Average Calculator — Mean, Median, Mode
Enter your numbers separated by commas or one per line. This calculator computes the mean, median, mode, range, count, sum, minimum, and maximum — all at once, with step-by-step working for each statistic.
Understanding Averages: Mean, Median, and Mode
In statistics, "average" usually refers to the arithmetic mean, but there are actually three main measures of central tendency: mean, median, and mode. Each answers the question "what is a typical value?" in a different way, and choosing the right one depends on your data and what you are trying to understand.
Formulas
Mean = Sum / Count = (x1 + x2 + ... + xn) / n
Median = Middle value of sorted data
Mode = Most frequently occurring value(s)
Range = Max − Min
Mean (Arithmetic Average)
The mean is calculated by adding all values and dividing by the count. It is the most commonly used average. However, it is sensitive to outliers — a single very large or small value can pull the mean significantly. For example, the mean of [10, 20, 30, 40, 1000] is 220, which does not represent most of the data well.
Median (Middle Value)
The median is found by sorting the data and picking the middle value. For an even number of values, it is the average of the two middle values. The median is robust against outliers. For [10, 20, 30, 40, 1000], the median is 30 — much more representative of the typical value than the mean of 220.
Mode (Most Frequent)
The mode is the value that appears most often. A data set can have no mode (all values unique), one mode (unimodal), or multiple modes (bimodal, multimodal). Mode is the only measure of central tendency that works with categorical (non-numeric) data. For example, the mode of favorite colors in a class might be "blue."
When to Use Each
Mean: Best for symmetric data without extreme outliers (test scores, temperatures). Median: Best for skewed data or data with outliers (income, house prices, response times). Mode: Best for categorical data or finding the most common value (shoe sizes, survey responses).