THEOREM 1 If x is the arithmetic mean of n observations a, a, x, . X t

1.	THEOREM 1 If x is the arithmetic mean of n observations a, a, x, . X t
Answer» 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,

Answer»

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,

Discussion