Average, Mean, Median & Mode Calculator

Average & Statistics Calculator

— Count
— Sum
— Mean (Average)
— Median
— Mode
— Minimum
— Maximum
— Range (Max − Min)
— Variance (Population)
— Std Dev (Population σ)

Average Calculator – Mean, Median, Mode, and More

This free online statistics calculator computes ten descriptive statistics from any list of numbers: count, sum, mean (average), median, mode, minimum, maximum, range, variance, and standard deviation. Just type or paste your numbers — separated by commas or on separate lines — and click Calculate. All results update instantly without reloading the page.

Mean vs Median vs Mode: What Is the Difference?

Mean (Average): The sum of all values divided by the count. Most commonly used, but sensitive to outliers. For [1, 2, 3, 100], mean = 26.5 — far from most of the data.

Median: The middle value when data is sorted. If there are two middle values, their average is taken. Resistant to outliers. For [1, 2, 3, 100], median = 2.5 — much more representative.

Mode: The most frequently occurring value(s). A dataset can have no mode (all values appear once), one mode (unimodal), or multiple modes (bimodal, multimodal). For [1, 2, 2, 3, 3, 3], mode = 3.

Variance and Standard Deviation

Both measure spread — how far values deviate from the mean.

  • Variance (σ²): The average of squared differences from the mean. Large variance = data is spread out.
  • Standard deviation (σ): The square root of variance, expressed in the same units as the original data. More intuitive than variance.

This calculator uses population formulas (divide by N), appropriate when your data represents the complete population. For a sample, you would divide by N−1 (sample standard deviation). If your data is a sample from a larger population, the population std dev shown here slightly underestimates the true spread.

Range

Range = Maximum − Minimum. It gives a quick sense of how spread out the data is, but is highly sensitive to extreme values (outliers).

Practical Uses

  • Academic performance: Find the class mean, median grade, and standard deviation.
  • Finance: Analyze return distribution, volatility (std dev), and central tendency.
  • Science: Summarize experimental measurements and assess variability.
  • Sports: Analyze player statistics across a season.
  • Quality control: Measure process consistency using variance and std dev.

Frequently Asked Questions

When should I use the median instead of the mean?
Use the median when your data has outliers or is skewed. Income data is a classic example: a few very high earners pull the mean far above what most people earn, while the median better represents the typical value. House prices, salaries, and medical costs are all situations where median is often more informative.
What does a high standard deviation mean?
A high standard deviation means data points are widely spread from the mean, indicating high variability. A low standard deviation means values cluster closely around the mean, indicating consistency. In finance, high standard deviation of investment returns indicates high risk (volatility).
Can I enter negative numbers?
Yes. The calculator handles negative numbers, decimals, and any mix. For example, you can analyze temperature readings, profit/loss figures, or any real-valued dataset.
What is the difference between population and sample standard deviation?
Population std dev divides by N and is used when you have data on every member of the group. Sample std dev divides by N−1 (Bessel's correction) and is used when your data is a sample. For large datasets the difference is small, but for small samples it can be significant.
How many numbers can I analyze at once?
There is no hard limit — the calculator processes whatever you enter. Hundreds or thousands of numbers are handled fine in the browser. For very large datasets (tens of thousands of values), performance may vary depending on your device.