Multiple choice

Mean score of $25$ observation is $80$ and that of another $75$ observation is $60$ The mean score of all observation taken together is

  1. $65$
  2. $75$
  3. $85$

  4. None of these above
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A Correct answer
Explanation

The combined mean is (n1 * mean1 + n2 * mean2) / (n1 + n2). (25 * 80 + 75 * 60) / (25 + 75) = (2000 + 4500) / 100 = 6500 / 100 = 65.

AI explanation

Use the combined mean formula, which is the total sum of all observations divided by the total number of observations. The sum of the first 25 observations is 25 * 80 equals 2000, and the sum of the other 75 observations is 75 * 60 equals 4500. The combined mean is (2000 + 4500) / (25 + 75), which simplifies to 6500 / 100, resulting in a mean of 65.

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