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Statistics & Probability
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Statistics & Probability Calculators
Descriptive statistics and probability tools for datasets, distributions, and combinatorics.
All tools
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σ
Standard Deviation Calculator
Compute sample (n−1) and population (n) standard deviation from a list of numbers.
σ²
Variance Calculator
Sample (n−1) and population (n) variance — the square of standard deviation.
%
Percentile Calculator
Find the value at the kth percentile in a dataset (linear interpolation).
ƶ
Z-Score Calculator
z = (x − μ) / σ — how many standard deviations a value is above or below the mean.
t
T-Score Calculator
t = (x̄ − μ₀) / (s/√n) — for testing a sample mean against a hypothesized population mean.
┃
Interquartile Range (IQR) Calculator
IQR = Q3 − Q1 — the middle 50% spread, robust to outliers.
CV
Coefficient of Variation (CV) Calculator
CV = σ / μ — relative variability as a percentage. Useful for comparing spread across different scales.
gm
Geometric Mean Calculator
GM = (x₁ · x₂ · ... · xₙ)^(1/n). Right "average" for ratios, growth rates, multiplicative quantities.
C(n,r)
Combinations Calculator C(n, r)
C(n, r) = n! / (r!(n−r)!). Number of ways to choose r items from n where order doesn't matter.
P(n,r)
Permutations Calculator P(n, r)
P(n, r) = n! / (n−r)!. Number of ways to arrange r items from n where order matters.
p
P-Value Calculator (z to p)
Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.
CI
Confidence Interval Calculator
CI = mean ± z × (σ/√n). 90 / 95 / 99 % standard intervals.
N
Normal Distribution Calculator (PDF + CDF)
Compute probability density and cumulative probability at x for given μ, σ.
B
Binomial Probability Calculator
P(X = k) = C(n,k) p^k (1−p)^(n−k). Probability of exactly k successes in n trials.
r
Pearson Correlation Coefficient
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² Σ(yᵢ−ȳ)²). Linear correlation [−1, 1].
t
Two-Sample t-Test (Welch's)
Test whether two means differ. t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂).
z
One-Sample z-Test
z = (x̄ − μ) / (σ/√n). Compare sample mean to known population.
χ²
Chi-Square Goodness-of-Fit
χ² = Σ(O−E)²/E. Test if observed frequencies match expected.
F
One-Way ANOVA F-Statistic
F = MS_between / MS_within. Test if 3+ group means differ.
y=mx+b
Linear Regression (Slope + Intercept)
y = mx + b via least squares. Returns m, b, r², SE.
n
Sample Size for Margin of Error
n = (z × σ / E)². Required sample size for given margin E at confidence z.
📊
Mean, Median & Mode Calculator
Paste a list of numbers to get the mean, median, mode, range, count, and sum — the core measures of central tendency.
📈
Standard Deviation Calculator
Compute sample and population standard deviation and variance from a pasted list of numbers, with the mean and formulas shown.
📦
Quartile, IQR & Outlier Calculator
Find Q1, Q2 (median), Q3, the interquartile range, and outliers using the 1.5×IQR rule from a pasted dataset.
🎯
Confidence Interval Calculator (Mean)
Build a confidence interval for a population mean from the sample mean, standard deviation, size, and confidence level using the t-distribution.
🧮
Bayes’ Theorem Calculator
Compute the posterior probability P(A|B) from the prior P(A), the evidence P(B), and the likelihood P(B|A).
🎲
Compound Probability Calculator (AND / OR)
Compute P(A and B), P(A or B), and P(A|B) for two events, whether they are independent or dependent.
🎂
Birthday Paradox Calculator
Find the probability that at least two people in a group share a birthday — the famous, counterintuitive birthday problem.
✳️
Chi-Square Test Calculator
Run a chi-square goodness-of-fit test from observed and expected frequencies — get the χ² statistic, degrees of freedom, and p-value.
📉
Linear Regression Calculator (Line of Best Fit)
Fit a least-squares line to paired X and Y data — get the slope, intercept, equation, correlation, and R².
🔗
Pearson Correlation Coefficient (r) Calculator
Compute Pearson’s r for two paired data columns, with R² and a plain-language interpretation of strength and direction.
📶
Histogram Bins Calculator
Find the optimal number of histogram bins and bin width by three rules — Sturges, Scott, and Freedman-Diaconis — from your data.
⚖️
Prisoner’s Dilemma Payoff Calculator
Enter a 2×2 payoff matrix to find each player’s dominant strategy, the Nash equilibrium, and whether it is a true prisoner’s dilemma.