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CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion

The frequency distribution of monthly overtime hours of 50 workers in a Surat textile unit is: 0–10: 5; 10–20: 10; 20–30: 20; 30–40: 10; 40–50: 5. What is the median overtime?

The median overtime is 25 hours. Half of 50 is 25, which falls in the 20–30 class, where the cumulative frequency before it is 15 and its frequency is 20. So the median is 20 + (10/20)×10 = 25.

  1. A30
  2. B25Correct
  3. C22.5
  4. D35

Explanation

N = 50, so N/2 = 25. Cumulative frequencies are 5, 15, 35, 45, 50, so the median class is 20–30 with cf before it = 15 and f = 20. Median = 20 + (25 − 15)/20 × 10 = 25. Using 5 as the preceding cumulative frequency would give 30, which is wrong.

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