CMA Foundation · Fundamentals of Business Mathematics and Statistics · Statistical Representation of Data
A 'less than' ogive for 80 workers' daily wages (in rupees hundreds) passes through the points (4, 0), (8, 10), (12, 30), (16, 60), (20, 80). Using linear interpolation, the first quartile Q1 is:
Q1 is 10. The quarter position is 80/4 = 20, which lies between cumulative 10 at 8 and 30 at 12, so Q1 = 8 + (10/20) x 4 = 10 hundred rupees.
- A8.0
- B10.0Correct
- C11.0
- D9.5
Explanation
Q1 position = N/4 = 20, which lies between 10 (at 8) and 30 (at 12). Q1 = 8 + (20-10)/(30-10) x 4 = 8 + 2 = 10. Using 3N/4 or the class 12-16 would give wrong values.
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