Overview
What this calculator gives you
Paste a list of numbers and get every common descriptive statistic at once: count, sum, mean, median, mode, range, minimum, maximum, variance, and standard deviation (both sample and population). It accepts numbers separated by commas, spaces, semicolons, or new lines, so you can paste straight from a spreadsheet column.
The three averages
Mean, median, and mode
"Average" is ambiguous — there are three, and they answer different questions.
Mean (arithmetic average)
Add every value and divide by the count. (2 + 4 + 9) / 3 = 5. The mean uses all the data but is sensitive to outliers — one huge value drags it up.
Median (the middle)
Sort the values; the median is the one in the middle (or the average of the two middle ones). It ignores how extreme the outliers are, which makes it the honest "typical value" for skewed data like income or house prices.
Mode (most frequent)
The value that appears most often. Useful for categorical or repeated data ("most common shoe size"). A dataset can have no mode, one mode, or several.
Reading skew
When mean and median diverge
If the mean is much higher than the median, the data is right-skewed — a few large values pull the average up. Classic example: in a room with 9 people earning $50k and one earning $5 million, the mean income is $545k but the median is $50k. The median tells the truer story of a "typical" person.
Report more than one
Measuring spread
Standard deviation and variance
The averages tell you the center. Standard deviation tells you how spread out the data is around that center.
- Low standard deviation: values cluster tightly near the mean
- High standard deviation: values are widely scattered
- Variance is the standard deviation squared — same information, different units
For a bell-shaped (normal) distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. This is the "68-95-99.7 rule".
The n vs n−1 question
Sample vs population standard deviation
This trips up students constantly. There are two formulas:
Population (divide by n)
Use this when your data IS the entire group you care about — every student in a class, every product in a batch. You have the whole population.
Sample (divide by n−1)
Use this when your data is a SAMPLE drawn from a larger population you're trying to estimate. Dividing by n−1 (Bessel's correction) compensates for the fact that a sample tends to underestimate the true spread. This is the more common real-world case, so when in doubt, use the sample value.
Who needs this
Common uses
Students
Homework and exam prep for statistics, algebra, and science courses. See every step's result at once.
Teachers
Summarize class test scores: mean for the average, median for the typical student, standard deviation for the spread.
Researchers
Quick descriptive statistics before running deeper analysis. Sample standard deviation for inferential work.
Analysts
Summarize a column of metrics — response times, sales figures, survey scores — without opening a spreadsheet.
Quality control
Monitor consistency. A rising standard deviation in measurements signals a process drifting out of control.
Sports & fitness
Average pace, most common rep count, the spread in your lap times across a season.
Behind the scenes
Privacy and how it runs
Runs in your browser
Common questions
How do I calculate the mean?
Add all the numbers, then divide by how many there are. For 5, 10, 15: sum is 30, count is 3, mean is 10. The calculator does this and shows the sum and count separately.
What if my data has two modes?
That's bimodal data — both modes are listed. If three or more values tie for most frequent, all are shown. If every value is unique, there's no mode.
Why is my standard deviation different from another tool?
Almost always sample vs population. We show both. If another tool gives a slightly larger number, it's probably using the sample formula (n−1); a slightly smaller one uses population (n).
Can I paste data from Excel or Google Sheets?
Yes. Copy a column and paste it in — the new-line separation is handled automatically. Mixed separators (commas and spaces and line breaks together) also work.
What's the range?
The difference between the largest and smallest value: max minus min. It's the simplest measure of spread, though it only uses two data points so it's sensitive to outliers.
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Last reviewed: · Methodology based on US building code standards, contractor pricing surveys, and manufacturer specifications.