Question

The mean of $13$ observations is $14$. If the mean of the first $7$ observations is $12$ and that of the last $7$ observations is $16$, then the $7^{th}$ observation is ___________.

• A. $12$
• B. $14$
• C. $16$
• D. $18$

Answer 1

The correct option is B $14$

Sum of all observations $=13\times 14=182$

Sum of the first $7$ observations $=7\times 12=84$

Sum of the last $7$ observations$=7\times 16=112$

Sum of the first $7$ observations $+$ Sum of the last $7$ observations $=$ sum of total terms $+$ $7^{th}$ term$

$\Rightarrow 84+112=182+7^{th}$ term

Therefore, $7^{th}$ term $=196-182=14$