Wikipedia: Moment about the mean

Difference (from prior major revision) (minor diff)

Changed: 1c1

A moment about the mean (also known as a central moment) is... what exactly is a 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.

Changed: 3,14c3

*The first moment about the mean is the mean.
*The second moment about the mean is variance.
*The third moment about the mean is skewness.
*The fourth moment about the mean is kurtosis.

It is possible to define fifth, sixth and any higher order moments as well; but only the first four commonly have names.

The kth central moment of a distribution is defined as:

μ_k = E(x-x_mean)^k

where E(x) is the expected value of x.

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.