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

A firm records the number of employees in the following classes of monthly wages (₹ thousand): Under 20 - 12; 20-40 - 18; 40-60 - 25; 60-80 - 15; 80 and above - 10. The class 'Under 20' is treated as having a width equal to the next class. What is the mid-value of the 'Under 20' class, and what is the total number of employees?

The mid-value is 10 and the total is 80 employees. An open class 'Under 20' with the same width as the next class (20) becomes 0-20, giving a mid-value of 10. Adding the frequencies 12, 18, 25, 15 and 10 gives 80.

  1. AMid-value 10; total 80Correct
  2. BMid-value 10; total 70
  3. CMid-value 15; total 80
  4. DMid-value 20; total 70

Explanation

Open-end 'Under 20' takes width 20, so class is 0-20 and mid-value is 10. Total = 12+18+25+15+10 = 80. Total 70 omits the open-ended 10 or miscounts; mid-value 15 wrongly assumes width 10.

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