Descriptive Statistics Calculator
Paste a list of numbers to get a complete descriptive statistics summary at once: count, sum, mean, median and mode, the minimum, maximum and range, population and sample variance and standard deviation, and the quartiles with the interquartile range. Everything updates as you type.
How to summarize a data set
- Type or paste your numbers, separated by commas, spaces or new lines.
- Read the center (mean, median, mode) and the spread (standard deviation, range, IQR) from the result cards.
- Copy the full report if you need it for a spreadsheet, homework or notes.
Examples
Classic eight-value data set
2, 4, 4, 4, 5, 5, 7, 9
Mean = 5, median = 4.5, mode = 4, population SD = 2, sample variance about 4.571, Q1 = 4, Q3 = 5.5, IQR = 1.5
List with two modes
1, 1, 2, 2, 3
Mode = 1 and 2 (both appear twice), mean = 1.8, median = 2
Frequently asked questions
What are descriptive statistics?
Descriptive statistics summarize a data set with a few numbers instead of listing every value. They cover the center of the data (mean, median, mode), how spread out it is (range, variance, standard deviation, interquartile range), and its boundaries (minimum, maximum and the quartiles).
How are the quartiles and interquartile range calculated?
This calculator finds quartiles by linear interpolation, the same method spreadsheets use for PERCENTILE.INC and NumPy uses by default. The target position is (n - 1) times the percentile on a sorted list, and the result is a blend of the two nearest values. Q1 is the 25th percentile, Q3 is the 75th, and the interquartile range is Q3 minus Q1. Other tools may use a slightly different rule, so quartiles can differ a little between calculators.
What is the difference between population and sample standard deviation?
Population standard deviation divides the squared differences by N, the count of values, and fits when your numbers cover the whole group. Sample standard deviation divides by N minus 1 to correct for the bias of estimating a larger population from a smaller sample. This calculator shows both so you can pick the one that matches your data.
What does it mean when there is no mode?
If every number appears the same number of times, no single value is the most frequent, so the mode is reported as empty. When several values tie for the most appearances, the calculator lists all of them, such as a data set with two modes.
What happens if I enter only one number?
The center figures still work: the mean, median, minimum, maximum and quartiles all equal that single value. The range is zero, and both variance and standard deviation are zero because a single point has no spread to measure.
Does this calculator send my data anywhere?
No. The math runs entirely in your browser, so your numbers never leave your device.
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