Statistics Calculator

The tool reports the population standard deviation, which divides the sum of squared deviations by <em>n</em>. If you are working with a sample and want the unbiased sample standard deviation, multiply the displayed variance by <em>n</em>/(<em>n</em>-1) before taking the square root, or equivalently divide the sum of squared deviations by <em>n</em>-1. The two converge for large datasets but disagree meaningfully when <em>n</em> is under 30.

The naive two-pass formula <code>variance = sum((x - mean)&sup2;) / n</code> requires the full mean before it can start accumulating squared deviations, and it suffers catastrophic cancellation when the values are large and close together. Welford&apos;s 1962 algorithm updates a running mean and a running sum of squared deviations in one pass using a numerically stable recurrence. Knuth describes it in <em>TAOCP</em> Vol. 2, and every serious stats library uses it or a variant internally.

No. The calculator is a client-side Preact component, and the parser, summariser, and Welford accumulator all live in that component. There is no fetch call to a backend, no analytics event attached to your dataset, and no localStorage write. You can paste sensitive data (salary figures, medical measurements, proprietary metrics) with the same confidence as pasting into a desktop app.

Strictly speaking every value is tied for highest frequency, so there is no unique mode. Different textbooks handle this differently: some say there is no mode, others say every value is a mode. This tool takes the second, more literal view and lists all values. If you see a huge mode list, that is the signal that your data has no repeat.

The tool sorts the values ascending and takes the arithmetic mean of the two middle elements. For <em>n</em> = 6 that is <code>(sorted[2] + sorted[3]) / 2</code>, using zero-based indexing. This matches the definition used by <code>numpy.median</code>, <code>R</code>&apos;s <code>median()</code>, and ISO 80000-2. Some older textbooks pick the lower of the two instead, which the tool does not do.

Yes. The parser splits on any of commas, semicolons, tabs, spaces, and newlines, and tolerates mixed delimiters, so a single-column CSV paste from a spreadsheet or a newline-separated log both work. Values that fail <code>Number()</code> are silently ignored, so a header row like &quot;value&quot; at the top of the paste will be skipped instead of crashing the count.

Somewhere north of a million values per run is handled comfortably on a modern laptop; the bottleneck is the copy-to-sort step for the median rather than the Welford pass. For datasets larger than that, or for streaming situations where you cannot hold everything in memory, switch to a tool that can work incrementally (pandas with chunked reads, DuckDB, or <code>awk</code>) or roll a server-side summary.

IEEE 754 double-precision floating point has 52-bit mantissa resolution (about 15 to 17 decimal digits). Summing thousands of numbers with fractional parts can accumulate enough rounding error that the displayed sum deviates from the true mathematical sum by a few ULPs. Welford&apos;s algorithm controls this for the variance; for the sum itself a Kahan summation would eliminate it entirely but at a small performance cost.

Range is the single number <code>max - min</code>, useful but highly sensitive to outliers. Variance is the average squared deviation from the mean, expressed in the square of the original unit. Standard deviation is the square root of variance, back in the original unit, and is the usual measure of spread because it is directly comparable to the mean. Together they give three increasingly informative views of how spread out the data is.

Not in the current build. The panel shows the five measures of central tendency plus spread metrics (variance, standard deviation, range) but does not compute Q1, Q3, the interquartile range, or arbitrary percentiles. Those live in a separate statistical summary tool, or you can get them from <code>numpy.percentile</code> or a spreadsheet function like <code>QUARTILE.INC</code>.

Sort stability does not affect the results because equal values are indistinguishable for median, mode, min, and max. V8, SpiderMonkey, and JavaScriptCore all use stable sorts in modern versions.

Yes. Paste the ages as a comma- or newline-separated list and the median row gives the central age in seconds, no special "median age calculator" branding required. For a sample of 17 ages it is the 9th value in sorted order; for an even count it is the mean of the two middle values. Use the same input box for any other midpoint statistic - median income, median response time, median sentence length - because the formula is the same.

It is built for elementary statistics use. Mean, median, mode, range, variance, and standard deviation are the six descriptive measures that appear in every introductory textbook, and the panel labels them in the same order. Students can paste a small dataset, see all six side by side, and verify hand calculations. For inferential statistics - confidence intervals, hypothesis tests, regression - move to a dedicated package like R or Python because that level of analysis is out of scope here.