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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion

A firm records the daily output (units) of its workers with these frequencies: 0-10: 4; 10-20: 10; 20-30: 16; 30-40: 12; 40-50: 8. The mode of this distribution, using the interpolation formula, is:

The mode is 26. The modal class is 20-30 with frequency 16, preceded by 10 and followed by 12. Applying L + (f1−f0)/(2f1−f0−f2) × h gives 20 + 6/10 × 10 = 26. Reversing the neighbouring frequencies gives 24, which is wrong.

  1. A26Correct
  2. B24
  3. C25
  4. D28

Explanation

The modal class is 20-30, so L = 20, h = 10, f1 = 16, f0 = 10 and f2 = 12. Mode = L + (f1−f0)/(2f1−f0−f2) × h = 20 + 6/(32−22) × 10 = 20 + 6 = 26. The value 24 comes from using the preceding and following frequency gaps the wrong way round (4/10).

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