M&S 問題 (stat)

2010-05-30 9:38 pm

The passmark of an examination is set at 40. Below show the mark of 200 students who took the exam.

mark range number of students mean standard deviation
X>=40 160 64.0 6.0
X<40 40 32.0 4.0
The teacher wants to sacle the marks so that more students will pass the exam. The new mark corresponding to X is

y= 50+ 5/6(x-40), if x >=40,
y=(5/4)X if x <40.

(a) Find the median and standard deviation of the new marks of the 200 students.

(b) The median of the original 200marks is 52. Find the median of the new marks.

更新1:

the answer in b should be 60

更新2:

and i don't know how to calculate the combined standand dev also in line7 , how to obtain 25? and what is the formula?

更新3:

-if u can , plz explain line 11-13 , thz

回答 (2)

六呎將軍

2010-05-30 10:45 pm

✔ 最佳答案

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 "<"

參考: Myself

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用戶9112

2010-05-31 3:12 am

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

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