Question

The Average of 7 numbers is calculated to be 35 If each number is increased by 8, find the mean of new numbers.​

Answer 1

Answer:

Let the numbers be: x1,x2,x3,...….x75

Then, 75i=1∑75xi=35

i=1∑75xi=2625 …………(1)

Now, numbers: x1+5,x2+5,x3+5...…..x75+5

75i=1∑75(xi+5)=?

⇒75i=1∑75xi+5×75

=75i=1∑75xi+755×75

=35+5

∴New mean=40.

Answer 2

Given : The average of 7 numbers is calculated to be 35. Each number is increased by 8,

To find : The mean of new numbers.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the mean of new numbers)

Mean (or, average) of initial 7 numbers = 35

So,

Sum of initial 7 numbers :

= Mean of initial 7 numbers × 7

= 35 × 7

= 245

Now, each of the 7 numbers is increased by 8

So,

For 1 number the increase amount is = 8

For 7 numbers the increase amount is = 8 × 7 = 56

Total increase amount = 56

Sum of 7 new numbers :

= Sum of initial 7 numbers + Total increase amount

= 245 + 56

= 301

So, mean of 7 new numbers :

= Sum of 7 new numbers ÷ 7

= 301 ÷ 7

= 43

(This will be considered as the final result.)

Used formula :

• Mean of n terms = Sum of n terms ÷ n
• Sum of n terms = Mean of n terms × n

Hence, the mean of new numbers is 43