Multiple choice

Directions: The mean and standard deviation of 100 items are 50, 5 and that of 150 items are 40, 6 respectively. What is the combined mean of all 250 items?

  1. 43

  2. 44

  3. 45

  4. 46
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B Correct answer
Explanation

Combined mean = (n1*m1 + n2*m2) / (n1 + n2) = (100*50 + 150*40) / (100 + 150) = (5000 + 6000) / 250 = 11000 / 250 = 44.

AI explanation

Using the combined mean formula, the total sum of the first 100 items is 100 multiplied by 50, which equals 5000. The total sum of the remaining 150 items is 150 multiplied by 40, which equals 6000. The combined mean of all 250 items is the total sum divided by the total number of items, calculated as (5000 + 6000) divided by 250, resulting in 11000 divided by 250, which equals 44.

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