The arithmetic mean is the sum of all values divided by the number of values. NIST describes it as the sum of the data points divided by the number of data points, and it is the quantity usually called the average. It is written x̄ ("x-bar") for a sample and μ for a whole population. Because it uses every value, it is sensitive to extreme values, which NIST notes distort the mean but not the median.
Formula
mean = (x₁ + x₂ + … + xₙ) ÷ n
- x₁ … xₙ: the individual values.
- n: how many values there are.
Example
Five weekly grocery bills: $82, $95, $78, $110, $90.
Sum = 455; n = 5; mean = 455 ÷ 5 = $91.
Use the average calculator for longer lists, and the guide to calculating an average for the median, mode and weighted versions.
Common mistakes
- Averaging group averages without weighting them (see weighted mean).
- Reporting only the mean for skewed data, where an outlier can dominate.