How to use the Statistics Calculator
- Paste your numbers into the box, for example a column copied from a spreadsheet, or type them separated by commas or spaces.
- Read the count, sum, mean, median, mode, minimum, maximum and range as you type.
- Use the sample statistics when your data is a sample of a larger group, and the population ones when it is the whole group.
- Choose a quartile method if you need to match a textbook or Excel, then check the IQR, outlier fences and sorted data.
Features
- Mean, median, mode(s), range, minimum and maximum
- Sample and population variance and standard deviation
- Quartiles by median of halves or Excel QUARTILE.INC
- IQR, 1.5 × IQR fences and a list of outliers
- Sorted data you can copy, and warnings for skipped text
- Handles thousands of values instantly in your browser
What each statistic means
- Mean: the sum divided by the count, x̄ = Σx ÷ n. It uses every value, so extreme values pull it strongly.
- Median: the middle value after sorting, or the average of the two middle values when n is even. It barely moves when one value is extreme.
- Mode: the value that appears most often. A data set can have several modes, or none if no value repeats.
- Range: maximum − minimum, the simplest measure of spread.
Variance and standard deviation
Variance measures how far values spread from the mean: square each value's distance from the mean, add the squares and divide. Standard deviation is the square root of the variance, which puts the spread back into the original units.
- Population (σ²): divide by n. Use it when your data covers the whole group you care about, such as the scores of every student in one class.
- Sample (s²): divide by n − 1. Use it when your data is a sample used to estimate a larger population. Dividing by n − 1 (Bessel's correction) offsets a sample's tendency to underestimate the true spread.
Example: for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the squared distances from it add up to 32. The population variance is 32 ÷ 8 = 4, so σ = 2. The sample variance is 32 ÷ 7 ≈ 4.571, so s ≈ 2.138.
Quartiles: which method?
Quartiles split sorted data into four equal parts: Q1 is the 25th percentile, the median is Q2 and Q3 is the 75th percentile. Several methods exist and software disagrees, so you can choose:
- Median of halves (default): split the sorted data at the median, leaving the median itself out of both halves when n is odd. Q1 is the median of the lower half and Q3 the median of the upper half. This is the method taught in most introductory statistics courses and used by TI-83 and TI-84 calculators.
- Excel QUARTILE.INC: linear interpolation at position (n − 1) × p in the sorted list, counting from zero. It matches Excel's QUARTILE.INC, Google Sheets' QUARTILE and the default quantile method in R and NumPy.
For 2, 4, 4, 4, 5, 5, 7, 9 the first method gives Q1 = 4 and Q3 = 6, while QUARTILE.INC gives Q1 = 4 and Q3 = 5.5. Both are legitimate; just use the same method throughout a report.
Interquartile range and outliers
The interquartile range, IQR = Q3 − Q1, is the spread of the middle half of the data. Tukey's rule flags a value as an outlier when it lies more than 1.5 × IQR beyond the quartiles:
lower fence = Q1 − 1.5 × IQR and upper fence = Q3 + 1.5 × IQR
In the sample data loaded on this page, Q1 = 13.5 and Q3 = 17.5, so IQR = 4 and the fences are 7.5 and 23.5. The value 42 lies above the upper fence and is flagged. An outlier is not automatically a mistake, but it deserves a second look: it may be a typo, a measurement problem or a genuinely unusual case.
Tips for entering data
- Paste a column straight from a spreadsheet; line breaks work as separators.
- Leave out thousands separators, because 1,250 would be read as two numbers, 1 and 250. Negative numbers, decimals and E notation such as 2.5e3 are fine.
- Anything that is not a number is skipped and listed in a warning, so stray headings or units are easy to spot.
For growth rates and shares, see the Percentage Calculator; for formulas with functions, use the Scientific Calculator.
Frequently asked questions
Should I use sample or population standard deviation?
Use the population version when your numbers cover the entire group you are describing. Use the sample version, which divides by n − 1, when your numbers are a sample used to draw conclusions about a larger group.
Why are my quartiles different from Excel?
There are several quartile methods. Select "Excel QUARTILE.INC" to match Excel and Google Sheets, or keep "median of halves" to match most textbooks and TI calculators.
What if no value repeats?
Then the data has no mode, and the calculator says so. If several values tie for the highest count, all of them are listed.
How are outliers identified?
With Tukey’s rule: any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged. The fences are shown so you can see exactly where the cut-offs are.
Is my data uploaded anywhere?
No. All calculations run in your browser, and the numbers are only kept in this browser’s local storage so they are still there when you come back.