What does the standard deviation of variance mean? What are their characteristics?

First of all, the standard deviation reflects the degree of dispersion among individuals in the group. There are two characteristics:

The result of measuring the distribution degree is non-negative and has the same unit as the measured data.

There is a difference between the standard deviation of a population or random variable and the standard deviation of the number of samples in a subset. Simply put, the standard deviation is a measure of the deviation of the average value of a set of data. The standard deviation is large, indicating that most of the values are quite different from their average values; A smaller standard deviation means that these values are closer to the average.

Standard deviation can be used to measure uncertainty.

For example, in physical science, when repeated measurements are made, the standard deviation of the set of measured values represents the accuracy of these measurements. When determining whether the measured value meets the predicted value, the standard deviation of the measured value plays a decisive role:

If the difference between the measured average value and the predicted value is too far (compared with the standard deviation value at the same time), it is considered that the measured value is contradictory to the predicted value. This is easy to understand, because if the measured value falls outside a certain numerical range, it can be reasonably inferred whether the predicted value is correct or not.

2. Variance It reflects the degree of deviation between random variables and their mathematical expectations (that is, the average value). Has the following characteristics

1, let c be a constant, then D(C)=0.

2. let x be a random variable and c be a constant, and then what?

3, let x and y be two random variables, then

Where is the covariance?

Especially, when X and Y are two unrelated random variables, then

This property can be extended to the sum of finite unrelated random variables.

Type and variance calculation of extended data

1, discrete variance

What is the formula for calculating the discrete variance? , among them.

After expanding the above formula, we can get:

2. Continuous variance

What is the formula for calculating the continuous variance? , among them.