Question

The mean of $9$ observations is $36$. If the mean of the first $5$ observations is $32$ and that of the last $5$ observations is $39$, then the fifth observation is __________.

• A. $28$
• B. $31$
• C. $43$
• D. $37$

Answer 1

Answer: (B)

$31$

Mean of $9$ observations $=36$

$\Rightarrow$ Sum of these $9$ observations $=324$

Sum of first five observations $=32\times 5=160$

Sum of last five observations $=39\times 5=195$

$\therefore$ Fifth observation $=$ Sum of first five observations $+$ Sum of last five observations $-$ Sum of all $9$ observations

$=160+195-324=31$