question_answer

The mean of 5 observations is 7. If mean of the first three observations is 5 and that of the last three is 9, then the third observation is.

A)  5                                

B)  10            

C)  7        

D)  9

Correct Answer: C

Solution :

(c): Observations: \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+{{x}_{4}}+{{x}_{5}}=5\times 7=35\] \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}=5\times 3=15\Rightarrow {{x}_{4}}+{{x}_{5}}=20\] \[{{x}_{3}}+{{x}_{4}}+{{x}_{5}}=9\times 3=27\Rightarrow {{x}_{1}}+{{x}_{2}}=8\] \[\Rightarrow \,\,\,{{x}_{3}}=35-20-8=7\] You may learn to use this kind of a box way of arranging numbers \[{{x}_{1}}\] to \[{{x}_{5}}\]. It will help you visualize tricky problems.