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Statistics calculator

Paste your data for a complete summary: center, spread, quartiles with the method stated, outliers, skewness and a box plot.

By the Calcist team · Checked against known answers · Updated October 27, 2026

Private: calculated on your device. Nothing you type is sent anywhere.

Next: Want the working for the standard deviation? Use the standard deviation calculator. Estimating the true mean? Try the confidence interval calculator.

What each number means

  • Mean, median and mode describe the center. The median is the middle value once the data is sorted.
  • Quartiles split the sorted data into four parts. Q1 has a quarter of the values below it and Q3 has three quarters. The interquartile range, IQR = Q3 − Q1, is the spread of the middle half.
  • Outliers are values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR (Tukey's rule).
  • Standard deviation is the typical distance from the mean. The coefficient of variation is the sample SD as a percent of the mean.
  • Skewness measures lopsidedness: positive when there's a long tail of high values. Excess kurtosis compares the tails with a normal distribution, which scores 0.

How the quartiles are found

There's no single agreed way to compute quartiles. Hyndman and Fan (1996) list nine methods used by statistics software. The main results here use the method of the TI-83/TI-84 and most US statistics textbooks (Moore and McCabe):

Q1 = median of the lower half, Q3 = median of the upper half
(with an odd count, the median itself is left out of both halves)

Tukey's hinges include the median in both halves instead, and Excel and R interpolate between values. All four are shown under the results so you can match your class or software. They agree more closely as the data set grows.

Worked example

For 12, 15, 17, 18, 20, 21, 22, 25, 26, 48 (n = 10): the sum is 224, so the mean is 22.4. The median is (20 + 21) ÷ 2 = 20.5. The lower half 12, 15, 17, 18, 20 gives Q1 = 17, and the upper half 21, 22, 25, 26, 48 gives Q3 = 25. So IQR = 8, and the fences are 17 − 12 = 5 and 25 + 12 = 37. That makes 48 an outlier, which also explains why the mean is above the median and the skewness is positive.

Formulas

Sample skewness G₁ = √(n(n − 1)) ÷ (n − 2) × m₃ ÷ m₂^1.5
Excess kurtosis G₂ = (n − 1) ÷ ((n − 2)(n − 3)) × ((n + 1) × (m₄ ÷ m₂² − 3) + 6)
where m_k = Σ(x − x)ᵏ ÷ n

These match Excel's SKEW and KURT functions. The population skewness g₁ = m₃ ÷ m₂^1.5 is shown too.

Limits

  • With fewer than 3 values there's no skewness, and with fewer than 4 no kurtosis.
  • The 1.5 × IQR rule flags values for a closer look. It doesn't prove they're errors, and in large data sets some flagged values are expected.
  • Up to 100,000 numbers can be pasted. Use a point as the decimal mark.

Sources

How we checked this

Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:

  • 10 values: Q1 = 17, Q3 = 25 (TI-84 method) ✓
  • 48 is an outlier by the 1.5 × IQR rule ✓
  • Sample skewness G₁ = 2.1102315 (matches Excel SKEW) ✓
  • Excess kurtosis G₂ = 5.5098197 (matches Excel KURT) ✓
  • 1 to 7: TI-84 quartiles 2 and 6, Tukey hinges 2.5 and 5.5 ✓
  • One number only: no spread ✓

Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.

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Questions people ask

How do I find Q1 and Q3?

Sort the data and split it at the median. Q1 is the median of the lower half and Q3 the median of the upper half. With an odd count, leave the median out of both halves (the TI-84 method).

Why does my calculator or Excel give different quartiles?

They use different methods. Excel's QUARTILE.INC interpolates, and Tukey's hinges keep the median in each half. The table under the results shows each method's answer.

How do you find outliers?

Work out the IQR = Q3 − Q1. Anything below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier by Tukey's rule.

What is the five-number summary?

Minimum, Q1, median, Q3 and maximum. It's what a box plot draws.

What does a positive skewness mean?

The data has a longer tail of high values, like incomes. The mean is then usually above the median.

Related calculators

Standard deviation calculatorSample and population SD and variance, with a step-by-step table.Average calculatorMean, median, mode, range and standard deviation.Z-score calculatorZ-scores, percentiles and normal probabilities, with a bell curve.Confidence interval calculatorIntervals for a mean (t or z) or a proportion (Wilson and Wald).