Multiple choice

If $150$ is the mean of $200$ observations and $100$ is the mean of some $300$ other observations, find the mean of the combination.

  1. $90$
  2. $100$
  3. $120$
  4. $150$
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C Correct answer
Explanation

Combined mean = (n1*m1 + n2*m2) / (n1 + n2) = (200*150 + 300*100) / (200 + 300) = (30000 + 30000) / 500 = 60000 / 500 = 120.

AI explanation

The combined mean is found by dividing the total sum of all observations by the combined total count. The sum of the first 200 observations is 150 times 200, which is 30000, and the sum of the 300 other observations is 100 times 300, which is 30000. The total sum is 60000, and dividing this by the total of 500 observations gives a mean of 120.

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