Máy tính thống kê và xác suất

Compare R-7, R-6 and Tukey conventions on the same sample, including how the selected method changes an outlier boundary.

Choose the divisor that matches whether you have the whole group or a sample, then inspect the worked calculation.

Compare the average with the middle and most common values before using one number to describe the data.

Descriptive statistics calculator: mean, median, mode, standard deviation, variance, quartiles, IQR, outliers, skewness and kurtosis, with a histogram.

Grade curve calculator: rescale a class's scores to a target mean and standard deviation, or add flat points, with z-scores and percentile ranks.

Binomial distribution calculator: exact P(X = k), P(X ≤ k), tails and ranges for binomial, Poisson, geometric, negative binomial and hypergeometric.

Normal distribution calculator: z-scores, the probability below, above or between values, and the value at any percentile (inverse normal).

t, chi-square and F distribution calculator: tail areas, p-values, densities and critical values, plus exponential and uniform distributions.

Confidence interval calculator for a mean (t or z), a proportion (Wilson or Wald) or a difference of two means, with the margin of error and both bounds.

Sample size calculator for surveys and studies: n for a margin of error on a proportion or mean, and the per-group n for a target power.

t-test calculator for one-sample, two-sample (Welch or pooled) and paired tests, plus z-tests for a mean or proportion: p-value, critical value, decision.

Chi-square test calculator for goodness of fit and independence in a contingency table: χ², p-value, expected counts and Cramér's V.

One-way ANOVA calculator: the F statistic, p-value, sums of squares, mean squares and η² for two or more groups, with the full ANOVA table.

Linear regression calculator: least-squares line of best fit with R², standard errors, p-values and predictions, plus polynomial and exponential fits.

Correlation coefficient calculator: Pearson's r or Spearman's rank correlation for paired data, with r², a t statistic and a two-sided p-value.

Calculate nCr and nPr exactly: combinations and permutations with or without repetition, for poker hands, lottery odds and PIN codes.

Calculate P(A or B), P(A and B) and P(A | B) for two events, or apply Bayes' theorem to a test result, with a probability tree and Venn diagram.

Exact probability of dice sums, coin-flip heads and streaks, drawing special cards from a deck and each 5-card poker hand, as a fraction and 1 in N.

Calculate expected value E[X], variance and standard deviation for a bet, game or decision from its outcomes and their probabilities or weights.

Convert odds between fractional, decimal and American (moneyline) formats and get the implied probability, worked in exact fractions.

Generate random numbers from a seed: integers in a range, decimals, lottery-style draws without repeats and dice rolls, repeatable with xoshiro256**.