Mean

The mean is the sum of a set of values divided by how many values there are, the most commonly used measure of central tendency and what most people simply call the "average." It's the anchor point for many other statistical calculations, including variance and standard deviation, both of which measure how far individual values spread out relative to this mean.

While mean is intuitive and widely used, it has a real limitation: it's sensitive to outliers. A single extreme value can pull the mean away from where most of the data actually sits, which is why median is sometimes preferred for skewed datasets like income or home prices.

Mean (μ) = Σx / n

Where Σx is the sum of all values and n is the number of values.

A dataset of five test scores: 65, 70, 75, 80, 95.

• Sum: 65 + 70 + 75 + 80 + 95 = 385
• Mean: 385 / 5 = 77

Note that four of the five scores are below this mean, the 95 pulls the average upward, illustrating how a single higher value can shift the mean away from where most values actually cluster.

• Every value in the dataset affects the mean equally. This is what makes it sensitive to outliers, one extreme value has real pulling power on the final result.
• Median is often better for skewed data. Income, home prices, and similar heavily right-skewed datasets often report median specifically because the mean gets distorted by a small number of very high values.
• The mean underlies variance and standard deviation calculations. Both measure how far each value deviates from the mean, so understanding the mean is foundational to interpreting spread statistics.
• The mean doesn't have to match any actual data point. It's a calculated summary value, often falling between observed values rather than equal to any single one of them.
• Population mean and sample mean use the same formula, different contexts. The calculation is identical, whether you're averaging an entire population or a sample drawn from it, the distinction matters more for variance calculations than for the mean itself.