Question

For four observations X,X2,X3,X4, it is given that ,$∑x_i^{2}=656$ and $∑x_i=32$. Then, the variance of these four observations is ?

• A. $144$
• B. $730$
• C. $120$
• D. $248$
• E. $182.5$
• F. $100$

Answer 1

Answer: (F)

$100$

Answer 2

Given data

The data are X_1, X_2, X_3 , X_4

so no. of observations($N$)= 4

$∑x_i^{2}=656$

$∑x_i=32$

Hence variance ($σ^2$)$= \dfrac{∑x_i^{2}}{N}-\dfrac{(∑x_i)^{2}}{N^2}$

                         $=\dfrac{656}{4}-\dfrac{32^2}{4^2}$

                         $=100$ (_Ans.)