The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, then find the $13 t h$ observation.

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answer is C.

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Detailed Solution

It is given that the mean of 25 observations is 36.
The mean of the first 13 observations is 32 and that of the last 13 observations is 40.
We have to find the 13th observation.
Let

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

be the numbers, then mean is given by,

x ¯ = x 1 + x 2 + .... + x n n

It is given that,

x 1 + x 2 + .... + x 25 25 = 36 x 1 + x 2 + .... + x 25 = 900

According to the condition, the mean of the first 13 observations is 32. So,

x 1 + x 2 + .... + x 13 13 = 32 x 1 + x 2 + .... + x 13 = 416

Also, the mean of the last 13 observations is 40.

x 13 + x 14 + .... + x 25 13 = 40 x 1 + x 2 + .... + x 13 = 520

The value of the 13th observation is given by,
900 - (520 + 416) = 36
The value of the 13th observation is 36.
Hence, option 3 is correct.

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