Question

Variance of 5 numbers is 36 if each number is doubled find standard deviation

Answer 1

Answer:

144

Step-by-step explanation:

Given Variance of 5 numbers is 36 if each number is doubled find standard deviation

Let the numbers be x1,x2,x3,x4,x5 and x bar be their mean.

Given variance = 36 and n = 5

We know that

Variance = 1/n ∑(xi – x bar)^2

         36 = 1/5 ∑ (xi – x bar)^2

          ∑ (xi – x bar)^2 = 180 ------------1

Now each (xi – x bar)^2 Number is doubled,

So let new numbers be y1,y2,y3,y4,y5

yi = 2(xi)----------------------2

we need to find variance for new numbers.

New variance = 1/n ∑ (yi – y bar)^2

     y bar = 1/n ∑ yi

we know that

         yi = 2 (xi)

     y bar = 1/n ∑ 2 xi  

      y bar = 1/5 ∑ 2 xi

   y bar = 2 x bar ---------------3

from 1 we get

  ∑ (xi – x bar)^2 = 180  [ from 2 and 3 xi = ½ yi and x bar = ½ y bar)

 ∑ (1/2 yi – 1/2 y bar)^2 = 180

 ∑  (1/4)(yi – y bar)^2 = 180

∑ (yi – y bar)^2 = 720

Now new variance will be = 1/n ∑ (yi – y bar)^2

                                         = 1/5 x 720

                                       = 144