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CA Foundation · Quantitative Aptitude · Statistical Description of Data

The relative frequencies of five classes in a distribution of 400 observations are 0.10, 0.25, x, 0.20 and 0.15 in order. What is the 'less than' cumulative frequency (number of observations) at the upper limit of the third class?

The cumulative frequency is 260. The missing relative frequency is 0.30 because all must sum to 1. Adding the first three gives 0.65, and multiplying by 400 observations gives 260. The value 120 is only the third class frequency, not cumulative.

  1. A120
  2. B140
  3. C260Correct
  4. D220

Explanation

The relative frequencies sum to 1, so x = 1 − (0.10+0.25+0.20+0.15) = 0.30. Cumulative relative frequency up to class 3 = 0.10+0.25+0.30 = 0.65, and 0.65 × 400 = 260. Option 120 is x × 400 only, the third class frequency.

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