Mean

The arithmetic average -- the sum of all values in a dataset divided by the number of values.

Descriptive StatisticsBeginnerFree

In Plain English

Add up every value, divide by how many there are -- that's the mean. It's the most common single number used to describe a typical value in a dataset, though it's sensitive to extreme values (outliers) in a way the median isn't.

Definition

For a sample of $n$ values $X_{1}, \dots, X_{n}$ , the arithmetic mean is $\overset{ˉ}{X} = \frac{1}{n} \sum_{i = 1}^{n} X_{i}$ , the sum of all values divided by the count.

Formula

\overset{ˉ}{X} = \frac{1}{n} i = 1 \sum n X_{i}

Notation

\overset{ˉ}{X}

—Sample mean

n

—Number of observations

X_{i}

—The i-th observation

Properties

The mean is the value that minimizes the sum of squared deviations from every point in the dataset -- the least-squares property that makes it central to so much of statistics.
Because every value contributes to the sum, a single extreme outlier can pull the mean substantially away from where most of the data actually sits -- the median doesn't have this problem.
For symmetric distributions, the mean and median coincide; for skewed distributions, they diverge, with the mean pulled toward the longer tail.

At a Glance

Sensitive tooutliers -- a single extreme value can shift it substantially

Balances atthe mean is the dataset's "center of mass"

Alternative for skewed datathe median

Used to buildvariance, standard deviation, and most inferential statistics

Related Terms

Median Central Tendency Weighted Mean

Last updated August 8, 2026← Back to the Dictionary