Statistics Calculator
Free online statistics calculator: paste a list of numbers and get count, sum, mean, median, mode, sample and population variance and SD, CV, quartiles, skewness, kurtosis, a histogram and a box plot instantly.
What is the difference between sample and population standard deviation?
Population standard deviation (σ) divides the squared deviations by n and describes the whole population. Sample standard deviation (s) divides by n−1 — Bessel's correction — and is used when your data is a sample estimating a larger group. Use s for measured samples, σ only when you truly have every value.
How do I enter my data?
Paste or type numbers into the text area separated by spaces, commas, tabs, semicolons or new lines — any mix works. The parser ignores letters and other junk, so you can paste straight from a spreadsheet column or a messy log file.
Can there be more than one mode?
Yes. If several values share the highest frequency, all of them are listed. If every value appears exactly once, the tool reports "None", because a data set where nothing repeats has no mode.
How are Q1, Q3 and the IQR calculated?
Quartiles use linear interpolation, the same default method as Excel and NumPy: Q1 sits at position (n−1)·0.25 and Q3 at (n−1)·0.75 in the sorted data, interpolating between neighbouring values. The IQR is simply Q3 − Q1.
What does the coefficient of variation (CV) mean?
CV is the sample standard deviation divided by the mean, shown as a percentage. It compares relative spread between data sets with different units or scales — a CV of 10% means the values typically vary by about a tenth of their average.
What do skewness and kurtosis tell me?
Skewness measures asymmetry: positive means a longer right tail, negative a longer left tail. Kurtosis is reported as excess kurtosis, where 0 matches the normal distribution, positive means heavier tails and a sharper peak, negative flatter tails.
How does the histogram choose its bins?
The number of bins follows Sturges' rule (1 + log2 n), clamped between 4 and 20, spread evenly between the minimum and maximum. Counts are drawn above each bar, and the chart redraws automatically when you switch between light and dark theme.
What does the box plot show?
The box spans Q1 to Q3 with a line at the median. Whiskers extend to the most extreme points within 1.5 × IQR of the quartiles, and anything beyond is drawn as an individual dot — those are your potential outliers.
Is my data uploaded anywhere?
No. Everything — parsing, statistics and charts — is computed locally in your browser. Your numbers never leave the page and no account is needed.
How to Use Statistics Calculator
This statistics calculator turns a pasted list of numbers into a full descriptive summary: count, sum, mean, median, mode, sample and population variance and standard deviation, coefficient of variation, min/max, quartiles, IQR, skewness and excess kurtosis, plus a histogram and a box plot. Everything is computed locally in your browser — your data never leaves the page.
- Paste your numbers into the text area. Spaces, commas, tabs, semicolons and new lines all work as separators, in any combination, so you can paste straight from a spreadsheet column or a log file.
- Results appear instantly as you type (with a short debounce): 17 statistic cards on top, then the histogram and box plot, then your data sorted in ascending order.
- Read the histogram to see the shape of the distribution — bin counts are drawn above each bar, and the number of bins follows Sturges' rule. The box plot shows the five-number summary with 1.5 × IQR whiskers and individual dots for outliers.
- Use the Example button to load a ready-made data set, or Clear to empty the input; if no valid numbers are found, a clear message tells you what to fix.
- Sample statistics (s, s²) divide by n−1 and are what you want for measured samples; population statistics (σ, σ²) divide by n. CV is the sample standard deviation as a percentage of the mean.
Skewness above +1 or below −1 signals a strongly asymmetric distribution, and excess kurtosis far from 0 means tails much heavier or lighter than the normal distribution. If the mode shows "None", no value repeats in your data.
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