Log-Normal Distribution μ & σ Calculator
Calculates the PDF, CDF, mean, median, mode, and variance of a log-normal distribution from its log-scale parameters μ a...
Probability, sampling, and descriptive statistics made readable.
Means, medians, standard deviations, confidence intervals, and sample size planning — with formulas and worked examples for each tool.
Calculates the PDF, CDF, mean, median, mode, and variance of a log-normal distribution from its log-scale parameters μ a...
Calculates F-ratio = MS_between / MS_within from sum of squares between and within groups. Returns F, degrees of freedom...
Calculates the Mann-Whitney U statistic from group sizes and the rank sum of group 1 to test for differences between two...
Calculates probability mass, mean μ = (a+b)/2, variance σ² = (n²−1)/12, and P(X ≤ k) for a discrete uniform distribution...
Calculates Spearman's rank correlation coefficient ρ from the sum of squared rank differences and sample size.
Calculates Spearman's rank correlation coefficient rs from the sum of squared rank differences and number of observation...
Calculates Kendall's tau τ = (C − D) / (n(n−1)/2), where C is concordant pairs and D is discordant pairs. Robust alterna...
Computes OLS regression slope b1 and intercept b0 from summary statistics (means, variances, covariance), and predicts ŷ...
Calculates the confidence interval for a population mean from sample mean, known standard deviation, sample size, and co...
Calculates the probability of exactly r failures before the k-th success in independent Bernoulli trials using the negat...
Calculates OLS regression coefficients from summary statistics: slope b = Sxy/Sxx, intercept a = ȳ − b·x̄, R² = Sxy²/(Sx...
Calculates the interquartile range (IQR), Tukey lower/upper fences for outlier detection, and box-plot summary from Q1,...
Calculates the one-sample Kolmogorov-Smirnov test statistic D from the maximum deviation between empirical and theoretic...
Given Q1, median, Q3, min, and max, calculates IQR = Q3 − Q1, inner fences (Q1 − 1.5×IQR, Q3 + 1.5×IQR) for outlier dete...
Calculates the total probability of event B using the law of total probability: P(B) = P(B|A₁)·P(A₁) + P(B|A₂)·P(A₂) + P...
Calculates the minimum sample size needed for a survey or proportion estimate at a specified confidence level and margin...
Calculates the coefficient of variation (CV) as a percentage to compare variability between datasets with different mean...
Applies Chebyshev's inequality to give a distribution-free bound on the probability of a value lying more than k standar...
Calculates odds ratio OR = (a·d)/(b·c) and relative risk RR = (a/(a+b)) / (c/(c+d)) from a 2×2 exposure/outcome continge...
Calculates the 10% trimmed mean (removes top 10% and bottom 10%) given n, overall mean, and the sum of the α-fraction va...
Applies Bayes' theorem to update a prior probability with new evidence, outputting the posterior probability and likelih...
Estimates standard error from a sample using the bootstrap approximation from sample standard deviation and sample size.
Calculates sample covariance Cov(X,Y) = [ΣXY − (ΣX)(ΣY)/n] / (n−1) and population covariance / (n). Also shows the sign...
Calculates the log-normal mean E[X] = exp(μ+σ²/2), median exp(μ), mode exp(μ−σ²), and variance (e^(σ²)−1)·e^(2μ+σ²) from...