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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Statistical Representation of Data

A 'less than' ogive and a 'more than' ogive are drawn for the same data of 100 items with class limits 0-20, 20-40, 40-60, 60-80, frequencies 10, 30, 40, 20. At the point where they intersect, what are the coordinates (value, frequency)?

The two ogives meet at the median, with height N/2 = 50. Cumulative frequencies are 10, 40, 80, 100, so the median is 40 + (10/40) x 20 = 45, giving the point (45, 50).

  1. A(50, 50)
  2. B(45, 50)
  3. C(48, 50)Correct
  4. D(50, 45)

Explanation

The curves intersect at the median, at height N/2 = 50. Cumulative less than: 10, 40, 80, 100. Median class is 40-60: 40 + (50-40)/40 x 20 = 40 + 5 = 45. So the intersection is (45, 50). Distractor 50 uses the class midpoint.

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