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Question

The average marks of 10 students in a class was 60 with a standard deviation of 4, while the average marks of other ten students was 40 with a standard deviation of 6. If all the 20 students are taken together and σ is the combined standard deviation, then the value of [σ] is
([] represents the greatest integer function)

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Solution

¯¯¯x=60
xi=600
σ2(xi)=42=16
16=x2i10(60)2
x2i=36160

¯¯¯y=40
yi=400
σ2(yi)=62=36
36=y2i10(40)2
y2i=16360

Combined variance,
σ2=110+10(x2i+y2i)(xi+yi10+10)2
=36160+1636020(600+40020)2
=26262500
=126
[σ]=11

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