Question

The mean of a data is $p$. If each observation is multiplied by $3$ and then $1$ is added to each result, then the mean of the new observations so obtained is _________.

• A. $p$
• B. $3p$
• C. $p+1$
• D. $3p+1$

Answer 1

The correct option is D $3p+1$

Let number of terms in data be $n$

Given that,

Mean $=p$

$\Rightarrow$ Sum of data $=pn$

If each term is multiplied by $3$, new sum becomes thrice, i.e. $3pn$

Also given that $1$ is added in each term, hence, $n$ is added in sum, i.e. New sum $=3pn+n$

Mean of new observations $=\frac{3pn+n}{n}=3p+1$