Math formula
Average Formula
Learn the arithmetic mean formula and how sum and count determine the average of a set of numbers.
Formula
Average = sum of values ÷ number of valuesWhat the formula means.
Add all values in the set, then divide the total by how many values were included.
Every included value contributes to the sum and count.
The arithmetic mean can be affected strongly by extreme values.
Mean, median and mode answer different questions.
Variables.
ΣxSum
Total of all included values.
nCount
Number of values included.
x̄Average
Arithmetic mean of the values.
Worked example.
10, 20, 30, 40, 50
- 10 + 20 + 30 + 40 + 50 = 150
- 150 ÷ 5 = 30
Try your own numbersAverage Calculator
↗Common mistakes.
- Dividing by the wrong number of values.
- Forgetting repeated values in the count.
- Using the mean as though it always represents a typical value in a skewed distribution.
Quick questions.
Is average always the arithmetic mean?
In everyday use it often is, but “average” can also refer to measures such as median or mode depending on context.
Can an average be outside the range of the values?
The arithmetic mean of finite real values lies between the minimum and maximum values.