There are 10 known data x1, X2 The average number of x 10 is 4, and the sum of the squares of these 10 numbers is 200

There are 10 known data x1, X2 The average number of x 10 is 4, and the sum of the squares of these 10 numbers is 200

∵x1+x2+… +x10=40，x21+x22+… +x210=200∴S2=110[（x1-4）2+（x2-4）2+… +（x10-4）2]=110[（x21+x22+… +x210）-8（x1+x2+… +x10）+160]=110[200-320+160]=4．

If the sum of squares of five data is 845 and the average is 5, what is the variance of this group of data

σ^2=(∑(X-x))^2/n
=(∑(X^2-2*X*x+x^2))/n
=(∑(X^2)-2*x*∑(X)+∑(x^2))/n
=(845-2*5*5*5+5*5^2)/5
=720/5=144
Where x is five of them, and X is the average of them
∑(X)=∑(x)=5*5=25
∑(X^2)=845

Some books say that the formula of sample variance is: sum the square of the difference between random variables and sample mean, and then divide by N; some books say that sum the square of the difference between random variables and sample mean, and then divide by n-1; which of these two formulas is right, and what's the difference between them?

Divided by N is biased sample variance, divided by N - 1 is unbiased sample variance
When n is large and N is 30, there is no difference between the two sample variances, so both can be used. But if n is small, about 15 or 20, then unbiased sample variance must be used. Divide n-1 by n-1