Multiple choice

If the combined mean of the two group is $\dfrac { 40 }{ 3 } $ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is

  1. $\dfrac { 46 }{ 3 } $
  2. $\dfrac { 35 }{ 4 } $
  3. $\dfrac { 45 }{ 4 } $
  4. $\dfrac { 41 }{ 4 } $
  5. $\dfrac { 43 }{ 4 } $
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C Correct answer
Explanation

Combined mean = (n1*m1 + n2*m2) / (n1 + n2). 40/3 = (10*15 + 8*m2) / 18. 40/3 = (150 + 8*m2) / 18. 240 = 150 + 8*m2. 90 = 8*m2. m2 = 90/8 = 45/4.

AI explanation

The combined mean formula is the total sum of all observations divided by the total number of observations. The total sum is calculated as (10 multiplied by 15) plus (8 multiplied by x), which equals 150 plus 8x. The total number of observations is 18, so the equation becomes 150 plus 8x divided by 18 equals 40/3. Multiplying by 18 gives 150 plus 8x equals 240, meaning 8x equals 90, and the mean of the second group is 45/4.

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