KVPY Sample Paper KVPY Stream-SX Model Paper-20

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is:

A) 7

B) 5

C) 1

D) 3

Correct Answer: A

Solution :

Mean \[\overline{x}=4,{{\sigma }^{2}}=5.2,\]\[n=5,\]\[{{x}_{1}}=3,\]\[{{x}_{2}}=4={{x}_{2}}\]
\[\sum{xi}=20\]
\[{{x}_{4}}+{{x}_{5}}=9\]	? (i)
\[\frac{\sum{x_{i}^{2}}}{x}-{{(\overline{x})}^{2}}={{\sigma }^{2}}\]\[\Rightarrow \] \[\sum{x_{i}^{2}=106}\]
\[x_{4}^{2}+x_{5}^{2}=65\]	? (iii)
Using (i) and (iii),
\[{{({{x}_{4}}+{{x}_{5}})}^{2}}=49\]
\[\left\| {{x}_{4}}-{{x}_{5}} \right\|=7.\]