Statistics Calculator
Mean, median, mode, standard deviation, quartiles & outliers
Paste a column straight out of a spreadsheet. Line breaks, commas, tabs and negative numbers are all handled.
Five-number summary, quartiles & outliers
| Measure | Value | Meaning |
|---|
Frequency table
| Value | Count | Share |
|---|
How to Use
- 1Paste or type your numbers. Any separator works.
- 2Choose sample if the data is part of a bigger group, population if it is everything.
- 3Read the mean, then the tiles for median, mode and spread.
- 4Open the summary table for quartiles and any outliers.
The Formulas
- Meanx̄ = Σx / n
- Sample variances² = Σ(x − x̄)² / (n − 1)
- Population varianceσ² = Σ(x − x̄)² / n
- Std deviation√variance
- IQRQ3 − Q1
- OutlierBeyond Q1/Q3 ± 1.5 × IQR
Quick Examples
Tap an example to load it above.
Everything about the Statistics Calculator
Centre, spread and shape, and what each number actually tells you.
This statistics calculator takes a list of numbers and returns the full set of descriptive statistics: mean, median and mode for the centre, range, variance and standard deviation for the spread, plus the five-number summary, the interquartile range and any outliers.
Everything updates as you type, and the sorted data is printed underneath so you can check the calculator read your numbers the way you meant them.
Sample or population? Choose population only when your numbers are the entire group you care about, such as every student in one class or every item in one shipment. If they are a subset used to estimate something bigger, choose sample: dividing by n − 1 corrects a bias that would otherwise make the spread look smaller than it really is.
Three kinds of "average"
| Measure | What it is | Best when |
|---|---|---|
| Mean | Sum ÷ count | Data is roughly symmetric |
| Median | Middle value when sorted | There are outliers or heavy skew |
| Mode | Most frequent value | Categories, shoe sizes, survey scores |
Load the "With an outlier" example above: the mean jumps well past every ordinary value while the median barely moves. That gap is exactly why house prices and salaries are reported as medians.
Reading the spread
- 1Range
Maximum minus minimum. Simple, but a single extreme value controls it entirely.
- 2Standard deviation
The typical distance from the mean, in the same units as your data. Roughly two thirds of a normally-distributed set falls within one standard deviation of the mean.
- 3Variance
The standard deviation squared. Harder to interpret because the units are squared, but it is what most statistical formulas actually use.
- 4Interquartile range
The spread of the middle 50%. Because it ignores both tails, it is the spread measure to quote whenever outliers are present.
How the quartiles are calculated
This calculator uses Tukey's hinges: sort the data, split it at the median, then take the
median of each half. When the count is odd the middle value is left out of both halves. It is the method taught
in most statistics courses and the one used to draw box plots. Note that spreadsheet functions such as
QUARTILE.INC interpolate instead, so they can return slightly different quartiles for the same
data, and neither is wrong, they are different conventions.
Outliers are flagged, never deleted
Any value more than 1.5 × IQR below Q1 or above Q3 is listed as an outlier, and the fences are shown so you can see how far out it is. An outlier is a prompt to investigate, whether a typo, a broken sensor, or a genuinely unusual case, rather than an automatic reason to drop the value.
Frequently Asked Questions
What is the difference between sample and population standard deviation?
Population standard deviation divides the squared deviations by n; sample standard deviation divides by n − 1. The n − 1 version, called Bessel's correction, compensates for the fact that the mean was estimated from the same data. Use population only when your numbers cover the entire group you are describing.
How do I find the mean, median and mode?
The mean is the sum divided by the count, the median is the middle value once the data is sorted, and the mode is the value that appears most often. This calculator shows all three at once, plus the sorted list so you can verify the median yourself.
What if my data has no mode, or more than one?
If every value appears exactly once the set has no mode, and the tile says "None" rather than picking an arbitrary value. If several values tie for the highest frequency, all of them are listed, because a set can legitimately be bimodal or multimodal.
How are the quartiles Q1 and Q3 calculated?
By Tukey's method: sort the data, split it at the median, then take the median of the lower half for Q1 and of the upper half for Q3. With an odd number of values the median itself is excluded from both halves. Spreadsheets that interpolate, such as QUARTILE.INC, may report slightly different values.
How does the calculator decide something is an outlier?
It applies the standard 1.5 × IQR rule: anything below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged. Both fences are shown in the summary table so you can see how extreme a value is, and nothing is removed from the calculation automatically.
Can I paste a column from Excel or Google Sheets?
Yes. Copy the column and paste it straight in, because line breaks, tabs, commas and spaces are all accepted as separators, and negative numbers and decimals are read correctly. Any text mixed in is ignored rather than breaking the calculation.
Why does the mean look wrong compared with the median?
A large gap between the two means the data is skewed, usually by one or two extreme values. The mean is pulled toward them, the median is not. Check the outlier row in the summary table, and if values are flagged, quote the median and the IQR rather than the mean and standard deviation.
Is the statistics calculator free and is my data uploaded?
It is completely free with no sign-up, and every statistic is computed inside your browser, so your data set is never transmitted or stored and it is safe to paste confidential figures.