Statistics Calculator
Mean, median, mode, standard deviation, quartiles and outliers. Runs in your browser.
About this statistics calculator
This statistics calculator gives you the mean, median, mode, range, variance, standard deviation, quartiles, IQR and outliers for any list of numbers, with a box plot and a histogram. Paste the numbers in almost any format and the results appear as you type.
It shows sample and population standard deviation side by side, so you never have to guess which one a textbook or a lab report wants. It also lets you choose the quartile method, because Excel, a TI-84 and most textbooks don't agree on Q1 and Q3.
Your data stays in your browser. Nothing is uploaded, which matters when the numbers are grades, salaries or patient readings.
Features
Paste anything
Commas, spaces, tabs, semicolons, pipes and new lines all separate values. A column pasted from a spreadsheet works, and stray words are skipped and listed.
Sample and population side by side
Variance and standard deviation are shown both ways: divided by n − 1 for a sample, and by n for a whole population.
Four quartile methods
Median of halves (exclusive, as on a TI-84), Tukey's inclusive hinges, linear interpolation (Excel QUARTILE.INC and the R default) and Excel QUARTILE.EXC.
Outliers with the 1.5 × IQR rule
Lower and upper fences are worked out and every value outside them is flagged. Values beyond 3 × IQR are marked as extreme.
Box plot and histogram
Both are drawn from your data. The histogram uses Sturges' rule for the bin count, or you can set 2 to 30 bins yourself.
Extra measures
Standard error of the mean, coefficient of variation, skewness and excess kurtosis (matching Excel's SKEW and KURT), geometric mean and a frequency table.
How to use the statistics calculator
- 1Paste or type your numbers, separated by commas, spaces or new lines.
- 2Pick a quartile method if your class or software uses a specific one.
- 3Read the summary, box plot, histogram and outliers, then copy the results.
When to use it
Class test results
Paste 30 scores to see the average, the spread and whether one very low score is an outlier before you curve anything. Each student's own course standing is a job for the grade calculator.
Lab measurements
Five repeat readings give a mean and a sample SD for the error bars. Round them to the right precision with the significant figures calculator.
Checking a spreadsheet
Copy a column out of Excel or Google Sheets and confirm its STDEV.S, QUARTILE.INC and SKEW values match.
Before a hypothesis test
Summaries and outliers come first. Once you have a test statistic, the p-value calculator tells you whether the result is significant.
How do you calculate standard deviation?
Find the mean, subtract it from every value, square each difference, and add the squares. That total is the sum of squares. Divide it by n − 1 for a sample or by n for a population to get the variance. The standard deviation is the square root of the variance.
For the values 4, 8, 6, 5 and 3, the mean is 26 ÷ 5 = 5.2. The squared differences are 1.44, 7.84, 0.64, 0.04 and 4.84, which add up to 14.8. The sample variance is 14.8 ÷ 4 = 3.7, so the sample SD is about 1.924. The population variance is 14.8 ÷ 5 = 2.96 and the population SD is about 1.720.
Sample or population standard deviation: which should I use?
Use the sample SD, written s, when your numbers are a sample drawn from a bigger group: 20 students out of a school, or 50 bolts out of a production run. Dividing by n − 1 instead of n (Bessel's correction) stops the sample from understating the spread of the whole group.
Use the population SD, written σ, only when your list is the entire group you care about, such as every employee in a 12-person company. When in doubt, the sample version is the safe choice. In Excel, STDEV.S is the sample formula and STDEV.P is the population one.
Why do quartile calculators give different answers?
There is no single agreed definition of a quartile for a small data set. The sample data on this page has 20 test scores. With the exclusive median-of-halves method, Q1 = 69.5 and Q3 = 86.5. With linear interpolation, the Excel QUARTILE.INC method, Q1 = 70.25 and Q3 = 85.75. Both are correct under their own rules.
Pick the method your course or software uses. Most introductory textbooks and TI calculators split the data at the median and leave the median out. R and Excel's QUARTILE.INC interpolate.
- Exclusive median of halves: TI-83/84, many textbooks
- Inclusive median of halves: Tukey's hinges, used for some box plots
- Linear interpolation: Excel QUARTILE.INC and PERCENTILE.INC, R type 7, NumPy default
- Linear exclusive: Excel QUARTILE.EXC, R type 6
How are outliers found?
The common rule, from John Tukey's box plot, puts fences 1.5 IQRs beyond the quartiles. Anything below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is an outlier. In the sample scores, IQR = 86.5 − 69.5 = 17, so the lower fence is 69.5 − 25.5 = 44, and the score of 38 is flagged.
An outlier is a prompt to check, not a value to delete. It may be a typing error, or it may be the most interesting number you have.
Why use Mavros
| Mavros | Typical upload sites | |
|---|---|---|
| Input | Any separator, spreadsheet columns, decimal comma option | Commas only |
| Standard deviation | Sample and population shown together | One at a time |
| Quartiles | Four named methods to match your software | One unnamed method |
| Outliers | 1.5 × IQR fences with values listed | Not shown |
| Charts | Box plot and histogram | Numbers only |
| Privacy | Data never leaves your browser | Sent to a server |
Tips
- If your numbers use a decimal comma, as in 1,5 and 2,25, tick Decimal comma. Commas then stop acting as separators.
- Thousands separators break parsing: 1,200 would be read as 1 and 200. Remove them first, or paste the raw spreadsheet values.
- Mode shows none when every value appears once. That is common with measured data, and a histogram tells you more.
- Mean far from the median? The data is skewed, and the median is usually the better typical value. House prices are the classic case.
- Copy all results gives a plain-text summary you can paste into a report or keep in the online notepad.
Questions
How do I find the mean, median and mode?
Paste your numbers and all three appear at once. The mean is the sum divided by the count, the median is the middle value once sorted, and the mode is the most frequent value.
What is the difference between sample and population standard deviation?
Sample SD divides the sum of squares by n − 1, and population SD divides by n. Use the sample version unless your data covers every member of the group.
What does the standard deviation tell me?
It is the typical distance of values from the mean, in the data's own units. For roughly bell-shaped data, about 68% of values fall within one SD of the mean and about 95% within two.
How do you calculate the interquartile range?
Subtract the first quartile from the third: IQR = Q3 − Q1. It covers the middle 50% of the data and, unlike the range, is not thrown off by a single extreme value.
Why doesn't my Q1 match Excel?
Excel's QUARTILE.INC uses linear interpolation. Choose Linear interpolation in the quartile method menu and the results will match Excel, R and NumPy.
What if there is more than one mode?
All of them are listed. A data set with two modes is called bimodal. If every value appears once, there is no mode.
What is the standard error of the mean?
It is the sample SD divided by the square root of n. It measures how precisely the sample mean estimates the true mean, and it shrinks as the sample grows.
How many numbers can I enter?
Tens of thousands of values work fine, since everything runs in your browser. Very large pastes may take a moment while the charts redraw.