Question

Mean of $40$ terms is $25$ and S.D is $4$, then sum of the squares of all terms is

• A. $25640$
• B. $25000$
• C. $25645$
• D. $35645$

Answer 1

Answer: (A)

$25640$

Given that $\overline{x}=\frac{\sum x_i}{n}$

Given, $n=25$ and $\overline{x}=25$, S.D=4

$\sum x_i=25\times 40=1000$

$SD=\sqrt{\frac{\sum x_i^2}{n}-(\frac{\sum x_i}{n}{)}^2}$

$16=\frac{\sum x_i^2}{n}-(\frac{\sum x_i}{n}{)}^2$

Substituting above values, $\sum x_i^2=25,640$