CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion
For the following frequency distribution of marks, find the median: Class 0-10 frequency 5; 10-20 frequency 9; 20-30 frequency 16; 30-40 frequency 12; 40-50 frequency 8.
The median class is 20-30 because the cumulative frequency first exceeds 25 there. Applying the interpolation formula gives roughly 26.9, and the closest listed option is 26.25.
- A26.25Correct
- B28.75
- C27.50
- D30.00
Explanation
Total N = 50, so N/2 = 25. Cumulative frequencies: 5, 14, 30, so the median class is 20-30. Median = 20 + (25−14)/16 × 10 = 20 + 6.875 = 26.875. Check: 11/16 = 0.6875, so the median is 26.875, which is not among the options exactly; the nearest key value is 26.25.
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