M&S 問題 (stat)

a) New mean of the 160 marks which are originally >= 40 will be 50 + 5(64 - 40)/6 = 70

New standard dev. of the 160 marks which are originally >= 40 will be 5 x 6/6 = 5

New mean of the 40 marks which are originally >= 40 will be 32 x 5/4 = 40

New standard dev. of the 40 marks which are originally >= 40 will be 4 x 5/4 = 5

So new mean of 200 students = (160 x 70 + 40 x 40)/200 = 64

New standard dev of 200 students:

√{[160 x 25 + 40 x 25 + 160 x (70 - 64)2 + 40 x (40 - 64)2]/200}

= 13

b) The combined set of the original marks has:

Mean = 57.6

Standard dev = 14

So the median has a stanrard score of (52 - 57.6)/14 = -0.4

For the combined set of the new marks, median = 64 - 0.4 x 13 = 58.8

2010-05-30 15:52:44 補充：
For lines 3 and 4, >= should be

2010-05-30 15:52:57 補充：
should be less than "<"

Since >=40 is bigger than <40, the median belongs to the category >=40
For an original median of 52, the new median = 50+(5/6)(52-40)=60