Compute mean, median, mode, variance, standard deviation, range and quartiles from a data set.
A descriptive statistics calculator computes mean, median, mode, standard deviation, variance, quartiles, and range from a data set. These summary statistics distil a complete data set into a few interpretable numbers — the foundation of every statistical analysis.
Mean tells you the central tendency; standard deviation tells you the spread; quartiles tell you the distribution shape. Always look at all three — a low mean does not always mean low values (it can mask high outliers), and a low standard deviation does not always mean tight data (it can mask bimodal distributions).
\bar{x} = \frac{1}{n}\sum x_i \;;\; s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2
Inputs: Data set: {2, 4, 4, 4, 5, 5, 7, 9}
Use median when the data has outliers, is skewed, or is ordinal (e.g. survey responses on a 1–5 scale). The median is robust — it ignores extreme values. Use mean for symmetric or near-normal data without outliers. Income, house prices, and engineering test results almost always need median for fair representation; weights, heights, and exam scores work fine with mean.
Dividing by n−1 gives the unbiased estimator of population variance (Bessel's correction). With a finite sample, dividing by n systematically underestimates the true population variance because the sample mean is itself estimated from the same data. The n−1 correction compensates. For large n (> 30) the difference is negligible; for small n it matters.
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