Statistics · 5 min read
How to Calculate an Average (Mean)
Sum divided by count — the balance point of a list
The arithmetic mean is the sum of the values divided by how many values there are. This tutorial walks through x̄ = (1/n) Σ xᵢ, a 1, 2, 2, 3, 4, 5 worked example, and a tiny-set playground that places the mean as a fulcrum on a number line. It is a teaching sketch, not a full statistics package.
Written by the My Calculator Stack editorial team. About our methods
This is the arithmetic mean (sum / n), not the median or the mode. Sample versus population does not change the mean. The playground is a teaching sketch, not a diagnosis of the list.
1.What an average is
An average in this article means the arithmetic mean: add the numbers, then divide by the count. Each value pulls the result toward itself with equal weight, so a large outlier moves the mean more than it moves a middle or a most-common value. The mean is not the median (middle of the ordered list), not the mode (most frequent value), and not a claim that the data are “typical” in every sense. Think of it as a balance point.
2.The formula
Write the list as x₁, x₂, …, xₙ. Add every xᵢ, then divide by n — the number of values you added. Empty lists are undefined. The same formula is used for a sample mean and a population mean; sample versus population matters for variance and standard deviation, not for this average.
\[ \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i \]
3.Worked example
Take 1, 2, 2, 3, 4, 5 — the same defaults as the average calculator. The sum is 1 + 2 + 2 + 3 + 4 + 5 = 17 and n = 6, so the mean is 17/6 ≈ 2.833. That is the arithmetic mean, not the median (2.5) or the mode (2). If the last value jumped from 5 to 20, the mean would slide up while the middle of the ordered list would barely move.
\[ \bar{x}=17/6\approx 2.833 \]
4.Balance the list
Edit the six values and watch the fulcrum. Each point sits on a number line; the triangle is the mean — the place the list balances. Pull one value far to the right and the fulcrum follows. This is a teaching widget — no comma-separated paste box, no full calculator chrome. Open the average calculator when you want the standalone tool.
Inline playground
Tiny dataset
Arithmetic mean
2.833
Sum 17 · n = 6
17 / 6 ≈ 2.833
Teaching sketch only — the arithmetic mean is a balance point, not a median, a mode, or a diagnosis of the list.
Open the full average calculator →5.Open the full calculator
The average calculator uses the same sum-over-n formula and the same 1, 2, 2, 3, 4, 5 example, with How it works and related statistics tools on one page. Browse other statistics calculators if you need mean–median–mode or standard deviation next.
Try it yourself
Open the related calculator and put these formulas to work.