Multiple choice

The frequency distribution of the marks obtained by $100$ students in a test carrying $50$ marks then the mean is Marks 0-9 10-19 20-29 30-39 40-49 No. of students 8 15 20 45 12

  1. $28.3$
  2. $28$
  3. $27.3$
  4. $26.4$
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A Correct answer
Explanation

Using class midpoints 4.5, 14.5, 24.5, 34.5, and 44.5, the weighted total is 2,830. Dividing by 100 students gives a mean of 28.3 marks.

AI explanation

Using the step deviation method, the class marks for the intervals are 4.5, 14.5, 24.5, 34.5, and 44.5. Multiplying each class mark by its corresponding frequency of 8, 15, 20, 45, and 12 gives the products 36, 217.5, 490, 1552.5, and 534. The sum of these products is 2830, and dividing this by the total frequency of 100 students gives a mean of 28.3.

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