Statistics Calculator (Mean, Median, Mode, Standard Deviation)
Compute mean, median, mode, range, variance, and standard deviation from a list of numbers.
What this calculates
Descriptive statistics summarize a dataset with a handful of numbers. Mean tells you the average; median tells you the middle; mode tells you the most common; range tells you the spread; standard deviation tells you how typical the spread is. This calculator computes all five from any list of numbers (separated by spaces, commas, or new lines).
Formula & how it works
Mean = sum ÷ count. Median = middle value (or average of two middle values for even-count data). Mode = most frequent value (can be multiple or none). Variance = mean of squared deviations from mean. Standard deviation = sqrt(variance). Population SD divides by n; sample SD divides by n−1 (Bessel's correction).
Worked example
Data: 5, 8, 12, 8, 15, 10. Sorted: 5, 8, 8, 10, 12, 15. Mean = 58/6 = 9.67. Median = (8+10)/2 = 9. Mode = 8 (appears twice). Range = 15 − 5 = 10. Variance (sample) = 13.07. SD = 3.62.
Frequently asked questions
When should I use mean vs median?
Mean is best for symmetric distributions. Median is more representative when there are outliers (e.g., income). The classic example: average net worth in a room with Jeff Bezos is meaningless; median is honest.
What's the difference between population and sample SD?
Population SD divides by N (used when you have the entire population). Sample SD divides by N−1 (used when estimating from a sample). For most real-world cases, use sample SD.
Can a dataset have no mode?
Yes — if every value appears once. Can also have multiple modes (bimodal, trimodal). Mode is most useful for categorical data, less so for continuous data.
How big a sample do I need?
Rule of thumb: at least 30 for the central limit theorem to kick in. Smaller samples are fine for summary stats but produce wide confidence intervals.