How to Calculate Mean, Median, and Range
Measures of central tendency summarise a dataset with a single representative value. The mean (arithmetic average) is the most commonly used, but the median is often more appropriate when data contains outliers. Understanding all three gives a more complete picture of any dataset, from exam scores to house prices to scientific measurements.
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Formula
Average Calculator
Calculate mean, median, mode, range, and sum from a list of numbers.
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Worked Example
Given:
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FAQs
When should I use median instead of mean?
Use median when data contains outliers or is skewed. For example, average income in a city is misleading because a few billionaires pull the mean up dramatically. Median income better represents the typical person. House prices, salaries, and wealth distributions typically use median for this reason.
What is the mode and when is it useful?
The mode is the most frequently occurring value. It is most useful for categorical data (e.g. most common shoe size sold) or when you need the most typical value in a discrete dataset. A dataset can have no mode, one mode, or multiple modes (bimodal, multimodal).
What is the difference between range and standard deviation?
Range is the difference between the maximum and minimum values — simple but sensitive to outliers. Standard deviation measures how spread out all values are around the mean, providing a more representative picture of variability. A dataset with one extreme outlier has a large range but may have a moderate standard deviation.