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Statistics calculator
Mean, median, mode, quartiles, variance and standard deviation with the working, z-scores and a z-table, exact where they can be. Free, with no account or uploads.
What do you want to know?
Describe my numbersBest for mostMean, median, SDMean, median, mode, range, quartiles, variance and standard deviation, with the working.A z-scoreHow unusual a value isHow many standard deviations a value is from the mean, and the share below it.A z-tableProbability from zThe share of a normal distribution below, above or between z-scores.
These numbers are
A sampleThe whole population
A sample divides by n − 1, which corrects for seeing only part of the group.
Sample standard deviation
2.1381
Of 8 numbers: mean 5, median 4.5, mode 4.
- Count
- 8
- Sum
- 40
- Mean
- 5
- Median
- 4.5
- Mode
- 4 (3 times)
- Lowest and highest
- 2 and 9
- Range
- 7
- Quartiles (Q1, Q3)
- 4 and 5.5
- Interquartile range
- 1.5
- Variance
- 4.5714
- Standard deviation
- 2.13809
The working
- Mean = sum ÷ count = 40 ÷ 8 = 5.
- Take the mean from each number, square it and add: Σ(x − mean)² = 32.
- Divide by count − 1 = 7: variance = 4.5714.
- Standard deviation = √variance = 2.13809.
- Quartiles by straight lines between the sorted numbers at (n − 1) × ¼ and × ¾, as Excel's QUARTILE.INC and NumPy do; other methods give other quartiles.
Lead with
Standard deviationMeanVariance
Sums and means are exact; worked out in your browser, and nothing you type is sent anywhere or kept.
A little help along the way
Follow these steps. Every option is explained underneath. Everything runs in your browser; nothing is sent anywhere or kept.
- Say what you want to knowDescribe your numbers, a z-score, or a z-table.
- Paste or type your numbersSeparated by commas, spaces or new lines, and say whether they are a sample or a whole population.
- Read the answerThe figure you came for first, then every measure, and the working under it.
Every option explained
- Sample or population
- A sample divides the squared differences by n − 1 (Bessel's correction); a whole population by n.
- Quartiles
- By straight lines between the sorted numbers at (n − 1) × ¼ and ¾, as Excel's QUARTILE.INC and NumPy do; other methods give other quartiles.
- Exact
- Sums, means and variances are exact fractions; only square roots and the normal distribution are rounded.