Statistics Basic Calculator — Mean, Median, Variance, Quartiles, Histogram, Box Plot

Real-world use cases

• Check a homework problem set on descriptive statistics in one paste

  You have a problem that asks for the mean, median, sample variance, sample standard deviation, Q1, Q3, and IQR of {78, 85, 90, 72, 88, 95, 84, 91, 76, 89}. Paste the ten numbers in any layout and read every value off the summary card. The page shows both Tukey and R-7 quartiles side by side, so if your textbook uses the inclusive median-of-halves rule you get one set, and if it uses the Excel / R linear- interpolation rule you get the other — no confusion, no guessing which definition the answer key expected.

• Spot the outlier that's pulling the mean off

  A right-skewed income sample like 3.2, 3.5, 3.8, 4.1, 4.3, 4.5, 4.8, 5.1, 5.5, 6.2, 7.8, 15.0 has a mean (5.32) that's noticeably higher than the median (4.65). The calculator flags 15.0 as a Tukey-fence outlier in red on the box plot and lists it in the outliers panel. That's the visual proof for the textbook claim "the mean is sensitive to outliers, the median is not" — and a good place to explain to a student why median household income is what governments report, not mean.

• Decide on bin count for a histogram before plotting it in Python

  You have 60 reaction-time measurements and you want a clean histogram for a lab report. Paste them, accept the Sturges default (k=7), and see if the shape is what you expect. If the distribution looks too jagged, bump bins to 10 or 12 and check whether the new bins reveal real structure or just random fluctuation. Once you've picked a bin count visually you can replicate it in matplotlib with plt.hist(data, bins=k) and be confident the choice was data-driven, not guessed.

• Show a class the difference between sample and population variance

  Teaching the n−1 correction is easier with numbers. Pick a tiny set, e.g. {2, 4, 6, 8, 10}: the page shows σ² = 8 (÷5) and s² = 10 (÷4), and the standard deviations are 2.83 and 3.16. Students see immediately that the n−1 divisor makes the sample estimate slightly larger — the unbiased estimator that accounts for the fact that the sample mean is itself estimated from the data and "uses up" one degree of freedom.

• Verify five-number summary and box-plot outliers for a project

  For a data-analysis assignment you need to report the five-number summary (min, Q1, median, Q3, max) and identify outliers using Tukey's 1.5×IQR rule. Paste your dataset, read off the five numbers from the box plot labels, see the upper and lower fences printed directly under the chart, and copy any flagged values from the outliers panel. The "Copy all" button then dumps a clean text block for your writeup so you don't transcribe by hand.

Common pitfalls

• Using sample standard deviation s when describing the entire population, or population σ when generalizing from a sample. Rule of thumb — if you'd run a hypothesis test on these numbers later, you're treating them as a sample, so use s and s² (n−1 divisor). If the dataset is literally everyone you care about and you won't extrapolate, use σ and σ² (n divisor).

• Treating "no mode" as a calculator bug. When every value appears exactly once, there is no mode — that is the correct answer, not a missing one. Some textbooks then call all values "modes" with multiplicity 1, but the convention this calculator follows (and most statistics software) is to report "no mode" so you don't accidentally read meaning into noise.

• Picking a quartile algorithm without checking which one the assignment uses. Tukey (inclusive median-of-halves) and R-7 (linear interpolation) can both be called "the" quartile method depending on the country and the textbook, and they give different Q1 / Q3 on the same data for small n. Always match the dropdown to your course before turning in the answer.

• Reading a non-zero skewness or kurtosis as "the data is non-normal" without checking the sample size. On small samples (n < 20) skewness and kurtosis estimates have large standard errors, and you can easily get |G1| > 1 from purely normal data by chance. Use these statistics as a hint, not a verdict — for formal normality testing, use Shapiro–Wilk or a Q-Q plot.

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