The second-order central moment, also known as variance, tells us the fluctuation of random variables near their mean. The greater the variance, the greater the fluctuation. Variance is also equivalent to the moment of inertia with the center of gravity as the rotation axis in mechanical motion. The third-order central moment tells us the degree to which the random density function tilts to the left or right.
Variance not only expresses the degree of deviation from the mean, but also reveals the degree of fluctuation within the sample. It can also be understood that variance represents the expectation of sample fluctuation. Of course, this conclusion is currently established under the second-order statistical moment.
Extended data
The central moment is similar to variance. Firstly, the expected value of the sample, that is, the mean value, is obtained, and then a distance from the random variable to the mean value of the sample is calculated. Unlike variance, the distance mentioned here is no longer a square, but a k power.
Variance is the degree of deviation from the center, which is used to measure the fluctuation of a batch of data (that is, the degree of deviation from the average value of this batch of data). It is called the variance of this group of data and is recorded as S2. In the case of the same sample size, the greater the variance, the greater the data fluctuation and the more unstable it is.
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