Statistics Calculator
Enter any set of numbers to find the mean, median, mode, range, variance, and standard deviation.
What is Statistics Calculator?
The statistics calculator takes any list of numbers and returns the core descriptive statistics: central tendency (mean, median, mode), spread (range, variance, standard deviation), and basic summaries (count, sum, min, max).
Separate your numbers with commas, spaces, semicolons, or new lines — the calculator handles all of them.
Formula
- Mean = Σx / n
- Median = middle value of the sorted list (average of the two middle values if n is even)
- Mode = most frequent value(s)
- Sample variance = Σ(x − mean)² / (n − 1)
- Population variance = Σ(x − mean)² / n
- Standard deviation = √variance
Use sample variance when your data is a sample from a larger population (most real-world cases). Use population variance only when you have the complete population.
Worked example
For data: 5, 8, 12, 15, 20, 22, 25, 28, 30, 35
- n = 10, sum = 200
- Mean = 20.0, Median = 21.0
- Range = 35 − 5 = 30
- Sample std dev ≈ 10.03
How to use this calculator
- Paste or type your numbers into the input box.
- Use any separator — commas, spaces, line breaks — it all works.
- Results update automatically as you change the data.
Frequently asked questions
When should I use median instead of mean?
When your data has extreme values (outliers) that would pull the mean in one direction. Income, home prices, and response times are usually reported as medians for this reason.
What is the difference between sample and population std dev?
If your numbers are the entire population (e.g., test scores for a whole class), use population (divide by n). If they are a sample from a larger group (e.g., a survey of 50 customers representing all customers), use sample (divide by n − 1). Sample std dev is larger — it corrects for the fact that a sample tends to slightly under-estimate the true population spread.
What does "no mode" mean?
When every number appears exactly once, there is no single most-frequent value, so no mode. Sometimes a data set is bimodal (two modes tied for most frequent) or multimodal — those are shown as a comma-separated list.
How accurate are the results?
Computations are done in double-precision floating point, accurate to about 15 decimal digits. Results are displayed rounded to 4 decimals by default.