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Statistics calculator

Paste a list of numbers or a frequency table and get the mean, median, mode, variance and standard deviation (sample and population), quartiles, IQR, outliers, z-scores, a histogram and a box plot — with every working step, like your teacher wants to see it.

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  • Private — runs in your browser

How do I find the mean, median, mode and standard deviation?

  1. 1Type or paste your numbers — any separators work — or switch to a frequency table, with values or classes (10-20) and how often each occurs.
  2. 2Say whether your data is a sample or the whole population, and pick the quartile method your course uses.
  3. 3Read the results: centre, spread, quartiles and outliers; type a value to get its z-score.
  4. 4Scroll down for the histogram, box plot, frequency table and the full step-by-step working.

What are the formulas for standard deviation and variance?

  1. 01Mean x̄ = Σx ÷ n
  2. 02Sample variance s² = Σ(x − x̄)² ÷ (n − 1) · population variance σ² = Σ(x − x̄)² ÷ n
  3. 03Standard deviation = √variance · z = (x − x̄) ÷ SD
  4. 04IQR = Q3 − Q1 · outliers: below Q1 − 1.5·IQR or above Q3 + 1.5·IQR
  5. 05Grouped data: median = L + ((n/2 − CF) ÷ f) × h · mode = L + (f₁ − f₀) ÷ (2f₁ − f₀ − f₂) × h

The mean adds every value and divides by how many there are. The median is the middle value once the data is sorted (the average of the two middle values when n is even). The mode is the value that appears most often — there can be several, or none.

The standard deviation measures how spread out the values are around the mean. Square each value's distance from the mean, add the squares, divide, and take the square root. Divide by n − 1 for a sample (Bessel's correction, so the estimate isn't too small) and by n for a whole population. For 2, 4, 4, 4, 5, 5, 7, 9 the population SD is exactly 2 and the sample SD is 2.138.

Quartiles split the sorted data into four equal parts. Different books, calculators and spreadsheets use slightly different rules, which is why your answer may not match another tool's — so this calculator names its method and lets you choose: the TI-84 / textbook rule, Tukey's hinges, Excel's QUARTILE.INC or QUARTILE.EXC.

For grouped data (classes with frequencies) each class is represented by its midpoint, and the median, quartiles and mode come from the interpolation formulas taught in school. The calculator works in your browser; your numbers are not sent anywhere.

Good to know

  • Homework usually wants the sample standard deviation (n − 1) unless the question says the data is the whole population.
  • If your quartiles differ from the answer key, switch the quartile method — textbooks and Excel use different rules.
  • Paste data straight from Excel or Google Sheets: a copied column arrives one number per line.
  • The median and IQR are not moved much by outliers; the mean and SD are — compare them to spot skewed data.

Statistics questions

What is the difference between sample and population standard deviation?

Both measure spread. The population SD (σ) divides the sum of squared deviations by n and is used when your data is the entire group. The sample SD (s) divides by n − 1 and is used when your data is a sample from a bigger group; it is slightly larger.

How do you calculate standard deviation step by step?

Find the mean, subtract it from each value, square each difference, add the squares, divide by n − 1 (sample) or n (population), then take the square root. The working section above shows each step with your own numbers.

How do I find the mean, median and mode?

Mean: add all values and divide by how many there are. Median: sort the values and take the middle one (or the average of the two middle ones). Mode: the value that occurs most often.

Why are my quartiles different from my calculator or Excel?

There is no single rule for quartiles. TI calculators leave the median out of the halves, Excel's QUARTILE.INC interpolates at (n − 1)p and QUARTILE.EXC at (n + 1)p. Pick the same method here to match.

How do you find outliers using the IQR?

Work out IQR = Q3 − Q1. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier (Tukey's rule). These values are drawn as circles on the box plot.

How do you find the mean and median of grouped data?

Use each class midpoint x: mean = Σfx ÷ Σf. For the median, find the class holding the (n/2)th value and use median = L + ((n/2 − CF) ÷ f) × h, where L is its lower boundary, CF the cumulative frequency before it, f its frequency and h its width.

Sources

Formulas last reviewed: September 30, 2026 ·How we check our formulas

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