1, the meaning of this formula is that for each data point xi, we calculate the square of the difference between it and the average μ, then add up all the square differences, and finally divide by the number n of data to get the variance. The mathematical significance of variance is that it represents the degree of dispersion between data points and average values.
2. The greater the variance, the more discrete the data points, that is, the greater the difference between the data; The smaller the variance, the more concentrated the data points, that is, the smaller the difference between the data. Therefore, variance can be used to measure the stability or reliability of data. Variance is a very important concept in statistics, which is widely used in various statistical analysis and inference.
3. In regression analysis, we usually use variance to test the fitting degree of the model; In sampling survey, we usually use variance to estimate the parameters of the population. It should be noted that in practical application, the calculation of variance needs to consider the dimension and unit of data.
4. Because variance is a measure of data deviation, variance is usually greatly influenced by outliers or outliers. In order to solve this problem, we usually standardize the variance and get the standard deviation.
The difference between variance and standard deviation is as follows:
1, and the variance calculation formula is (1/n) * σ (xi-μ)? Where n is the number of data, xi is each data point, and μ is the average value of data. Variance represents the degree of dispersion between data points and the average, that is, the difference between data.
2. The calculation formula of standard deviation is the difference below the root sign, which is the square root of variance. The standard deviation has nothing to do with the average value of the data, so it is more stable and reliable. An important feature of standard deviation is that it has nothing to do with the actual value of the data, but only with the degree of dispersion of the data.
3. Variance and standard deviation are different in application. Variance is mainly used to measure the dispersion of data, which can help us understand the differences between data. For example, in regression analysis, variance can be used to test the fitting degree of the model; In sampling survey, variance can be used to estimate the parameters of the population.
4. The standard deviation is mainly used to describe the relationship between data points and mean values, which can help us to judge whether data points are abnormal or outliers. For example, in the financial field, if the standard deviation of a portfolio is large, it means that the risk of the portfolio is high.