Statistics Calculator

Calculate mean, median, mode, variance and standard deviation

What is it and how does it work?

Descriptive statistics summarise a dataset with a handful of numbers that capture its centre, spread and shape. Rather than reading hundreds of raw values, you get measures like mean (average), median (middle value), mode (most frequent value), standard deviation (typical distance from the mean), variance, range, and percentiles — all at a glance. These are the first things a data analyst checks when encountering a new dataset.

This calculator accepts a list of numbers (comma or newline separated) and computes the full descriptive statistics suite: count, sum, minimum, maximum, range, mean, median, mode, variance, standard deviation, and quartiles (Q1, Q2, Q3). It distinguishes between population and sample standard deviation — a detail that matters when your data is a sample rather than the whole population.

Common use cases

• Grade analysis: enter student scores to find the mean and median grade, identify outliers via the min/max, and see the spread through standard deviation.
• Performance benchmarking: paste response times from a load test to find median latency (more robust than mean for skewed data) and p75/p90/p95 percentiles.
• Quality control: check whether a manufacturing measurement dataset has a standard deviation within tolerance before accepting a production batch.

Frequently asked questions

When should I use median instead of mean?

Use median when your data is skewed or contains outliers. A dataset of salaries where most earn $50k but a few earn $1M has a mean of ~$200k that misrepresents most people. The median ($52k) is more representative. Mean is preferred for symmetric distributions without outliers.

What is the difference between population and sample standard deviation?

Population SD divides by N (all data points); sample SD divides by N-1 (Bessel's correction). Use sample SD when your data is a subset drawn from a larger population — the N-1 correction compensates for the fact that a sample tends to underestimate the true population spread.

What do Q1, Q2 and Q3 mean?

Quartiles divide sorted data into four equal parts. Q1 (25th percentile) is the value below which 25% of data falls; Q2 (50th percentile) is the median; Q3 (75th percentile) is the value below which 75% falls. The IQR (interquartile range, Q3 − Q1) is a robust measure of spread.

What is a bimodal distribution and how does it affect the mode?

If two values appear equally often as the most frequent, the dataset is bimodal — there are two modes. This often indicates two distinct subgroups in the data (e.g., two peaks in height data combining men and women). The calculator reports all modes when multiple values tie.

Math

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