Question

If mean of n observations is X and each value is multiplied by a . find the new mean

Answer 1

total = xn
if each is ×ed by a then total increases by na
therefore new mean =[n (x+a)]÷n
ans=x+a

Answer 2

Answer:

The new Mean = X·a

Step-by-step explanation:

Mean = X

Number of observations = n

Let the values in the sample are :

$x_1,x_2,x_3,...........x_n\\\\\implies Mean=X=\frac{x_1+x_2+x_3+...........+x_n}{n}$

Now, every value is multiplied by a. Then the values in the sample are :

$ax_1,ax_2,ax_3,.............ax_n\\\\\implies Mean=\frac {ax_1+a x_2+ax_3 +........... + ax_n}{n}\\\\\implies Mean=\frac {a(x_1+ x_2+x_3+...........+x_n)}{n}\\\\\implies Mean=a\times \frac{x_1+x_2 +x_3+...........+x_n}{n}\\\\\implies Mean = a\times X\\\\\implies Mean = X\cdot a$