2023 · Q47
A grouped frequency distribution is given below: Weekly wages (Rs.): 2050–2550 (5 workers), 2550–3050 (10), 3050–3550 (k), 3550–4050 (8), 4050–4550 (2), 4550–5050 (10). If average weekly wages earned by a worker is Rs. 3,520, then what is the value of k?
Elementary MathematicsStatistics
- A10
- B12
- C15
- D20
Explanation
Using class midpoints 2300, 2800, 3300, 3800, 4300, 4800 with frequencies 5, 10, k, 8, 2, 10: total wages = 2300·5 + 2800·10 + 3300k + 3800·8 + 4300·2 + 4800·10 = 126500 + 3300k, and total workers N = 35 + k. The mean equation (126500 + 3300k)/(35 + k) = 3520 gives 126500 + 3300k = 123200 + 3520k, so 220k = 3300 and k = 15. The answer is (C).