Question

Mean of 9 observations is 12, what would be the new mean after multiplication by 3 in all observations?

• A. 48
• B. 12
• C. can not be calulated
• D. 36

Answer 1

The correct option is D 36

Since all values are affected by the same multiplicative values, the measure of mean will also be affected similarly.
If each observation is multiplied by 3, the mean will also be multiplied by 3.

Thus, the new mean is 3 $\times$ 12 = 36.

Alternative Method

According to question,
Mean = $\frac{\text{Sum of observations}}{\text{Number of observations}}$
$\Rightarrow$ Sum of observations = 12 $\times$ 9 = 108
Sum after multiplication by 3 to all observations = 108 $\times$ 3 = 324

New mean
= $\frac{\text{Sum of observations after multiply by 3}}{\text{Number of observations}}$
= $\frac{324}{9}$ = 36
Thus, the new mean is 36 if each observation is multiplied by 3.