Understanding of freedom

The degree of freedom in mathematics generally refers to the number of variables that can be freely evaluated. the degree of freedom in mathematical statistics refers to the number of data that can be independently or freely varied in a sample when the overall parameters are estimated by the statistic of the sample.

When there are constraints, the degree of freedom is reduced, the degree of freedom Formula: degrees of freedom = number of samples-the number of constrained conditions of the sample data, that is, the degree of Freedom =n-k (n sample number, K constraint number). For example, a set of data, the average is certain, then this group of data has n-1 data can be freely changed, such as the average number of data sets, standard deviation is certain, only n-2 data can be freely changed.

Suppose a sample with a capacity of 10, if there is no other information or constraints on the sample, any of the 10 observations extracted from the population can form such a sample. In other words, these 10 observations can be arbitrarily replaced by other observations taken from the population as a whole. When we want to calculate the sample variance, we must first figure out the sample mean, set = 35. At this point, these 10 observations cannot be arbitrarily replaced by other observations taken in the population. Because the sum of the n=350,10 observations must be equal to 350. As a result, only 9 observations in the sample can be arbitrarily changed, because if any of the 9 observations are determined, the 10th observation is also determined by the 9 values. Thus, the degree of freedom equals 9 when calculating the sample variance. The effective sample capacity is reduced to n-1, on this basis, we can well understand why as the mean variance of the sample variance calculation, the degree of freedom to use the average rather than n

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Understanding of freedom