Question

If x is the mean of the data x1, x2 ……...., xn and a is a non – zero number, then show that


(i) the mean of the data x1 + a, x2 + a,…., xn + a is x + a.
(ii) the mean of the data ax1, ax2, ax3 …., axn is ax
pls tell the answer fast.

Answer 1

Answer:

(i) For finding the mean

mean = (sum of observations)/(Number of observations)

=> Mean = $\frac{x1 +a + x2 + a +......+xn + a}{n}$

=> Mean = $\frac{x1 + x2 + x3 +.....xn + (a+a+a+a+a.... n times}{n}$

Now Seperate the sums we get x + $\frac{na}{n}$

Which gives us Mean = x + a

(ii) Proceeding as above,

We get, Mean = $\frac{ax1 + ax2 +..... axn}{n}$

Take 'a' common from the numerator

=> Mean = $\frac{(a)(x1+ x2 + x3+ ...... + xn)}{n}$

We get Mean = ax

Hope this helps!