If the variance of four numbers w, x, y and z is 9 , then the variance of 5 w, 5 x, 5 y and 5 z is

Step-by-step solution

Let x be the mean of 4 number aligned & x = w+x+y+z 4 & New Mean = 5 w+5 x+5 y+5 z 4 & =5 [ w+x+y+z 4 ]=5 x & Variance = x^2 n - ( x n )^2 & a= w^2+x^2+y^2+z^2 4 - ( x 4 )^2 & New variance = 25 w^2+25 x^2+25 y^2+25 z^2 4 - 25 x ^2 16 & =25 [ w^2+x^2+y^2+z^2 4 - ( x 4 )^2 ] & =25 9=225 & aligned