Grafolyn

Statistics Calculator

Summary statistics, distributions, confidence intervals and hypothesis tests, with the working shown and every chart exportable. Nothing is sent to a server: your data stays on your device.

Mean, median, quartiles, histogram and box plot

No values yet

Enter at least one number to see the summary. Non-numeric text, such as a header row, is ignored.

What this covers

Five panels, matching the order a statistics problem usually goes in: work out the summary statistics, look at the shape of the data, find a probability, build an interval, then test a hypothesis.

One variable

Paste a column of numbers and get the full summary: n, mean, median, mode, the five-number summary, both standard deviations, variance, range, IQR, standard error, skewness and excess kurtosis, plus any outliers by the 1.5 × IQR rule. A histogram and a box plot are drawn alongside, and the bin count is adjustable.

The output is ordered and labelled to match the TI-84's 1-Var Stats screen, so you can read down both lists in parallel when checking your work.

Two variables

Paste two columns for the means and standard deviations of each variable, the sums, covariance, correlation coefficient r, r², and the least-squares slope and intercept. A scatter plot with the fitted line follows, and eight regression models are available: linear, quadratic, cubic, quartic, exponential, logarithmic, power and sinusoidal.

Distributions

Normal, Student's t, chi-square, binomial and Poisson. Choose a region — left tail, right tail, between two values, or exactly a value for the discrete distributions — and the probability is shown with the region shaded on the curve.

The shading matters more than it looks. The commonest error on this topic is not arithmetic, it is answering a different question from the one asked. Someone who needed P(X > 120) and computed P(X < 120) sees immediately that the shading is on the wrong side; a bare decimal would have looked perfectly reasonable.

Confidence intervals

For a population mean, a population proportion, or the difference of two means. Each result shows the point estimate, the margin of error, the standard error, the critical value and the degrees of freedom — not just the interval — because that is what the working requires.

Hypothesis tests

One-sample z and t tests for a mean, a z test for a proportion, and a two-sample test for the difference of means. You get the test statistic, the p-value, the critical value, a written conclusion in the form a course expects, and a shaded sampling distribution showing where the statistic fell.

Conventions, stated openly

Statistics has several places where reputable sources genuinely disagree. Rather than pick silently, here is what this tool does and why.

Choice What we do Why
Quartiles Median of each half, excluding the median when n is odd Matches the TI-84 and most US textbooks. Excel and R interpolate and can differ on small samples.
Standard deviation Both reported, sample first Sx (n−1) is almost always the one wanted; σx (n) only when the data is the whole population.
Interval for a mean t by default z is only correct when the population σ is genuinely known, which is rare outside textbook exercises.
Two-sample test Welch's by default The pooled test assumes equal variances and misbehaves when they differ. Welch's costs almost nothing when they are equal.
Proportion test SE Uses the null proportion A test asks what would happen if the null were true, so the null value belongs in the standard error.
Outliers Beyond 1.5 × IQR from the nearer quartile The standard rule, and the one box plots are built on.

On accuracy

The underlying functions are the part you have no way to check by eye, so they are worth being specific about. The normal CDF uses a Chebyshev-fitted rational approximation rather than the widely copied textbook polynomial, which loses precision badly in the tails — exactly where p-values live. The inverse normal adds a Halley refinement step to reach roughly machine precision. The t and chi-square distributions are built on continued-fraction expansions of the incomplete beta and gamma functions.

All of it is tested against published table values, including in the far tail where a careless implementation quietly returns nonsense. Being accurate to the fourth decimal is not a detail here: everything built on top of these functions inherits their error.

What it does not do

Worth knowing before you rely on it:

Questions

Why does this give a different quartile to Excel?

Because there are several accepted methods and they genuinely disagree on small samples. This uses the method the TI-84 and most US textbooks use: split the sorted data at the median, excluding the median itself when n is odd, then take the median of each half. Excel QUARTILE and R default to interpolating instead. Neither is wrong; check which your course expects.

What is the difference between Sx and sigma-x?

Sx is the sample standard deviation, dividing by n minus 1, and is what you use when your data is a sample from a larger population. Sigma-x is the population standard deviation, dividing by n, and is only correct when your data is the entire population. Almost every homework question wants Sx.

Should I use z or t for a confidence interval?

Use t unless the question actually gives you the population standard deviation sigma, which is rare outside textbook exercises. If you computed the standard deviation from your sample, you need t. The tool defaults to t for exactly this reason.

Why is the standard error different in a proportion test and a proportion interval?

A test computes the standard error using the null proportion, because it asks what would happen if the null were true. An interval uses the sample proportion, because there is no null to assume. This is why a test and an interval can occasionally disagree near the boundary, and it is a favourite exam question.

Does this work for AP Statistics?

Yes. It covers one- and two-variable statistics, the normal, t, chi-square, binomial and Poisson distributions, confidence intervals and hypothesis tests for means and proportions, using the same conventions as the TI-84. You cannot use it during the exam itself, though, since no web tool is permitted.

Can I export the charts?

Yes. Every chart has SVG and PNG buttons. SVG gives a true vector file with selectable text that stays sharp at any size, which is the one to use for a printed lab report.