Question

the mean of data is 12. if each observation is multiplied by 4 and then 2 added to each result find the mean of new observations so obtained​

Answer 1

Step-by-step explanation:

Let number of terms in data be n

Given that,

Mean =p

⇒ 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 =

n

3pn+n

=3p+1

Answer 2

Let no. of initial observations be n.

Given, $\frac{\Sigma x_{i}}{n}=12$

For new observations,$\frac{\Sigma (4x_{i}+2)}{n}= \frac{(\Sigma 4x_{i} )+2n}{n}=\frac{4\Sigma x_{i}}{n}+2=4\times 12+2=50$

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