Question

if x bar is the arithmetic mean of n observations x1,x2.....xn find the arithmetic mean of ax1,ax2.....axn

Answer 1

Mean = Sum of Observations / No. of Observations,

Here sum of Observations = x1+ x2 + ....... + xn,
No. of observations = n,

Mean = x bar , As the bar can't be represented here I am taking it as a, i.e x bar = b, for better understanding,

Now,
b = (x1+ x2 + ......+ xn)/n
=> bn = x1 + x2 + x3 + ..... + xn,
Multiple both the sides with a,
=> abn = ax1 + ax2 + ax3 + ..... + axn ,

Now we got the value of ax1 + ax2 + ... + axn,
Remember that no. of observations won't change,

Now new mean or Required mean is,

New mean = (ax1+ ax2 + ... + axn )/n
=> New mean = abn/n
=> New mean = ab,

Here b = x bar, As I said above , So the new mean = a * Previous mean or ,

New mean = a * x bar,

Hope you understand, Have a great day !

Answer 2

Answer:

New arithmetic mean Will be

old arithmetic mean *a

x bar*a