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

$36$

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Solution

The correct option is A
$36$

Use the formula, $m e a n = \frac{s u m o f o b s e r v a t i o n}{t o t a l n u m b e r o f o b s e r v a t i o n}$
Given that, The mean of $25$ observations $= 36$
Sum of $25$ observations $= 25 \times 36 = 900$
Mean of the first $13$ observations $= 32$
Sum of first $13$ observations $= 32 \times 13 = 416$
Mean of the last $13$ observations $= 40$
Sum of last $13$ observations $= 40 \times 13 = 520$
Sum of first $13$ observations $+$ sum of last $13$ observations $- 13 t h$ observation $=$ sum of $25$ observations
$\Rightarrow 416 + 520 - 13 t h o b s e r v a t i o n = 900 \Rightarrow 13 t h o b s e r v a t i o n = 936 - 900 = 36$
Hence, the $13 t h$ observation is $36$ .

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The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 40, find the 13th observation.

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