Moment about the mean

The k^th moment about the mean (or k^th central moment) of a real-valued random variable X is the quantity E[(X-E[X])^k], where E is the expectation operator. Some random variables have no mean, in which case the moment about the mean is not defined. The k^th moment about the mean is often denoted μ_k.

The first moment about the mean is zero. The second moment about the mean is called the variance, and is usually denoted σ², where σ represents the standard deviation. The third and fourth moments about the mean are used to define skewness and kurtosis, respectively.