Question

if the mean of x1 and x2 is M1 and that of x1,x2,x3,x4,is m2 ,then mean of ax1,ax2,x3/a,x4/a is

Answer 1

if the mean of x1 and x2 is M1 and that of x1,x2,x3,x4,is m2 ,then mean of ax1,ax2,x3/a,x4/a  = (M1(a² - 1) + 2M2)/2a

Step-by-step explanation:

mean of x1 and x2 is M1

=> x1 + x2 = 2M1

mean of x1,x2,x3,x4 is M2

=> x1 + x2 + x3 + x4 = 4M2

=> 2M1 + x3 + x4  = 4M2

=>  x3 + x4 = 4M2 - 2M1

mean of ax1,ax2,x3/a,x4/a

=  (ax1 + ax2  +  x3/2  + x4/a) /4

= (a²x1 + a²x2 + x3 + x4)/4a

= (a²(x1 + x2)  + (x3 + x4) )/4a

= (a²*2M1 + 4M2 - 2M1) / 4a

= 2(M1(a² - 1) + 2M2)/4a

= (M1(a² - 1) + 2M2)/2a