M1 Statistics

Old Mean = 65
Old Total marks / 38 = 65

Correct mean
= Correct total marks / 38
= [Old total marks - 50 + 60 ]/38
= Old Total marks / 38 +10/38
= 65 + 10/38
=1240/19
=65.326...
=65.3 (3 sig. fig.)

[Old S.D]^2
= mean of square - square of mean
=(∑xi^2) / 38 - 65^2 = (2√2)^2 = 8

=> (∑xi^2) / 38 = 8 + 65^2 = 4233 .............(*)

where xi are the old marks.

[New S.D,]^2
= mean of square - square of mean
= (∑yi^2) / 38 - 65.3^2 , where yi are the old marks.
= [(∑xi^2) - 50^2 + 60^2 ]/ 38 - 65.3^2
= (∑xi^2) / 38 +1100/38 - 65.3^2
= 4233 + 1100/38 -65.3^2 [Using (*)]
= 2.6676...

New S.D. = 1.63 (3 sig. fig.)


2010-07-24 14:41:55 補充：
yi are the new(not old) marks.

2010-07-24 14:53:11 補充：
I guess if we use:
S.D.^2 =∑(xi - u)^2 / N ,u=mean, it very difficult to answer this question becuase:
u has changed and it is inside a "square".

Rather, if we use

S.D.^2 = mean of square - square of mean
=(∑xi^2) / N - u^2

u becomes more separable from xi.

2010-07-24 16:59:07 補充：
STEVIE-G™ :
The mean u has already changed, so even you replace x1 by x1+10, the mean in x2-u, x3-u, ..., x38-u doesn't change.

Thanks for your remainder. I do it wrongly and I appreciate your work.