Question

If xdash is mean of x1 x2 ........xn fing the mean of x1+a ..........xn+a

Answer 1

Answer

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


Answers

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 2

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