Question

The mean of 15 numbers is 27. If each number is multiplied by 4, what will be the new mean of the new numbers?

Answer 1

given the mean of 15 number is = 27

let the number be x₁,x₂,x₃.............x₁₅

= x₁,x₂,x₃.................,x₁₅ / 15 = 27

= x₁,x₂,x₃.................,x₁₅  = 27 * 15 = 405 ...... eqn first

now the each number is multiplied by 4 then, new set of 15 number is , so new mean is

x₁*4 ,x₂*4 ,x₃*4 .................,x₁₅*4 / 15 = 4* { x₁,x₂,x₃.................,x₁₅} / 15 = 4*27 = 108 [ using eqn first ]

hence new mean is = 108

Answer 2

Given, mean of 15 numbers is 27

Let the 15 numbers be, x1, x2, x3 -----x15

= x1,x2,x3 ----x15/15 = 27

= x1,x2,,x3 -----x15

= 27*5

= 405 (this is an equation 1)

Now we will multiply this number with 4

the new set of numbers will be:

x1*4

x2*4

x3*4

x4*4

x5*4

x6*4

x7*4

x8*4

x9*4

x10*4

x11*4

x12*4

x13*4

x14*4

x15*4

= answer /15

= 4*27 = 108 (now we will use the equation 1)

So the answer to this will be 108.

I hope this helps you, let us know if there is any confusion.