If X1 ¯ and X2¯ the means of two distributions such that X1 

If X1 ¯ and X2¯ the means of two distributions such that X1 <X2¯ and X¯ is the mean of the combined distribution then

  1. A

    X¯<X¯1

  2. B

    X¯>X¯2

  3. C

    X¯=X¯1+X¯22

  4. D

    X¯1<X¯<X¯2

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    Solution:

    Let n1 and n2 be the number of observations in two groups having means X1 and X2 respectively. Then 

    X¯=n1X¯1+n2X¯2n1+n2

    Now,

    X¯X¯1=n1X¯1+n2X¯2n1+n2X¯1X¯X¯1=n2X¯2X¯1n1+n2>0X¯>X¯1 And, X¯X¯2=nX¯1X¯2n1+n2<0 X¯<X¯2

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