Question

The mean of $100$ items is $50$ and their S.D. is $4$. The sum of the item and also the sum of the squares of the items is

• A. $5000,251600$
• B. $4000,251600$
• C. $5000,261600$
• D. None of these

Answer 1

The correct option is A $5000,251600$

Here $n=100,A=50,\sigma =4$

Now, $A=\frac{\sum x}{n}\Rightarrow \sum x=nA=100\times 50=5,000$

Again, from the formula,

${\sigma }^2+A^2=\frac{\sum x^2}{n}\Rightarrow \sum x^2=n({\sigma }^2+A^2)$

$\therefore \sum x^2=n({\sigma }^2+A^2)=100(16+2500)=251600$