Multiple choice

The arithmetic mean of a set of numbers is 8. The mean of another set of numbers is 15. If the combined mean of both is 12.5, what will be the ratio of frequencies of both sets?

  1. 2: 3

  2. 5: 6

  3. 5: 9

  4. 16: 25
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C Correct answer
Explanation

Let n1 and n2 be frequencies. Combined mean = (8n1 + 15n2)/(n1 + n2) = 12.5. Solving: 8n1 + 15n2 = 12.5n1 + 12.5n2, which gives 4.5n1 = 2.5n2, so n1/n2 = 2.5/4.5 = 5/9.

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