Question

3, 7, 8, 5, 6, 4, 9, 10, 7, 8, 6, 5 Using the previous question 's scores, If three points were added to every score in this distribution, what would be the new mean? If three points were added to every score in this distribution, what would be the new standard deviation. Remember, you have already calculated population standard deviation in a previous problem. This problem requires two answers.

Answer 1

solution:

Given scores

  3, 7, 8, 5, 6, 4, 9, 10, 7, 8, 6, 5

No.of observation (n) = 12

we know that

Mean () = = (X1+X2+X3.....+Xn) / n

Standard deviation (S) =

    Let's find mean for above scores

Mean = (3+7+ 8+5+6+4+9+10+7+8+6+5 ) / 12 = 6.5

Standard deviation (S) =  

= 2.067

If we add some k to each observation then

Mean (1) = ((X1+k) + (X2+k) + (X3+k) +.....+ (Xn+k) ) / n

= (X1+X2+X3.....+Xn + nk ) / n

= (X1+X2+X3.....+Xn) / n + k

1 = + k

Standard deviation (S1) =

=

= S

Therefore after adding 3 to each observation

Mean (1) = + k = 6.5+3 = 9.5  [Increases by 3 ]

Standard deviation (S1) = S = 2.067 [ Remains same ]