Statistics Calculator

Enter a data set to instantly get the count, sum, mean, median, mode, range, variance, standard deviation, quartiles, and more.

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Data Set (comma, space, or newline separated)

Sorted:

Count (n)

sum = 40

Mean

Arithmetic average

Median

4.5

Middle value

Mode

Most frequent

Range

Max − Min

Variance (Pop)

σ² — divide by n

Variance (Samp)

4.571

s² — divide by n−1

SD (Population)

SD (Sample)

2.138

Statistic	Value

Step-by-step: Mean

Paste in any dataset to instantly get a full descriptive statistics summary — mean, median, mode, variance, standard deviation, quartiles, skewness, and kurtosis.

How It Works

How Statistics Calculator Works

Basic measures (mean, median, mode, range) are computed the standard way, and the calculator reports both population and sample variance and standard deviation side by side — dividing by n for population, or by n−1 for sample — so you can use whichever is correct for whether your data represents an entire group or just a sample from it.

Quartiles Q1 and Q3 are found using linear interpolation on the sorted dataset — the same method most spreadsheet software uses by default — and the interquartile range (IQR = Q3 − Q1) describes how spread out the middle 50% of your data is, ignoring extreme outliers at either end.

Skewness (using Fisher's adjusted formula) measures whether the data leans left or right of the mean — positive skew means a longer tail toward higher values — while excess kurtosis measures how much heavier or lighter the distribution's tails are compared to a normal distribution; these need at least 3 and 4 data points respectively to compute.

Worked Example

See It In Action

For the dataset 2, 4, 4, 4, 5, 5, 7, 9 (n=8): sum = 40, mean = 40/8 = 5. Sorted, the two middle values are 4 and 5, so median = (4+5)/2 = 4.5, and mode = 4 (it appears three times, more than any other value). Population variance = 32/8 = 4 (population SD = 2), while sample variance = 32/7 ≈ 4.571 (sample SD ≈ 2.138).

Real-World Use Cases

Who Uses Statistics Calculator and Why

Getting a complete descriptive statistics summary for a dataset pasted from a spreadsheet or survey export.
Checking a distribution's skewness and kurtosis before deciding whether a statistical test's normality assumption is reasonable.
Comparing the interquartile range (IQR) of two datasets to judge spread while ignoring extreme outliers.
Cross-checking quartile values against spreadsheet software output for a stats assignment.

Common Mistakes

Mistakes to Avoid

Expecting skewness or kurtosis to display for a very small dataset — they require at least 3 and 4 data points respectively to compute at all.
Assuming this calculator's quartile values will match every textbook method — it uses linear interpolation, the same approach most spreadsheet software defaults to, which can differ slightly from a nearest-rank method.
Mixing up the population and sample variance/standard deviation figures when reporting results, since both are shown side by side.

Pro Tips

Tips for Best Results

Since quartiles use linear interpolation, expect this tool's Q1/Q3 values to match Excel or Google Sheets' QUARTILE function rather than a nearest-rank textbook method.
Check that your dataset has at least 4 points before relying on the kurtosis figure, and at least 3 before relying on skewness.

Troubleshooting

Fixing Common Problems

Skewness or kurtosis shows as unavailable. — These measures need a minimum dataset size to compute — at least 3 points for skewness and 4 for kurtosis. Add more data points if your set is smaller than that.

Glossary

Terms Explained

Interquartile range (IQR): The range between the first quartile (Q1) and third quartile (Q3), describing the spread of the middle 50% of a dataset while ignoring extreme outliers.

Skewness: A measure of a distribution's asymmetry — positive skew means a longer tail toward higher values, computed here using Fisher's adjusted formula.

FAQ

Frequently Asked Questions

Why are population and sample variance different for the same data?

Population variance divides the sum of squared deviations by n, while sample variance divides by n−1 — a correction that compensates for the tendency of a sample to underestimate the true variability of the full population it was drawn from.

What do skewness and kurtosis tell me about my data's shape?

Skewness measures asymmetry — whether more of the data trails off to the left or right of the mean. Kurtosis measures "tailedness" — whether extreme values are more or less common than in a standard bell-curve (normal) distribution.

How are quartiles calculated when they fall between two data points?

The calculator uses linear interpolation, blending the two nearest sorted values proportionally based on exactly where the quartile's position falls between them, rather than simply rounding to the nearest actual data point.

What if my dataset has more than one mode?

If two or more values are tied for the highest frequency, all of them are listed as modes (this is called "multimodal" data). If every value appears exactly once, the calculator reports that there is no mode.