Question

The mean weight of 8 numbers is 15. If each number is multiplied by 2, what will be the new mean?

Answer 1

GIVEN:-

• $\rm{Mean\:weight\:of\:8\:Numbers=15}$.

• each number is multiplied by 2.

TO FIND:-

• The new mean.

FORMULAE USED

$\sum\limit_{i=1}^{n}$

We can also write it as a

$\rm{\bar{X}=\dfrac{x_{1}+x_{2}+.........+x_{3}}{n}}$

Where,

• $\rm{x_{1}+x_{2}+.........+x_{3}}$= Sum of all observation.

• $\rm{n=Number\:of\: observation}$

• $\rm{\bar{X}=mean}$

Now,

$\implies\rm{15=\dfrac{x_{1}+x_{2}+.........+x_{3}}{8}}$

$\implies\rm{120=x_{1}+x_{2}+.........+x_{3}}$.......1

Now,

According to the question

Let New mean be $\rm{\bar{X`}}$.

$\rm{\bar{X`}=\dfrac{2(x_{1})+2(x_{2})+.........+2(x_{3})}{8}}$

$\rm{\bar{X`}=\dfrac{2(x_{1}+x_{2}+.........+x_{3}}{8})}$

$\rm{\bar{X`}=2(\dfrac{120}{8})}$ From....1

$\rm{\bar{X`}=\dfrac{240}{8}}$

$\rm{\bar{X`}=30}$.

Hence, The New mean is 30.

Answer 2

→ Given mean weight of 8 Numbers

→ (x) = 15kg

★ If each Number is multiplied by 2,

• then new mean = 2 x

→ 2 x 15kg

→ 30 kg $\sf$