Multiple choice

If the mean of frequency distribution is 7.5 and ∑fi xi = 120 + 3k, ∑fi = 30, then k is equal to:

  1. 50

  2. 30

  3. 45

  4. 35
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D Correct answer
Explanation

Mean = sum(fi*xi) / sum(fi). 7.5 = (120 + 3k) / 30. 225 = 120 + 3k. 105 = 3k. k = 35.

AI explanation

The formula for the mean of a frequency distribution is the sum of (fi times xi) divided by the sum of fi. Substituting the given values gives 7.5 = (120 + 3k) / 30. Multiplying both sides by 30 results in 225 = 120 + 3k. Subtracting 120 from 225 leaves 105 = 3k, so dividing by 3 gives k = 35.

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