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For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is

Options

  1. A13 2
  2. B5 2
  3. C11 2
  4. D15 2

Correct answer

C. 11 2

Step-by-step solution

We have n ₁=5, ₁ ^2=4, x ₁=2 and n ₂=5, ₂ ^2=5, x ₂=4 here combined mean = x _c= (5)(2)+(5)(4) (5)+(5) =3 d ₁= x ₁- x _ c =2-3=1 and d ₂= x ₂- x _ c =4-3=1 Combined variance = = n ₁ ( ₁^2+ d ₁^2 )+ n ₂ ( ₂^2+ d ₂^2 ) n ₁+ n ₂ = 5(4+1)+5(5+1) 5+5 = 11 2

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