Mean
Mean is the arithmetic average of a dataset, found by summing all values and dividing by the count of observations. It is the most common measure of central location and provides an unbiased estimate of the true population mean.
Also known asaverage · arithmetic mean
See it move
The infographic is a formula card displaying the arithmetic mean x̄ = (x₁ + x₂ + ⋯ + xₙ) ÷ n, with x̄ denoting the sample mean, xᵢ each individual observation, and n the number of observations. A worked example uses a bakery's daily revenue over five days — €420, €380, €510, €460, and €430 — summing to €2,200 and giving a mean of €440 per day. Two additional points note that the OLS regression line always passes through (x̄, ȳ), and that the mean is sensitive to outliers so the median may describe skewed data more faithfully.
The formula
Variables
- Sample mean
- Individual observation i
- Number of observations in the sample
The population mean μ = Σxᵢ ÷ N uses all N population values. The sample mean x̄ is an unbiased estimator of μ.
Check yourself
A sample of six student exam scores is: 54, 68, 72, 79, 80, 87. A classmate claims: 'The sample mean is an unbiased estimator, so our calculated average must equal the true class average.' What is wrong with this claim?