Average Calculator

How the Average Calculator Works

The average most people mean is the arithmetic mean: add every value together, then divide by how many values there are. This tool reports the mean along with the other summary statistics a data set is usually judged by, so you can see the centre and the spread at a glance.

The formulas

mean = ( x₁ + x₂ + … + xₙ ) / n

variance σ² = Σ( xᵢ − mean )² / n

population σ = √variance    sample s = √( Σ( xᵢ − mean )² / (n−1) )

What each figure tells you

• Median — the middle value once sorted; unaffected by extreme outliers.
• Mode — the value that appears most often, if any value repeats.
• Range — the distance from the smallest to the largest value.
• Standard deviation — the typical distance of a value from the mean.

Population versus sample

Use population σ when your numbers are the entire group you care about. Use sample s when they are a sample meant to estimate a larger population; dividing by n−1 corrects the bias that a small sample introduces.