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CA Foundation · Quantitative Aptitude · Statistical Description of Data

A histogram is to be drawn for unequal class intervals of daily wages (₹): 100–200 with frequency 30; 200–400 with frequency 80; 400–800 with frequency 60. Taking the 100–200 class as the standard width, what are the adjusted heights (frequency densities) of the three rectangles in order?

The adjusted heights are 30, 40 and 15. Each frequency is divided by the class width expressed in units of the standard width: 30/1, 80/2 and 60/4. Using raw frequencies or multiplying would distort the areas.

  1. A30, 80, 60
  2. B30, 40, 15Correct
  3. C30, 40, 30
  4. D30, 160, 240

Explanation

Adjust each frequency by dividing by the class width in multiples of the standard width 100. 100–200: 30/1 = 30. 200–400: width 2 units, 80/2 = 40. 400–800: width 4 units, 60/4 = 15. Using raw frequencies ignores unequal widths; multiplying instead of dividing gives 160 and 240.

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