Question

A. M. of 40 observations of a variable is 25 and S. D. is 4. The sum of squares of all observations is

​

Answer 1

Answer:

25624

Step-by-step explanation:

A.M (arithmetic mean )= 25

S.D (standard deviation)= 4

n (sample size) = 40

The formula for variance S^2 is

$$\begin{lgathered}S^2=\frac{1}{n-1}*\sum (x_i- \bar x)^2\\ \\S^2=\frac{1}{n-1}*[ \sum x_i^2- n \bar x ^2]\\ \\\end{lgathered}$$

the second equation is a simplified from of the former.

Now, we substitute the values given and make the missing value the subject of the formula as;

$$\begin{lgathered}4^2=\frac{1}{40-1}*[ \sum x_i^2 - 40*25^2]\\ 16=\frac{1}{39}*[\sum x_i^2 -25000]\\\\ 16*39=\sum x_i^2 -25000\\\\\sum x_i^2=16*39+25000\\\\\sum x_i^2=25624\end{lgathered}$$

Therefore, The sum of square all observation is 25624

Step-by-step explanation:

Hope this help you bro