Every statistics formula is built from the same few raw ingredients — and this tool cooks them into finished results. Give it the sample size (n), the sum of values (Σx), the sum of squared values (Σx²), and a single observed value, and it derives the mean, the variance, and the z-score without needing the original dataset. A student who summarized 40 quiz scores as Σx = 3,200 and Σx² = 262,000 can recover the mean (80), the variance, and how unusual any single score was, all from two totals.

These summary statistics are the compressed form of data. Pollsters publish them, textbooks tabulate them, and calculators accept them because the full list of values is often long gone. The mean is Σx ÷ n; the variance uses Σx² to avoid re-summing squared deviations; the z-score places any observed value on the standard scale.

Enter your Sample Size (n), Sum of Values (Σx), Sum of Squares (Σx²), and the Observed Value (for z), and the tool returns the computed formulas' results — mean, variance, standard deviation, and z-score — ready to drop into homework or reports.

With the pre-filled defaults — Sample Size (n) 20, Sum of Values (Σx) 340, Sum of Squares (Σx²) 6,200, Observed Value (for z) 20 — the Statistics Formulas Sheet returns Mean (x̄ = Σx/n) 17.000000, Sample Variance (s² = (Σx²−nȳ²)/(n−1)) 22.105263, Std Deviation (s) 4.701623, Std Error (SE = s/√n) 1.051315, Coeff. of Variation (CV = s/x̄ × 100%) 27.6566%, Z-Score z = (x − x̄) / s 0.6381, 95% Range x̄ ± 2s 9.4032. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.