Question

If the mean of $10$ observations is $20$ and that of another $15$ observations is $16$, then the mean of $25$ observations is __________.

• A. $18$
• B. $18.2$
• C. $17.6$
• D. $17$

Answer 1

The correct option is C $17.6$

We know mean $=\frac{\text{Sum of observations}}{\text{Number of observation}}$.

For first $10$ observations:

$20=\frac{{\text{sum}}_1}{10}$

$⟹$ ${\text{sum}}_1=$sum of first $10$ observations

$⟹$${\text{sum}}_1=20\times 10=200$.

For another $15$ observations:

$16=\frac{{\text{sum}}_2}{15}$

$⟹$${\text{sum}}_2=$ sum of another $15$ observations

$⟹$${\text{sum}}_2=16\times 15=240$.

Therefore, Mean of all $25$ observations:

$\text{Mean}=\frac{{\text{sum}}_1+{\text{sum}}_2}{10+15}$

$⟹$$\text{Mean}=\frac{200+240}{25}=\frac{440}{25}=17.6$.

Hence, option $C$ is correct.