Average Calculator
Calculate the mean, median, mode, range, and more from a set of numbers. See also Percentage Calculator and Standard Deviation Calculator.
How to Calculate Average (Mean)
The arithmetic mean (average) is calculated by adding all numbers in a data set and dividing by the count of numbers. It is the most commonly used measure of central tendency. The median is the middle value when numbers are sorted, and the mode is the most frequently occurring value. Each measure provides different insights into the data distribution.
Average Formulas
Arithmetic Mean = Sum of all values / Count of values
Geometric Mean = (x1 × x2 × ... × xn)^(1/n)
Harmonic Mean = n / (1/x1 + 1/x2 + ... + 1/xn)
Example
Numbers: 10, 20, 30, 40, 50
Mean = (10 + 20 + 30 + 40 + 50) / 5 = 150 / 5 = 30
Median = 30 (middle value)
Mode = No mode (all values appear once)
Range = 50 − 10 = 40
Types of Averages
Arithmetic Mean is the standard average — best for evenly distributed data. Geometric Mean is used for growth rates, percentages, and ratios — it reduces the impact of extreme values. Harmonic Mean is used for rates and ratios like speed — it gives more weight to smaller values. Median is resistant to outliers and is preferred when data is skewed. Mode identifies the most common value and works with non-numeric data too.
Frequently Asked Questions
What is the difference between mean and median?
Mean is the sum divided by count — it is affected by outliers. Median is the middle value — it is not affected by extreme values. For example, in [1, 2, 3, 4, 100], the mean is 22 but the median is 3.
When should I use geometric mean?
Use geometric mean for growth rates, investment returns, and data that multiplies together. For example, if an investment grows 10%, 20%, and 30% over three years, the geometric mean gives the true average annual growth rate.
Can a data set have multiple modes?
Yes. A data set with two modes is bimodal, three modes is trimodal, and more is multimodal. If all values appear equally often, there is no mode.