standard deviation

2009-12-01 4:54 am
data groupA: 40 students, mean mark=50, standard deviation=15
data groupB: 40 students, mean mark= 40,standard deviation=10
if data group A is combined with data group B, what's the new mean and standard deviation?explain

回答 (1)

2009-12-01 5:05 am
✔ 最佳答案
Total mark of group A = 40 X 50 = 2000

Total mark of group B = 40 X 40 = 1600

Total mark of the two groups, u = 2000 + 1600 = 3600

So, the new mean = total mark of the two groups / Total number of people

= 3600 / (40 + 40)

= 45


New variance

= [40/(40 + 40)](50^2 + 15^2) + [40/(40 + 40)](40^2 + 10^2) - 45^2

= 187.5

So, the new standard deviation

= sqrt(187.5)

= 13.6931 (4 d.p.)
參考: Physics king


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