Question

the mean of 24 number is 35 if 3 is added to each number what will be the new mean?

Answer 1

Mean = 24
No. of terms = 35
Since,
Mean = sum of all terms / 35
24 = sum of all terms / 35
sum of all terms = 24 x 35
sum of all terms = 840

If 3 is added to each number
So 3 will be added to all 35 terms so total addition to the sum will be = 3 x 35
= 105

So, now sum of all terms becomes
new sum of all terms = sum of all terms + 105

new mean = new sum of all terms/35
new mean = (sum of all terms+105)/35
Separating numerator in RHS
new mean = sum of all terms/35 + (105/35)
But, sum of all terms/35 =mean ( By (1) )
new mean = mean+ (105/35)
new mean = 840 + (105/35)
new mean = 840 + 3
new mean = 843