Standard Deviation Calculator

Standard deviation quantifies how spread out values are around the mean. A small standard deviation means values cluster tightly around the average; a large one means they are widely spread. It is one of the most widely used statistics in research, quality control, finance, and data analysis. Entering data: Paste or type your values into the input box — separate them with commas, spaces, or new lines. The calculator accepts any numerical dataset. Remove commas from large numbers (use 1500 not 1,500). Click Calculate to process all values at once. Results: Count — total number of values in the dataset. Sum — total of all values. Mean (average) — sum divided by count. Median — middle value when sorted; more robust to outliers than mean. Mode — most frequently appearing value (multiple modes shown if tied). Range — difference between maximum and minimum. Variance — average of squared deviations from the mean. Standard deviation — square root of variance. The key measure of spread. Standard error of the mean — standard deviation divided by √n, used in hypothesis testing. Population vs. sample: Use Population mode when your dataset is the entire group you are describing (all test scores in one class, all products in one batch). Use Sample mode when your dataset is a subset of a larger population — the formula divides by n−1 instead of n to correct for the bias of sampling. Sample mode is correct for most statistical analysis in research and data science. Step-by-step working: Click Show Working to see the full calculation broken down: each deviation from the mean, each squared deviation, and the final formula. Useful for verifying calculations or understanding the math for homework and exam preparation. Common uses: test score analysis, process quality control (Six Sigma uses 3σ and 6σ benchmarks), financial return volatility, scientific measurement uncertainty, and academic statistics coursework.