Question

The mean of $25$ observations is $36$. The mean of first $13$ observations is $32$ and that of last $13$ observations is $39$. What is the value of 13th observation?

• A. $20$
• B. $23$
• C. $32$
• D. $40$

Answer 1

The correct option is B $23$

Let $a_1,a_2,...a_{25}$ be $25$ observation

$\Rightarrow \frac{a_1+a_2+a_{25}}{25}=36$

$\Rightarrow a_1+a_2+...+a_{25}=\mathrm{900...}\left(1\right)$

$\frac{a_1+a_2+...+a_{13}}{13}=32$

$\Rightarrow a_1+a_2+a_{13}=\mathrm{416...}\left(2\right)$

$\frac{a_{13}+...+a_{25}}{13}=39$

$\Rightarrow a_{13}+...+a_{25}=\mathrm{507...}\left(3\right)$

then $\left(3\right)+\left(2\right)-\left(1\right)$ give $a_{13}$

$\Rightarrow a_{13}=507+416-900=23$