# Problem on Standard Deviation

A man has observed the number of chocolates eaten by his son for 32 days.The total number of chocolates eaten by his son is 80 and the sum of the squares of the chocolates eaten everyday is 1000, then the standard deviation he calculated is

(a) 1

(b) 3

(c) 4

(d) 5

The answer given is (d) 5. But I don't know how?? Can anybody please help me to solve this..any hints will also be appreciated.

We know that $$\sigma = \sqrt{E(X^2)-E(X)^2}$$ Furthermore we know that $$E(X^2)=\frac{1000}{32}$$ and that $$E(X)^2=\bigg(\frac{80}{32}\bigg)^2$$ Now, plug in the numbers and you get the desired result
$$\sigma^2=\frac{\sum x^2}{n}-\mu^2=\frac{1000}{32}-(\frac{80}{32})^2=25 \\ \implies \sigma=5$$