Question

If the aritlunetic mean of $9$ observations is $100$ and that of $6$ observations is $80$, then the combined mean of all the $15$ observations will be

• A. $100$
• B. $80$
• C. $90$
• D. $92$

Answer 1

Answer: (D)

$92$

$\Rightarrow$ Given mean of $9$ observations $=100$

$\Rightarrow$ $Mean=\frac{sumofobservations}{numberofobservations}$

$\Rightarrow$ $100=\frac{sumofobservations}{9}$

$\therefore$ Sum of observations $=9\times 100=900$

$\Rightarrow$ Similarly sum of observations of other data $=6\times 80=480$

$\Rightarrow$ Sum of observations of both the data $=900+480=1380$

$\Rightarrow$ Total number of observations $=9+6=15$

$\Rightarrow$ New mean $=\frac{1380}{15}=92$

$\therefore$ The mean of all the $15$ observations will be $92$