Free Statistics Calculator
Mean, median, mode, range, variance, and standard deviation.
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Inputs
Result
Mean
16.6667
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Short answer
Mean is the average, median the middle value, mode the most frequent, variance the mean squared deviation, and standard deviation its square root.
What is the Statistics Calculator?
Descriptive statistics summarize a dataset with a handful of numbers — central tendency, dispersion, and shape.
How does the Statistics Calculator work?
Sum divided by count gives the mean. Sort for median. Count frequencies for mode. Squared deviations for variance.
Formula
Variables
μPopulation meanσ²Population variancenSample size
Explanation
Sample variance divides by (n−1) instead of n (Bessel's correction) to yield an unbiased estimator.
Examples
Example 1: 5, 8, 12, 15, 15, 18, 22, 25, 30
Mean 16.67, median 15, mode 15, std. dev. ≈ 7.75.
Applications
- Descriptive analysis
- Quality control
- Grade curves
Advantages
- Both population and sample std. dev.
- Mode handles ties (multi-modal)
Limitations
- Not designed for large datasets (>100 values)
Common mistakes
- Using population std. dev. when the data is a sample (use n−1 divisor)
Tips
- Report median alongside mean when data is skewed
Related concepts
The Statistics Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding Statistics
Descriptive statistics summarize a dataset with a handful of numbers — central tendency, dispersion, and shape. Within math calculators, statistics belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.
Learning how statistics is calculated
Sample variance divides by (n−1) instead of n (Bessel's correction) to yield an unbiased estimator. Working through the variables one at a time — μ, σ², n — makes the result reproducible by hand and easier to sanity-check.
Using statistics to make a decision
Descriptive analysis Quality control Grade curves Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How statistics compares with related measures
distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
Population vs sample?
Population = you have every member. Sample = a subset representing a larger group. Sample formulas use n−1 to correct bias.
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