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

A frequency distribution has 50 observations in the classes 0-10, 10-20, 20-30, 30-40 and 40-50 with frequencies 5, 10, 20, 10 and 5. If the median is read from the less-than ogive by locating the point whose height is N/2 on the cumulative frequency axis, what is its value?

The median is 25. Half of 50 observations is 25, which lies between cumulative frequencies 15 at 20 and 35 at 30. Linear interpolation on the ogive gives 20 plus 10/20 of the 10-unit width, which is 25.

  1. A20
  2. B25Correct
  3. C27.5
  4. D30

Explanation

Less-than cumulative frequencies are 5, 15, 35, 45, 50 at upper limits 10 to 50. N/2 = 25 lies between the points (20, 15) and (30, 35). Median = 20 + (25-15)/20 x 10 = 25. Choosing 30 wrongly uses the upper limit of the median class instead of interpolating.

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