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CA Foundation · Quantitative Aptitude · Statistical Description of Data

For a distribution of 120 workers' daily wages, the 'less than' cumulative frequencies are: less than 200: 12; less than 300: 40; less than 400: 82; less than 500: 108; less than 600: 120. Which of the following gives the median class and the frequency of the class 400–500?

The median class is 300–400 and the frequency of 400–500 is 26. Half of 120 is 60, which lies between the cumulative frequencies 40 and 82, so the median class is 300–400. The class 400–500 has 108 − 82 = 26 workers.

  1. AMedian class 300–400; frequency of 400–500 is 26Correct
  2. BMedian class 400–500; frequency of 400–500 is 26
  3. CMedian class 300–400; frequency of 400–500 is 108
  4. DMedian class 400–500; frequency of 400–500 is 82

Explanation

N/2 = 60. The cumulative frequency first exceeds 60 at 'less than 400' (82), and 40 < 60, so the median class is 300–400. Frequency of 400–500 = 108 − 82 = 26. Option with median class 400–500 wrongly treats the cumulative frequency 108 as the one just above 60.

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