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Question

If the mean of the data of observations 12, 7, 9, 5, 15, 10, 9, 8, 6, 4, 2, x, y, z is 8, where x, y, z are natural numbers and 5 < z < x < y < 12, then which of the following cannot be the value of x, y, z respectively?

A
x=9, y=10, z=6
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B
x=8, y=10, z=7
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C
x=8, y=11, z=6
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D
x=9, y=11, z=5
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Solution

The correct option is D x=9, y=11, z=5
Given that x, y, z are natural numbers and mean of the observations is 8.
Mean = SumofobservationsNumberofobservations
12+7+9+5+15+10+9+8+6+4+2+x+y+z14=8
87+x+y+z=112
x+y+z=25
Also, it is given that 5 < z < x < y < 12.
However, in option (4), the value of z = 5 which is not possible as z > 5.
Hence, the correct answer is option d.

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