Statistics, worked through

Five instruments that show every intermediate step — deviations, sums of squares, critical values — not just a final number. Everything runs in your browser.

Instrument Index

5 online / 27 queued
InstrumentInputPrimary output
Mean, Median & ModeData listFull descriptive summary
Standard DeviationData listσ and s, step by step
Z-ScoreValue + μ + σz and percentile
Confidence IntervalSample statsLower and upper bound
Linear RegressionPaired x, yy = a + bx, r, R²
Every instrument shows its full working — deviations, sums of squares, critical values — not just a final number.

What this site is for

Most statistics calculators online give you an answer and nothing else. You paste in numbers, a figure appears, and you are exactly as capable as you were before. That is fine if you already know what you are doing and just want to avoid arithmetic. It is useless if you are a student trying to understand a method, a researcher checking a result by hand, or an analyst who needs to explain to someone else how a figure was reached.

DatrixCalc is built the other way round. Every instrument here shows the intermediate steps: the deviations from the mean, the sum of squares, the critical value it looked up and why, the degrees of freedom it used. The final number is the smallest part of the output.

Everything runs in your browser. Nothing you paste is transmitted, logged or stored — there is no server-side processing on this site at all. That matters more than it sounds for statistics work, because the data people paste into these tools is frequently confidential: unpublished research, clinical measurements, commercial figures, exam marks.

Start with the right instrument

The five tools currently online cover the sequence most analyses actually follow, and they chain together. A short guide to which one you want:

If your question is…Use
What does this data look like overall?Mean, Median & Mode
How spread out is it?Standard Deviation
How unusual is this one value?Z-Score
How precise is my estimate of the average?Confidence Interval
Do these two variables move together?Linear Regression

The three ideas everything else is built on

Centre

A single number standing in for a whole dataset. The mean is the arithmetic average and uses every value, which makes it powerful and fragile in equal measure — one extreme observation drags it. The median is the middle value once sorted, and ignores how extreme the extremes are, which makes it robust. The mode is the most frequent value, and is the only one of the three that works on categorical data.

The choice between them is not a technicality. Reporting mean household income where a handful of very high earners exist produces a figure almost nobody actually earns; the median describes the typical household far better. Any time mean and median diverge substantially, the distribution is skewed, and that divergence is itself a finding worth reporting.

Spread

Two datasets can share a mean and be nothing alike. Standard deviation measures the typical distance of an observation from the mean, in the original units. It is the foundation of almost everything inferential: z-scores are distances measured in standard deviations, confidence intervals are built from the standard error which is derived from the standard deviation, and effect sizes express differences in standard deviation units.

The n vs n−1 question. Population standard deviation divides by n; sample standard deviation divides by n−1. The correction exists because a sample's own mean sits closer to its own data than the true population mean does, which systematically understates spread. Dividing by n−1 — Bessel's correction — compensates. Use the sample formula unless you genuinely have every member of the population.

Uncertainty

Any statistic computed from a sample is an estimate, and estimates have error bars. A confidence interval expresses that directly: a range of plausible values for the true population figure, given what you observed. It is the single most useful habit in applied statistics, because it forces the honest question that a bare point estimate lets you dodge — how much would this number move if I collected a different sample?

Common mistakes these tools will not catch

A calculator validates arithmetic, not reasoning. The most consequential errors in statistics happen before any number is entered:

  • Correlation read as causation. Ice cream sales correlate with drownings. Both track summer temperature. A regression line has no opinion on which variable causes which, or whether a third variable drives both.
  • The wrong measure of centre. Using a mean on strongly skewed data — income, response times, house prices — produces a technically correct number that misdescribes the typical case.
  • Population formula on a sample. Understates spread, which narrows confidence intervals and inflates apparent significance. The error compounds through every downstream calculation.
  • Extrapolating a regression. A line fitted between x = 10 and x = 50 says nothing reliable about x = 200. The relationship may be linear only within the range you observed.
  • Ignoring how the data arrived. No amount of correct arithmetic rescues a biased sample. If your respondents self-selected, your confidence interval is a precise statement about a group that does not represent the population you care about.

Notes on precision and method

A few things worth knowing about how these instruments compute:

  • Quantiles use linear interpolation between order statistics — the method R calls type 7 and the one Excel's PERCENTILE.INC uses. Other conventions exist and will give slightly different quartiles on small datasets. Where it matters, the tool says which it used.
  • The normal cumulative distribution is evaluated with the Abramowitz & Stegun 7.1.26 rational approximation, accurate to about 1.5 × 10−7 — far tighter than any published table.
  • Results are displayed to four decimal places by default, switching to scientific notation for very large or very small magnitudes. Full precision is retained internally throughout; only the display is rounded.
  • Every tool states its assumptions on the page. Where a method requires approximate normality, a minimum sample size, or independent observations, that is written down rather than left implicit.

What is queued

Twenty-seven further instruments are planned, in rough priority order: p-value from any test statistic, A/B test significance, one- and two-sample t-tests, combinations and permutations, the normal, binomial and Poisson distributions, percentiles and quartiles, outlier detection, chi-square, odds ratio and relative risk, and a frequency distribution builder. We add tools slowly and finish them properly rather than shipping thin pages. If there is one you keep needing, send it through — requests reorder the queue.

Frequently asked questions

Is my data sent anywhere?
No. Every calculation is JavaScript executing in your browser on the page you already loaded. There is no server-side processing, no logging and no storage. Closing the tab discards everything. The only things kept locally are your theme preference and your cookie choice.
Can I use these for coursework or a thesis?
For working through problems and checking results, yes — that is exactly what they are for. For anything submitted or published, verify the figures independently, ideally in software your institution recognises, and cite that. These are educational instruments, not validated statistical software.
Why do my quartiles differ from another calculator?
Because there are at least nine defensible ways to compute a quantile, and different packages pick different ones. We use linear interpolation between order statistics (R type 7, Excel PERCENTILE.INC). Minitab and some textbooks use a different convention. On large datasets the difference is negligible; on ten observations it can be visible.
How many data points do I need?
It depends entirely on the method. Descriptive statistics work on any n, though a mean of three numbers tells you very little. Confidence intervals using the t-distribution are valid at small n if the underlying data is roughly normal. Regression wants at least 20 to 30 paired observations before the slope estimate is stable enough to trust.
Do you handle missing values?
Anything that does not parse as a number is skipped, and the tool reports how many values it actually used. Check that count against what you expected — a mismatch usually means a stray character, a thousands separator, or a text label that came along with the paste.

Instruments