A free statistics calculator that gives every descriptive statistic at once, on NIST's definitions, with a box plot.
Paste your numbers and get every statistic at once: mean, median, mode, standard deviation, quartiles and outliers.
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Your result
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This free statistics calculator gives every descriptive statistic from a list of numbers at once: mean, median, mode, range, quartiles, standard deviation, variance and outliers.
Paste your numbers from anywhere, and it draws them on a box plot with the outliers marked.
I built it because a list of numbers shouldn't need a spreadsheet and 10 formulas to understand. Every method follows the US government's NIST handbook, so you can cite it.
Here's what each statistic means, a worked example, and why tools sometimes disagree.
TL;DRKey takeaways
What is a statistics calculator?
A statistics calculator summarizes a list of numbers: where its center is, how spread out it is, and which values stand out.
It answers the questions a teacher, a researcher or a manager asks first about any data.
The statistics, and what they mean
There are 3 kinds: the center, the spread and the shape.
Center: mean, median and mode
The NIST handbook defines the mean as the sum divided by the count, the median as the middle of the sorted list, and the mode as the most frequent value.
A list can have no mode, or more than one.
Spread: standard deviation and range
The standard deviation is the typical distance from the mean. NIST divides by N − 1 for a sample, which corrects for the sample being smaller than the population.
The range is the largest value minus the smallest. The IQR is the range of the middle half.
Outliers
NIST's fences sit 1.5 × IQR below Q1 and above Q3. A value beyond them is a mild outlier, and beyond 3 × IQR an extreme one.
A worked example
Here's the example the calculator loads, 12 test scores:
The quartiles are 68.5 and 79.5, so the IQR is 11. The fences sit at 52 and 96, so the top score of 95 is high but not an outlier.
Why tools disagree on quartiles
There are at least 9 published ways to find a quartile. This calculator uses NIST's p(N + 1) method, while Excel's QUARTILE.INC uses another.
On long lists they agree closely. On a short list, Q1 and Q3 can differ by a fraction, and both are correct.
Mistakes to avoid
These are the ways statistics mislead.
- Using the population standard deviation for a sample, which makes the spread look smaller
- Quoting the mean of skewed data, like incomes, when the median describes it better
- Deleting outliers without checking whether they're real
- Comparing quartiles from 2 tools that use different methods
Who is the statistics calculator for?
It's for students, researchers and anyone with a list of numbers, and these tools help around it.
- Standard deviation calculator – for the spread, with the working value by value
- Mean, median and mode calculator – for the center of your numbers
- Probability calculator – for chances and odds
- Percentage calculator – for percent changes between values
Summarize first, then decide what the numbers mean.
Plan your money with your AI
Take your numbers further in
Statistics Calculator FAQs
Questions about the statistics calculator? Here's what to know.
A statistics calculator summarizes a list of numbers with its mean, median, mode, spread and outliers.
This free one gives every statistic at once and draws a box plot.
The mean is the sum divided by the count, and the median is the middle value.
The median ignores extreme values, so it describes skewed data better.
Use the sample standard deviation when your numbers are a sample of a larger group.
Use the population one only when you have every value in the group.
This calculator uses NIST's p(N + 1) method, interpolating between the 2 nearest values.
NIST calls a value more than 1.5 × IQR past a quartile a mild outlier, and more than 3 × IQR an extreme one.
The interquartile range is Q3 minus Q1, the spread of the middle half of your numbers.
Excel's QUARTILE.INC uses a different published method from NIST's.
On short lists the 2 can differ slightly, and both are correct.
Copy the column and paste it in, since new lines count as separators.
Yes, it's free with no sign-up.
It runs in your browser, and your numbers stay on your device.
I did.
I'm Navid Moazzez, and I made the statistics calculator as one of my free tools on navid.me.
More about me.
Navid Moazzez
AI business strategist & AI OS builder
Navid Moazzez helps creators and founders master AI and build their own AI Operating System (AI OS) to automate their business and life.
Navid.me is reader-supported. When you buy through links on this site, I may earn an affiliate commission. Learn more.
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