Question 55

The average of 11 observations is 10, that of the first 6 being 9 and that of the last 6 being 11. What is the $$6^{th}$$ observation?

Solution

The average of 11 observations is 10.

Sum of 11 observations = $$11\times10$$ = 110 Eq.(i)

Average of the first 6 being 9.

Sum of the first 6 observation = $$6\times9$$ = 54 Eq.(ii)

Average of the last 6 being 11.

Sum of the last 6 observation = $$6\times11$$ = 66 Eq.(iii)

$$6^{th}$$ observation = Eq.(ii)+Eq.(iii)-Eq.(i)

= 54+66-110

= 120-110

= 10

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