Descriptive Statistics Calculator
Paste a data set to get the mean, median, mode, range, sample & population standard deviation and variance, quartiles, IQR, and the five-number summary — instantly, with both quartile methods.
Results appear here as you type.
How it's calculated
The mean is the sum of all values divided by the count: x̄ = Σxᵢ / n. The sample standard deviation measures spread around the mean:
s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
We compute the variance in two passes (sum the values, then sum the squared deviations) to avoid the rounding error of the "mean of squares minus square of mean" shortcut. Population variants divide by n instead of n − 1.
See the full sample mean and all statistics formulas.
FAQ
Should I use sample or population standard deviation?
Use sample standard deviation (divides by n − 1) when your data is a sample drawn from a larger population — this is the default in most statistics courses and matches the TI-84's Sx. Use population standard deviation (divides by n) only when your data is the entire population (the TI-84's σx). This calculator always shows both.
Why are my quartiles different from my calculator or textbook?
There is no single agreed quartile method. The TI-84 and most US textbooks use the 'median-split' method (split the data at the median; for an odd count exclude the middle value). Excel's QUARTILE.INC uses linear interpolation. They always agree on the median (Q2) but can differ on Q1 and Q3. Use the toggle to match the method you need.
What is the five-number summary?
The minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It is the basis for a box-and-whisker plot and a quick picture of a data set's spread.
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