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📐 Statistics Calculator

Enter a set of numbers to instantly calculate mean, median, mode, variance, standard deviation, quartiles, and more.

Data Set

Your Result

Mean

16.375

Count

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Sum

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Median

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Mode

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Range

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Min

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Max

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Variance (Pop.)

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Std. Deviation (Pop.)

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Sum of Squares

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Q1 (25th pct.)

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Q3 (75th pct.)

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IQR

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How the Statistics Calculator Works

This calculator computes common descriptive statistics for any data set, helping you understand its central tendency, spread, and distribution.

Formulas

Mean = sum of values / count
Population Variance = Σ(x − mean)² / n
Population Standard Deviation = √variance
Quartiles use linear interpolation: index = p × (n − 1)
IQR = Q3 − Q1

Frequently Asked Questions

What's the difference between population and sample standard deviation?

Population standard deviation divides by n (the total count), assuming your data is the entire population. Sample standard deviation divides by n−1 to correct for bias when your data is only a sample. This calculator uses the population formula.

How is the interquartile range (IQR) useful?

IQR measures the spread of the middle 50% of your data and is useful for identifying outliers — values are often considered outliers if they fall more than 1.5×IQR below Q1 or above Q3.

What if my data has no mode?

If every value appears exactly once, there is no mode. If multiple values tie for the highest frequency, all of them are shown as modes.