Mean, Median, Mode & Standard Deviation Calculator Online Free
Paste a dataset separated by commas, spaces or newlines and instantly get the classic descriptive statistics: count, sum, mean (average), median, mode set, range, min/max, variance and both population and sample standard deviation. A frequency distribution chart shows how often each value appears so multimodal shapes are obvious. Everything runs in your browser — student homework, lab reports and survey summaries never leave your machine.
Mean, Median, Mode & Standard Deviation Calculator In-Browser Workspace
Input data or select files to begin. 100% private, client-side execution with zero server transmission.
How to Use Mean, Median, Mode & Standard Deviation Calculator
- Step 1: Paste or type numbers separated by commas, spaces, tabs or line breaks.
- Step 2: Click Calculate Statistics to run mean, median, mode and deviation math.
- Step 3: Read the four headline cards: Mean, Median, Mode and Range.
- Step 4: Expand the detail panel for count, sum, min/max, σ, sample s and variance.
- Step 5: Use the frequency bars to confirm mode(s) and spot duplicate values.
About Mean, Median, Mode & Standard Deviation Calculator
Descriptive statistics summarize a sample without assuming a probability model. The mean is the arithmetic sum divided by count (Σxᵢ / n) and is sensitive to outliers. The median is the middle value after sorting — or the average of the two middle values when n is even — and is robust to skew. The mode is every value that achieves the highest frequency; a dataset can be unimodal, bimodal or multimodal, so the tool returns an array. Range is max − min. Population variance σ² averages squared deviations by n; sample variance s² uses Bessel’s correction (n − 1) so the estimator is unbiased when the sample estimates a larger population. Population standard deviation σ is √σ²; sample s is √s². For a small dataset like 4, 7, 13, 2, 7, 5, 9, 7, 1, 3 the mean is 5.8, the median sorts to 6, the mode is 7 (appears three times), population σ is about 3.40 and sample s is about 3.58. Use sample s when your numbers are a draw from a process; use σ when you truly observe the entire population. The tool also reports sorted order so you can verify the median by hand.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population σ divides by n; sample s divides by n − 1 (Bessel correction). Use s when your data is a sample of a larger process.
Can a dataset have more than one mode?
Yes. Every value with the maximum frequency is returned — the list can be bimodal or multimodal.
When should I use the median instead of the mean?
With skewed data or outliers (income, reaction times), the median better represents a typical value.
Does empty or invalid input break the calculator?
Invalid tokens are ignored; if nothing numeric remains you get a clear error instead of NaN results.
Is my data uploaded?
No — parsing and math run entirely in the browser tab.