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Average Calculator

Calculate mean, median, mode, standard deviation, min, max, and range from a list of numbers.

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📊Average Calculator

Mean, Median, Mode, and Standard Deviation Explained

There are three common measures of "average" — each tells a different story about your data:

Standard deviation measures how spread out values are from the mean. A small standard deviation means values cluster near the mean; a large one means they are spread out widely. For the dataset [10, 20, 30]: mean = 20, standard deviation = 8.16.

Frequently Asked Questions

When should I use median instead of mean?+
Use the median when your data has extreme outliers or is skewed. For example, when reporting average household income, the median is more useful than the mean because a few billionaires would pull the mean up dramatically while most people earn far less.
What is standard deviation used for?+
Standard deviation measures the dispersion of data. In finance, it measures investment volatility. In testing, it helps identify whether scores deviate significantly from the average. About 68% of values in a normal distribution fall within 1 standard deviation of the mean.
What is the difference between population and sample standard deviation?+
Population standard deviation (σ) divides by n; sample standard deviation (s) divides by n−1. Use population std when you have data for the entire group; use sample std when your data is a sample from a larger population.
What is the range?+
The range is the simplest measure of spread: max value minus min value. For [5, 10, 15, 20]: range = 20 − 5 = 15. It is sensitive to outliers but easy to understand.

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Mean, Median and Mode Explained

The arithmetic mean adds all values and divides by the count. The median is the middle value when sorted (average of the two middle values for even counts), and the mode is the most frequent value. Each tells a different story about your data.

Worked example

For the set 4, 7, 7, 10, 52: the mean is 16, the median 7, the mode 7. The single outlier (52) drags the mean far above the typical value — which is why house prices and incomes are usually reported as medians.

Frequently asked questions

When should I use a weighted average? When values carry different importance — course grades weighted by credits, portfolio returns weighted by position size.

What about the geometric mean? Use it for growth rates: the geometric mean of +50% and −50% correctly shows an overall loss, where the arithmetic mean misleadingly shows 0%.