Statistics

Paste one or more columns (tabs, commas, or spaces; an optional header row), or open a CSV.

Describe: n, mean, median, modes, sample and population standard deviation and variance, standard error, a confidence interval for the mean (t-based), quartiles (Excel/R type 7), IQR, skewness, excess kurtosis, and geometric and harmonic means — with a histogram, a fitted normal curve, and a box plot that marks outliers beyond 1.5 IQR.
Regression: linear, polynomial (degree 2–8), exponential, logarithmic, and power fits by least squares, with R², adjusted R², RMSE, a residual plot, and prediction at any x. Exponential and power fits are linearised with logarithms.
Correlation: Pearson and Spearman matrices for every pair of columns, with significance.
Distributions: normal, t, χ², F, exponential, uniform, binomial, and Poisson — density, cumulative probability, tails, and quantiles, with the area shaded.
Hypothesis tests: one-sample, Welch and pooled two-sample, and paired t-tests; χ² goodness of fit; and one- and two-proportion z-tests, each with a p-value and a sentence saying what it does and does not show.

Probabilities use the regularised incomplete gamma and beta functions; quantiles are found by bisection to about 13 significant digits.

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool.

Linking to an example

Companion to chapters 11, 12, 30, 31 and 33 of Mathematics, Reconnected. Every setting has a short parameter, and the tab comes from the # part of the address, for example /tools/stats/?data=2.1 3.4 2.9 4.0 3.3 2.7#describe or ?dist=normal&params=100. Long data sets are better shared with Share link, which compresses them into ?s=.











Tab
Parameter
Meaning
Example




all
data
the data: one line of numbers is one column; otherwise rows separated by | (or new lines), columns by spaces, commas or tabs, with an optional header row
data=x y|1 2|2 4


#describe
col, conf, bins
column (from 1), confidence level, histogram bins
conf=0.99


#regression
xcol, ycol
the x and y columns (from 1; default 1 and 2)
xcol=1&ycol=3


#regression
model, deg
linear, poly (with degree deg), exp, log, or power
model=exp


#regression
at
predict ŷ at this x
at=14


#distributions
dist, params
normal, t, chi2, f, exponential, uniform, binomial, poisson, and its parameters in order
dist=binomial&params=10,0.5


#distributions
x, p
the value for P(X ≤ x) and the probability for the quantile
x=7


#tests
test
one, two (Welch), pooled, paired, chi, prop1, prop2
test=prop1


#tests
a, b
the columns for samples A and B (from 1)
a=1&b=2


#tests
alt, alpha
two, less or greater; the significance level
alt=greater


#tests
mu
μ₀ (t-tests), p₀ (one proportion), or expected counts (χ²)
mu=0.5


#tests
counts
successes and trials: x₁ n₁ or x₁ n₁ x₂ n₂
counts=61 100



example
one of the presets below (it also picks the tab); other parameters override it
example=ch31-coin




Presets:




ch11-braking-distance — UK Highway Code braking distances against speed: a quadratic fits


ch12-two-point-fit — 500 cells at hour 2, 4,000 at hour 5: y = 125·2ᵗ


ch12-cases-fit — Exponential fit to 11 days of cases, k ≈ 0.374, day 14 ≈ 2,238


ch30-binomial-7-heads — Ten fair coin flips: P(exactly 7 heads) ≈ 0.117


ch30-poisson — Poisson with λ = 3


ch30-exponential-bus — Waiting for a bus at rate 0.5 per minute: P(T ≤ 3)


ch30-normal-iq — IQ ~ N(100, 15²): P(X > 130) ≈ 0.0228


ch31-quartiles — Quartiles, IQR and an outlier (940) in a box plot


ch31-coin — 61 heads in 100 flips: z = 2.2, p ≈ 0.028


ch31-welch-t — Old against new build latencies: Welch t ≈ 3.23


ch31-chi-squared-die — Is the die fair? χ² = 3.8 on 5 df


ch31-regression — Latency against load: ŷ = 46 + 4x, predict at 8


ch31-ab-test — A/B test: 1,650 of 15,000 against 1,500 of 15,000, z ≈ 2.83


ch33-least-squares — The study data: least-squares line through 5 points

Sharing

Linking to an example