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CA Foundation · Quantitative Aptitude · Statistical Description of Data

A histogram is drawn for the following distribution with unequal class widths: Class 0–10 has frequency 20; class 10–20 has frequency 30; class 20–40 has frequency 40; class 40–80 has frequency 60. Taking the class width 10 as the standard, what are the heights (adjusted frequencies) of the bars for the four classes, in order?

The bar heights are 20, 30, 20 and 15. With unequal class widths, each frequency is divided by the class width relative to the standard width of 10: 40 divided by 2 gives 20, and 60 divided by 4 gives 15, while the first two classes stay unchanged.

  1. A20, 30, 20, 15Correct
  2. B20, 30, 40, 60
  3. C20, 30, 80, 240
  4. D2, 3, 2, 1.5

Explanation

Adjusted height = frequency ÷ (class width ÷ 10). For 0–10 and 10–20 the width is 10, so the heights are 20 and 30. For 20–40 the width is 20, so 40/2 = 20. For 40–80 the width is 40, so 60/4 = 15. Option 3 multiplies instead of dividing, and option 4 divides by the width itself rather than by width over 10.

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