CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
For the following grouped data on monthly electricity bills (₹) of 60 households, find the mode using the interpolation formula. Class 0-200: 6; 200-400: 14; 400-600: 22; 600-800: 12; 800-1000: 6.
The modal class is 400-600 because it has the highest frequency, 22. Applying the formula with f0 = 14, f2 = 12 and h = 200 gives 400 + 8/18 × 200 = ₹488.89.
- A₹500
- B₹533.33Correct
- C₹550
- D₹566.67
Explanation
The modal class is 400-600 with f1=22. Then f0=14 and f2=12. Mode = L + (f1-f0)/(2f1-f0-f2) × h = 400 + 8/(44-14-12) × 200 = 400 + (8/18)×200 = 400 + 88.89 = ₹488.89. Recheck: 2f1-f0-f2 = 44-26 = 18, so mode = 488.89. Since 488.89 is not among the options, the option must be matched against the correct working: the intended data gives 488.89, not 533.33.
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