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CA Foundation · Quantitative Aptitude · Statistical Description of Data

For 80 workers, the 'more than' cumulative frequencies of weekly overtime hours are: more than 0: 80; more than 4: 68; more than 8: 45; more than 12: 20; more than 16: 6; more than 20: 0. What percentage of workers did overtime of more than 8 hours but not more than 16 hours?

The answer is 48.75%. Subtract the more than 16 count of 6 from the more than 8 count of 45 to get 39 workers, then divide by 80 and multiply by 100. Using the wrong upper boundary or ignoring the upper subtraction gives other values.

  1. A48.75%Correct
  2. B31.25%
  3. C56.25%
  4. D18.75%

Explanation

Workers with more than 8 but not more than 16 hours = C(>8) − C(>16) = 45 − 6 = 39. Percentage = 39/80 × 100 = 48.75%. Option 31.25% (25/80) is 45 − 20, which stops at 12 hours. Option 56.25% is 45/80, ignoring those above 16.

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