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Question
If the mean of five observations x, x+2, x+4, x+6, x+8, is 11, then the mean of first three observations is
Options
9
11
13
none of these
Solution
The given data is x, x + 2, x + 4, x + 6 and x + 8. They are 5 in numbers.
The mean is
`(x+(x+2)+(x+4)+(x+6)+(x+8))/5`
`=(x+x+2+x+4+x+6+x+8)/5`
` =(5x+20)/5`
`=(5(x+4))/5`
= x+4
But, it is given that the mean is 11. Hence, we have
x+4 =11
⇒ x = 11 - 4
⇒ x= 7
Then the first three observations are 7, 7 + 2, 7+4, that is, 7, 9, 11. Their mean is
`(7+9+11)/3`
`=27/3`
=9
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Is it the correct answer and why?
