Calculators that won't let you fool yourself.

Mean, Median & Mode

All three averages at once, with range and a number line — and when each one misleads.

Median

The middle value — the robust 50%-breakdown centre — plotted against the mean so you can see an outlier pull them apart.

Geometric Mean

The right average for growth and ratios, against the arithmetic and harmonic means — plus the true average return (CAGR) and the volatility drag the arithmetic mean hides.

Harmonic Mean

The right average for rates — with an average-speed mode that shows why 60 there and 30 back is 40, not 45 (you spend twice as long on the slow leg).

Weighted Mean

The weighted average for GPAs, grades and portfolios — each value’s contribution, the plain mean for contrast, and the result drawn as the data’s balance point.

Standard Deviation

Sample (n−1) and population (n) SD and variance, the full deviation table, CV and standard error — with ±σ bands.

Variance

Sample and population variance with every squared deviation drawn as a square — plus a mode that combines two variances (σ 3 and 4 make 5, not 7).

Mean Absolute Deviation

The average distance from the centre — about the mean and the median — beside the standard deviation, and why squaring makes the SD larger and outlier-sensitive.

Frequency

Relative Frequency

The full frequency distribution table — frequency, relative and cumulative — for values, categories or bins, with a histogram and ogive.

Grouped data

Grouped Data Mean & SD

Mean, variance and SD from a frequency table of classes — the full f·m working, with the midpoint-approximation caveat.

Frequency tables

Class Width

Histogram bin width = range ÷ classes, rounded up — with Sturges/√n/Rice suggestions, the intervals, frequencies and the honest catch that width changes the shape.

Charts

Pie Chart

Slice percentages and angles, drawn — beside a bar chart of the same data, because pies are hard to compare by eye.

Ranking

Percentile Rank

Where a score stands in a group — by all three definitions, because they disagree whenever values tie.

Ordering

Order Numbers

Sort any list least to greatest or greatest to least — and read off the order statistics it hands you: count, min, max, range, median.

Quartiles & Five-Number Summary

Q1, Q3, IQR and the box plot with outliers — by all three quartile methods, because they disagree on the same data.

Coefficient of Variation

Relative spread (SD ÷ mean) to compare variability across scales — one dataset or several, ranked by CV.

Error

Percent Error

Absolute, relative and percent error between a measured and a true value — plus percent difference when neither reading is the reference.

Standardising

Z-Score

Value ↔ z-score ↔ percentile, placed on a shaded normal curve.

Normal curve

Empirical Rule (68-95-99.7)

The 1σ/2σ/3σ ranges and how much of a bell curve each holds — plus Chebyshev's bound when it isn't normal.

Combined and conditional events, repeated trials, plus combinations (nCr) and permutations (nPr).

Conditional Probability

P(A|B) drawn as a probability tree — with the reverse P(B|A) beside it to expose the inversion fallacy, plus an independence test.

Birthday Paradox

Why 23 people give a better-than-even shared birthday — the famous curve, the pair count, and the contrast with someone sharing yours.

Dice & games

Dice Probability

The full distribution of any dice total (NdS) — average, spread, the odds of a target, and advantage/disadvantage.

Dice & games

Roulette Payout & Edge

Every bet's payout and true odds — and the house edge that quietly guarantees the casino wins.

Odds & betting

Implied Probability

Decimal, fractional and American odds ↔ probability — and the overround that makes the book's chances top 100%.

Dice & games

Coin Flip Probability

Heads odds and the full distribution, plus how likely a streak really is — and the gambler's fallacy.

Expected Value

The probability-weighted average of any payoff, with variance, SD and each outcome's contribution.

Diversity

Simpson's Diversity Index

Simpson's D, 1−D and the reciprocal (effective species), with Shannon, evenness and richness — diversity is richness plus evenness.

Ratings

Five-Star Rating

Average and Bayesian-adjusted star rating with the full breakdown — why a 5.0 from three shouldn't beat a 4.6 from thousands.

Sampling

Central Limit Theorem

The sampling distribution of the mean — standard error σ/√n and P(x̄ ≤ value), with the population and means drawn together.

Core inference

Confidence Interval

Mean, proportion, or difference between two groups — Wilson and Welch included.

Point Estimate

The MLE, Laplace, Jeffreys and Wilson estimates of a proportion — and why x/n misleads at small n or 0 successes (the rule of three).

Comparing means

t-Test

One-sample, two-sample (Welch/Student) and paired, from summary stats or raw data.

Test mechanics

t-Statistic

Just the t value — effect over standard error — for one-sample, two-sample (Welch/pooled) and paired data, with df, p and a shaded curve.

Known σ & proportions

Z-Test

One- and two-sample z-tests for means (known σ) and proportions — z, p, CI, effect size and a shaded curve.

Experiments

A/B Test

Conversion-rate significance and uplift with a difference CI — and blunt warnings about peeking and practical significance.

Several means

One-Way ANOVA

Compare 3+ groups: F, df, p, η² and ω², with the full ANOVA table.

Distribution-free

Nonparametric Tests

Mann–Whitney U, Wilcoxon signed-rank and Kruskal–Wallis — rank-based tests for non-normal data.

Association

Correlation & Regression

Pearson r with CI, the least-squares line and R², plotted with the fit.

Goodness of fit

Coefficient of Determination (R²)

The share of variance a model explains, from data or observed-vs-predicted — the variation split into explained and unexplained, and what a high R² can’t tell you.

Curve fitting

Nonlinear Regression

Quadratic, cubic, exponential, power and logarithmic fits with R² and a curve — and honest warnings on overfitting.

Curve fitting

Quadratic Regression

Fit a parabola y = ax² + bx + c — equation, R², the vertex and axis of symmetry, predictions and a plot, with the extrapolation trap spelled out.

Association

Covariance

Sample and population covariance with the correlation — and why covariance tells you direction but not strength.

Margin of Error

The ± margin for a proportion or mean, the interval, and the sample size for a tighter margin — sampling error only.

Standard Error

SE of the mean (s∕√n) or a proportion, with a 95% interval — and the standard error drawn against the standard deviation people confuse it with.

Categorical

Chi-Square Test

Independence in a table or goodness-of-fit, with Cramér's V and expected counts.

Exact 2×2

Fisher's Exact & McNemar

Exact tests for small or paired 2×2 tables — odds ratio, and two-sided and one-sided exact p-values.

Test mechanics

Degrees of Freedom

The df for every common test — t, Welch, χ², ANOVA and regression — with the formula and what df actually is.

Test mechanics

Critical Value

The z, t, χ² or F cut-off for any α — two-tailed, upper or lower — drawn on the curve, the table-lookup twin of the p-value.

Summarising

Descriptive Statistics

Centre, spread, shape and quartiles, with a histogram, box plot and outlier flags.

Probability & testing

Tail areas

p-value & Critical Value

Convert z, t, χ² or F statistics to p-values, or find critical values for any α.

Normal Distribution

Bell-curve probabilities below, above or between values — or the inverse, the value at a percentile — each with the z-score and a shaded curve.

Inverse Normal (invNorm)

Probability in, cut-off out — left, right or central. Finds critical values (central 95% → ±1.96) and percentile cut-offs, with the curve shaded.

Distribution Calculator

PDF/PMF, CDF, tails, intervals and quantiles for six distributions, with shaded plots.

Binomial Distribution

Every binomial probability at once — exactly, at most, at least — with the distribution drawn, the mean and SD, and the normal-approximation rule.

Poisson Distribution

Every Poisson probability at once from the rate λ — the rare-events distribution, with the curve drawn, mean = variance = λ, and an overdispersion warning.

Geometric Distribution

Trials until the first success — every probability from p, the mean of 1∕p, and why memorylessness makes the gambler’s fallacy a fallacy.

Negative Binomial

Trials until the r-th success — every probability, the mean r∕p, the geometric special case, and the overdispersed-count role.

Counting

Combinations & Permutations

nCr, nPr and both with-repetition variants at once, on a 2×2 grid of order against repetition — and which everyday question each answers.