Statistics Calculator

What is a statistics calculator?

A statistics calculator turns a raw list of numbers into a full set of descriptive statistics — the summary numbers that describe where your data is centered, how spread out it is, and how it's shaped. This tool computes count, sum, mean, median, mode, range, quartiles, interquartile range (IQR), variance, standard deviation, standard error of the mean, coefficient of variation, skewness, and excess kurtosis, along with a frequency distribution of every value in your dataset.

How this tool works

1. Paste or type your numbers into the Data box — separate them with commas, spaces, newlines, semicolons, or tabs (any mix works).
2. Choose Population or Sample for the variance/standard deviation calculation.
3. Results update automatically in the two output tables: Descriptive Statistics and Frequency Distribution.

Any non-numeric text in the input (stray words, symbols) is silently skipped — only valid numbers are counted. You need at least 2 numbers for the statistics to compute; a single value has no meaningful spread.

Population vs. sample variance

These two settings answer different questions, and the formulas differ by more than rounding:

• Population variance divides the sum of squared deviations by N — use it when your data is the entire group you care about (every student in one class, every unit produced today).
• Sample variance divides by N − 1 (Bessel's correction) — use it when your data is a sample drawn from a larger population and you're estimating that population's variance. This is the more common choice in practice and is the default here.

Standard deviation is simply the square root of whichever variance you picked, so it inherits the same population/sample distinction.

How median, mode, and quartiles are calculated

• Median: for an odd-length dataset it's the middle value once sorted; for an even-length dataset it's the average of the two middle values.
• Mode: the most frequently occurring value(s). If two or more values tie for the highest frequency, all of them are reported. If every value appears exactly once, the tool reports "No mode."
• Quartiles (Q1/Q3) and IQR: computed with linear interpolation — the same method used by Excel's PERCENTILE.INC, NumPy's default linear method, and R's "type 7." The position (n − 1) × q is located in the sorted array and interpolated between the two bracketing values when it falls between two data points.

Skewness and kurtosis

Skewness measures asymmetry — a positive value means a longer tail on the high side, negative means a longer tail on the low side, and 0 means a perfectly symmetric distribution. Excess kurtosis measures "tailedness" relative to a normal distribution (which has excess kurtosis of 0): positive values indicate heavier tails and more outliers, negative values indicate lighter tails.

Frequency distribution

The second table lists every distinct value in your dataset, sorted ascending, alongside its count and what percentage of the dataset it represents — useful for spotting clusters or repeated values at a glance.

Privacy

This tool runs entirely in your browser. Your data is never uploaded to a server.