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If the mean of the observations are $x, x + 3, x + 5, x + 7$ and $x + 10$ is 9, then find the mean of the last three observations.

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343

133

25

answer is B.

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Detailed Solution

It is given that, the observations are

x, x + 3, x + 5, x + 7

and

x + 10

and its mean is

9

.
We have to find the mean of all 3 observations.
Let

x 1, x 2, ...., x n

be the numbers, then mean is given by,
Mean

= \frac{x_{1} + x_{2} + . . . + x_{n}}{n}

.
Substitute the known values within the formula,

x + x + 3 + x + 5 + x + 7 + x + 10 5 = 9 5 x + 25 5 = 9 x + 5 = 9 x = 4

The last three observations are given by,

x + 5 = 4 + 5 = 9

x + 7 = 4 + 7 = 11

x + 10 = 4 + 10 = 14

The last three observations are

9, 11, 14

.
Hence, the mean of the last three observation is,

9 + 11 + 14 3 = 343

The mean of the last three terms is

343

.
Hence, option 2 is correct.

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