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Question
If the mean of the observations: x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observations is ______.
Options
`10 1/3`
`10 2/3`
`11 1/3`
`11 2/3`
Solution
If the mean of the observations: x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observations is `underlinebb(11 1/3)`.
Explanation:
Given that, the mean of the observations x, x + 3, x + 5, x + 7 and x + 10 is 9.
∴ `(x + x + 3 + x + 5 + x + 7 + x + 10)/5 = 9`
⇒ 5x + 25 = 45
⇒ 5x = 20
⇒ x = 4
∴ Last three observations are x + 5 = 4 + 5 = 9, x + 7 = 4 + 7 = 11
And x + 10 = 4 + 10 = 14
So, the mean of last three observations = `(9 + 11 + 14)/3 = 34/3 = 11 1/3`
Hence, the mean of last three observations is `11 1/3`.
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