Statistics calculators
A statistic is a summary, and every summary throws something away. These tools show what was discarded beside what was kept: the spread next to the mean, the sample size next to the confidence, the assumption next to the test that depends on it.
Average / Mean CalculatorMean, median and mode together with the spread, because which average is right depends on the shape of the data. One extreme value moves the mean and leaves the median where it was.Weighted Average CalculatorWeighted average with each item's contribution, and what a remaining item needs to score to hit a target. The gap against the simple average shows how much the weighting is doing.Median CalculatorThe median with the full summary alongside. The median resists outliers where the mean does not, which is why incomes and house prices are reported as medians and averages of them mislead.Mode CalculatorThe mode alongside the mean and median. Comparing all three is the fastest read on whether a distribution is skewed, and the mode is the only one that works on categories.Range and IQR CalculatorRange, quartiles and the interquartile range, with outliers flagged by the standard 1.5 rule. The IQR ignores the extremes entirely, which is exactly why it is more useful than the range.Standard Deviation CalculatorStandard deviation on both conventions, with the coefficient of variation that makes it comparable across datasets. A deviation of 5 means nothing until you know whether the mean is 10 or 10,000.Variance CalculatorVariance and standard deviation on both conventions. Dividing by n-1 rather than n is Bessel correction, and on small samples the two answers differ substantially.Z-Score CalculatorZ-score with the percentile and two-tailed p-value it implies, using the normal CDF.Confidence Interval CalculatorA confidence interval for a mean or a proportion. A 95 percent interval does not mean there is a 95 percent chance the true value sits inside this one: it means intervals built this way contain the true value 95 percent of the time.Sample Size CalculatorSample size for a survey, with the finite population correction. Precision costs quadratically: halving the margin of error needs four times the sample, which is why national polls stop at around a thousand.Correlation Coefficient CalculatorPearson correlation between two variables, with R squared and a caution about sample size. Correlation measures straight-line association only, and a strong curved relationship can show r near zero.Linear Regression CalculatorLeast-squares line of best fit, with R squared and a prediction. The line always passes through the mean of both variables, which is a useful check on any regression.