Question

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

Answer 1

Hint:Here, we have to find the new mean when each of the $8$ numbers are multiplied by $2$. First we will find the total sum of all the numbers by using the given formula and get the required solution,
Mean weight of all the numbers = $\dfrac{ Total\, weight\, of\, the\, numbers}{Number\, of\, terms}$

Complete step-by-step answer:
According to the given information, we know that,
Mean weight of all the numbers $ = 15$
Number of terms$ = 8$
Assume the total weight of all the numbers to be $'x'$
The formula to be used for attaining the final answer is,
Mean weight of all the numbers $ = $ Total weight of the numbersNumber of terms
Further, we need to substitute the numerical values of the quantities used in the formula to obtain the required solution.
Total weight of the numbers $ = $ Mean weight of all the numbers $ \times $number of terms
$ \Rightarrow x$ $ = 15 \times 8 = 120$
As we know, further each number is multiplied by $2$.
Then, there will be change in the total weight of all the numbers by a multiple of $2$.
Hence, the total weight of all the numbers $ = 2x = 2(120) = 240$
So, now the mean weight of the numbers will also change accordingly.
Therefore, new mean$ = \dfrac{{2x}}{8} = \dfrac{{240}}{8} = 30$.
Hence, the new mean weight of $8$ numbers will be $30.$

Note: Mean of a series of numbers or observations ${a_{1,}}{a_2},{a_3},...,{a_n}$ is given by the formula $\dfrac{{{a_1} + {a_2} + {a_3} + ... + {a_n}}}{n} = \dfrac{{\sum\limits_{i = 1}^n {{a_i}} }}{n}$, where $n$ equals to the number of terms or values in the series. To solve problems of this type, we need to have a good understanding over the topic of computing averages without committing any mistakes.