What descriptive statistics does
Before you test anything, model anything or conclude anything, you describe. Descriptive statistics takes a raw pile of numbers and answers three questions about it: where does it live (location), how widely does it disagree with itself (spread), and what shape does it make (shape)? The calculators in this section cover every standard answer to those questions.
Location: the averages
Mean Calculator
The balance point of the data.
Median Calculator
The middle value. It holds up well against outliers.
Mean, Median & Mode
All three averages compared.
Spread: how far values stray
Standard Deviation
The typical distance from the mean.
Variance
The mean squared distance from the mean.
Interquartile Range
The spread of the middle half.
Position: quartiles and summaries
Quartile Calculator
Q1, median, Q3.
Five Number Summary
The box-plot skeleton.
Full Descriptive Summary
Everything in one pass.
Percentile Rank
Where one score stands in the group.
Decile Calculator
The nine cuts into tenths.
Hypothesis tests
One-Sample t-Test
One mean against a claim, with effect size.
Two-Sample t-Test
Welch and pooled comparison of two means.
Paired t-Test
Before/after and matched-pairs tests.
One-Sample z-Test
For a genuinely known population SD.
One-Proportion z-Test
One rate against a claimed value.
Two-Proportion z-Test
Compare two rates, the A/B test workhorse.
Test Statistic Calculator
Four core tests from summary statistics.
P-values, critical values & intervals
P-Value Calculator
From z, t, chi-square or F statistics.
Critical Value Calculator
The fence for any α, any family.
Confidence Interval (Mean)
t-based intervals at five levels.
Proportion CI
Wilson and Wald intervals.
Difference of Means CI
Welch interval for μ1 − μ2.
Margin of Error
Margins and the sample sizes behind them.
P-Value from r
Significance of a correlation, from r and n.
Significance Level
Family-wise error when tests multiply.
Paired t-Test CI
The interval for a mean difference.
Regression CI
Slope, mean response and prediction intervals.
Probability, counting & distributions
Probability Calculator
Unions, intersections, conditionals. Relationship first.
Bayes' Theorem
Update a belief with evidence. Base rates included.
Combinations
C(n, r), with the order question settled first.
Binomial Probability
Exactly, at most, at least, all on one chart.
Poisson Probability
Counts from a rate, window converted.
Central Limit Theorem
What averaging does to noise: σ/√n in action.
Survey Sample Size
The 385 behind every poll, with the FPC.
Expected Value
E(X) and spread for any discrete distribution.
Odds Calculator
Probability and odds, converted both ways.
Coin Flip Probability
Heads counts for any n and bias.
Dice Probability
Every sum for up to six dice.
Random Number Generator
Fresh uniform draws on every click.
Permutations & Combinations
The order question, answered in numbers.
Combinations with Repetition
Multisets by stars and bars.
Geometric Distribution
The wait for the first success.
Hypergeometric Distribution
Draws that change the deck.
Negative Binomial
The wait for the r-th success.
Normal Approximation
The bell against the exact binomial.
Slovin's Formula
n = N/(1 + Ne^2), assumptions stated.
Cochran's Formula
The explicit sample-size formula.
Finite Population Correction
The small-population discount.
Response Rate
Three survey rates, honestly separated.
Beyond the t-test: ANOVA, chi-square, ranks & planning
One-Way ANOVA
Three or more means, one gatekeeper F.
Chi-Square Independence
Association in contingency tables, with Cramér's V.
Chi-Square Goodness of Fit
Do the counts fit the claimed distribution?
Mann-Whitney U
The rank-based two-sample test.
Wilcoxon Signed-Rank
Paired differences, ranked.
Effect Size
Cohen's d, Hedges' g, Glass's Δ, with a plain-language translation.
Test Power
Power and the n a study actually needs.
Correlation Test
Is r distinguishable from zero?
Two-Way ANOVA
Two factors and their interaction, balanced designs.
Fisher's Exact Test
Exact p-values for 2x2 tables.
Levene's Test
Equality of variances, Brown-Forsythe included.
One-Sample Variance Test
Chi-square test of a single variance.
Seeing the data: chart makers
Histogram Maker
The shape of a dataset, bin by bin.
Box Plot Maker
The five-number summary as a picture, outliers included.
Dot Plot Maker
Every value visible on the number line.
Which spread should you pair with which centre?
Mean travels with standard deviation; median travels with IQR. The first pair uses every value and suits symmetric data; the second pair resists outliers and suits skewed data. Mixing them, a median with a standard deviation, usually signals the writer has not looked at their own data's shape.