Statistics calculators
Every calculator here shows its steps and sits next to a short explainer and a worked example. The number gets your homework done; the steps get you the exam points.
Binomial probability calculator: exact, at least, at mostFind P(X = x), P(X >= 4), or P(X <= 3) for a binomial distribution. Enter n, p, and x. Worked example, mean and SD, and the BINS conditions checklist.Chi-square test calculator: 2x2 table and goodness-of-fitA chi-square test calculator finds expected counts, chi^2 = sum (O-E)^2/E, and df. A worked 2x2 table gives chi^2 = 14.0625 with df = 1.Confidence interval calculator (mean and proportion)Find a confidence interval for a mean or proportion. Enter your sample data to get the interval, margin of error, and z* or t* critical value.Empirical rule calculator: 68-95-99.7 intervalsAn empirical rule calculator finds the 68-95-99.7 intervals of a normal distribution. With mean 100 and SD 15 you get 85-115, 70-130, and 55-145.Expected value calculator: mean and SD of XFree expected value calculator for a discrete random variable. Enter outcomes and probabilities to get the mean and standard deviation, with steps.Five-number summary and boxplot calculatorA five-number summary calculator finds the min, Q1, median, Q3, and max, then the IQR and 1.5 x IQR fences to flag outliers and draw a boxplot.Margin of error calculator: formula and worked exampleMargin of error is a critical value times the standard error. Learn the proportion formula ME = z*sqrt(p-hat(1-p-hat)/n) with a worked poll example.Normal distribution calculator (area under curve)Find the area under the normal curve between any bounds. Enter the mean and standard deviation, then get left, right, between, or outside probabilities.One-sample t-test calculator with worked exampleFree one sample t test calculator. Enter your sample mean, standard deviation, and size to get t, degrees of freedom, and a p-value, with a worked example.P-value calculator (from z, t, or chi-square)Convert a z, t, or chi-square test statistic to a p-value: one- or two-tailed for z and t, right tail for chi-square, with worked examples.Proportion z test calculator: one and two-sampleRun a one or two proportion z test. The one-sample SE uses p0; the two-sample SE pools the proportions. See the formulas, conditions, and a worked example.Linear regression calculator (r, r-squared, line)Paste your x,y pairs to get the correlation coefficient r, r-squared, the least-squares line y-hat = a + bx, and each residual, with a worked example.Sample size calculator (target margin of error)Find the sample size for a target margin of error. For a proportion, n = (z*/ME)^2 times p*(1-p*) with p* = 0.5; round up. Worked AP examples.Standard deviation calculator (and variance)A standard deviation and variance calculator squares each deviation, then divides by n-1 (sample) or n (population). For 4, 7, 8, 10, 16, s ~= 4.47.Two-sample t-test calculator (Welch)Compare two independent means with a Welch two-sample t-test. Get the standard error, t statistic, degrees of freedom, and p-value, with a worked example.Z-score calculator: value to z to percentileA z-score calculator converts a raw value, mean, and SD into z = (x - mu) / sigma, then into a percentile. For 82, 70, 8 you get z = 1.5 and 93.32%.