartiles, skewness, a 95% confidence interval, outliers and a histogram.

Free, no sign-up. Calculations run in your browser; your data is never uploaded.

Numbers (separated by commas, spaces, tabs or new lines; you can paste a column straight from Excel)

My data is a whole population, not a sample

Decimal places

How to read the results

Mean vs median. The mean is the average; the median is the middle value. When the mean is much higher than the median, a few large values are pulling it up, which is common with incomes, prices and order values. Report the median as the “typical” value in that case.
Standard deviation measures how spread out the values are, in the same units as the data. By default this calculator uses the sample standard deviation (dividing by n − 1), which is what Excel’s STDEV.S and pandas’ .std() return. Tick the population option if your list contains every member of the group, to match STDEV.P.
Quartiles and IQR. Q1 and Q3 cut off the lowest and highest 25%. The interquartile range (IQR = Q3 − Q1) is the spread of the middle half and isn’t affected by outliers. Quartiles use the same method as Excel’s QUARTILE.INC and pandas’ .quantile().
Outliers are values more than 1.5 × IQR below Q1 or above Q3, the rule used by box plots. An outlier isn’t automatically an error; check it before removing it.
Skewness above about 1 means a long tail to the right; below −1, a long tail to the left. Kurtosis here is excess kurtosis, so a normal distribution scores about 0 and heavy tails score higher. Both match Excel’s SKEW and KURT.
95% confidence interval for the mean uses the t-distribution: if you repeated the sampling many times, about 95% of intervals built this way would contain the true mean.

The same statistics in Python

import pandas as pd

s = pd.Series([12, 15, 11, 19, 14, 22, 13, 17])
print(s.describe())                 # count, mean, std, min, quartiles, max
print(s.skew(), s.kurt())           # sample skewness and excess kurtosis

Our exploratory data analysis tutorial shows how to use these numbers to understand a whole dataset, and the Excel analysis guide covers the Analysis ToolPak’s descriptive statistics.

FAQ

Should I use the sample or population standard deviation?

Use the sample version (the default) when your numbers are a sample from a larger group, which is almost always the case in data analysis. Use the population version only when you have every value, for example the scores of every student in one class.

What counts as a separator?

Commas, spaces, tabs, semicolons and new lines. Thousands separators aren’t supported, so remove them first: write 1250, not 1,250.

Is my data stored?

No. The numbers are processed in your browser and nothing is sent to our server.