Question

If the average of seventy-five numbers is calculated, it is 35. If each number is increased by 5, then mean of new numbers is :

Answer 1

Mean=sum of all/no. of terms

=>35=sum/75

=>sum=35×75=2625

incresad value=75×5=375

after increasing no. becomes= 2625+75=2700

New Mean=2700/75=36

Hope it helps you

Answer 2

$\textbf{\huge{ANSWER:}}$

Let the numbers be = $x_{1} + x_{2} + x_{3} + ..... + x_{75}$

Then, we're $\sf{Given}$ that :-

$\frac{x_{1} + x_{2} + x_{3} + ..... + x_{75}}{75}$ = 35 ....(1)

And, we need to find the mean of the set of 75 numbers when 5 is added to every number

$\sf{Solution:}$

$x_{1} + x_{2} + x_{3} + ..... + x_{75}$ = 35 × 75

What we did : We just cross multiplied the numbers in $eq^n$ (1) so that we get the sum of the variables.

=》 $x_{1} + x_{2} + x_{3} + ..... + x_{75}$ = 2625

Now, if we add 5 to every number, we get :-

=》 $x_{1} + 5 + x_{2} + 5 + x_{3} + 5 + ..... + x_{75} + 5$

Now, their mean will be :-

=》 $\frac{x_{1} + 5 + x_{2} + 5 + x_{3} + 5 + ..... + x_{75} + 5}{75}$

Take the 5 common. It will be 75 times 5 as, the 5 will be added 75 times to the set of numbers.

=》 $\frac{x_{1} + x_{2} + x_{3} + ..... + x_{75} + 75(5)}{75}$

=》 $\frac{x_{1} + x_{2} + x_{3} + ..... + x_{75} + 75(5)}{75}$

We've already found that :-

$x_{1} + x_{2} + x_{3} + ..... + x_{75}$ = 2625

Put the value in the $eq^n$ :-

=》 $\frac{2625 + 75(5)}{75}$

=》 $\frac{2625 + 375}{75}$

=》 $\frac{3000}{75}$

=》 $\tt{40}$

Mean of the numbers when 5 is added to each of them = 40