2023 · Q48
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). What is the median (approximate value) of the distribution?
Elementary MathematicsStatistics
- ARs. 3,263
- BRs. 3,383
- CRs. 3,413
- DRs. 3,483
Explanation
With k = 15 the total frequency is N = 50, so N/2 = 25. Cumulative frequencies are 5, 15, 30, …; the 25th observation falls in the class 3050–3550. Using median = l + ((N/2 − cf)/f)·h with l = 3050, cf = 15, f = 15, h = 500: median = 3050 + (25 − 15)/15 × 500 = 3050 + 333.33 ≈ 3383. The answer is (B) Rs. 3,383.