Descriptive Statistics Calculator — Mean, Median, SD

Compute mean, median, mode, variance, standard deviation, range and quartiles from a data set.

About this calculator

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).

Formula

\bar{x} = \frac{1}{n}\sum x_i \;;\; s^2 = \frac{1}{n-1}\sum (x_i - \bar{x})^2

  • — Sample mean
  • — Sample variance (use n−1 not n)
  • s — Sample standard deviation = √s²
  • Median — 50th percentile (robust to outliers)

Worked example

Inputs: Data set: {2, 4, 4, 4, 5, 5, 7, 9}

  1. Mean = 40 / 8 = 5.0
  2. Median = (4 + 5)/2 = 4.5
  3. Mode = 4 (appears 3 times)
  4. Standard deviation s ≈ 2.14
  5. Q1 = 4, Q3 = 5.5; IQR = 1.5

Frequently asked questions

When should I use median vs mean?

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.

Why divide by n−1 instead of n for sample variance?

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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