Understand the subject
What is an arithmetic average?
An arithmetic average, or arithmetic mean, replaces several values with one equal-share value while preserving their total. It answers: “If the total were shared equally among all observations, how much would each receive?”
Use it for quantities that can sensibly be added—such as scores, measurements, costs, or daily counts. Every entered value contributes equally.
The relationship
Average formula
xᵢ is each value, Σxᵢ is their total, n is the number of values, and x̄ is the mean.
See the idea
The mean is a balance point
The left side totals 40. Moving 6 units from 16 fills the 4-unit and 2-unit gaps below 10, making four equal groups of 10. Nothing is created or lost.
Worked example
Average of 6, 8, 10, and 16
Add the four values, then divide by the number of values.
x̄ = (6 + 8 + 10 + 16) ÷ 4 = 40 ÷ 4 = 10
Interpret with care
When an average can hide information
The mean uses every value, so one extreme value can pull it away from where most observations lie. It also says nothing about spread: two datasets can share the same mean and look very different. For a fuller distribution summary, use the Mean, Median & Mode Calculator.