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Question

The mean of 15 observations is 8. If the mean of the values of first eight observations is 7 and that of the values of last eight observations is 10, then what is the value of the 8th observation?

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Solution

Let 15 observations be x1,x2,x3,,x15

Mean=Sum of values of all observationsNumber of observations

Sum of values of all observations = Mean x Number of observations
Sum of values of all observations = 15 × 8 = 120.
i.e., x1+x2+x3++ x15=120----(1)
[1 mark]

Mean of first 8 observations = 7
Hence, the sum of first 8 observation = 7 × 8 = 56
x1+x2+x3++ x8=56----(2)
[0.5 mark]

Mean of last 8 observations = 10
Hence, the sum of the last 8 observation = 10 ×8 = 80
x8+x9+x10++ x15=80-----(3)
[0.5 mark]

Adding 2 and 3 we get,
(x1+x2+x3+,,+ x8)+(x8+x9+x10+,,+ x15)=56+80

x1+x2+x3++ x15+x8=136
substituting 1 in the above equation, we get,
120+x8=136
x8=136120 =16

Hence, the value of x8 is 16
[1 mark]

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