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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Statistical Representation of Data

In a frequency distribution of 50 observations with equal class width 10, the classes are 0-10, 10-20, 20-30, 30-40, 40-50. The cumulative frequencies (less than type) at the upper limits 10, 20, 30, 40 and 50 are 4, 13, 31, 45 and 50 respectively. What is the frequency of the class 20-30 and the number of observations that are 30 or more?

The class 20-30 has frequency 18 and 19 observations are 30 or more. The class frequency is the difference between cumulative frequencies, 31 minus 13. Observations of 30 or more equal 50 minus 31, which is 19.

  1. AFrequency 18; observations 19Correct
  2. BFrequency 31; observations 19
  3. CFrequency 18; observations 31
  4. DFrequency 9; observations 19

Explanation

Frequency of 20-30 = 31 − 13 = 18. Observations that are 30 or more = total − cumulative frequency below 30 = 50 − 31 = 19. Check using classes: 30-40 has 45 − 31 = 14 and 40-50 has 5, and 14 + 5 = 19. Option with 31 confuses a cumulative figure with a class frequency.

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