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 $40$, the $13$th observation is :

The total sum of all 25 observations is 25 times 36, which equals 900. The sum of the first 13 observations is 13 times 32, or 416, and the sum of the last 13 observations is 13 times 40, or 520. When adding the sum of the first 13 and the last 13 observations, the 13th observation is counted twice, making that total 416 plus 520, or 936. Therefore, the 13th observation is the difference between this combined sum and the actual total sum of all observations: 936 minus 900 equals 36.

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