Variance

Data collected from experiments is normally very complex and difficult to describe by few parameters. The mean and the variance are statistical descriptors of data clusters that are normally utilized in such cases.

The mean of N samples is defined as

A physical interpretation for the mean is the center of mass of a body made up of samples of the same mass. It is the first moment of the probability density function (pdf).

We can have very different data distributions with the same mean, so the mean is not a powerful descriptor. Another descriptor very often used is the variance, which is defined as

The variance is the second moment around the mean, and it measures the dispersion of samples around the mean. The square root of the variance is called the standard deviation. Mean and variance are much better descriptors of data clusters. In fact, they define univocally Gaussian distributions, which are very good models for many real-world phenomena.

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