Discussion
Median can be calculated with
I. \(L_{1} + \frac{i}{f}\left(\frac{N}{2} - C\right)\)
II. \(L_{1} + \frac{L_{2} - L_{1}}{f}(m - C)\)
III. \(L_{1} + \frac{\frac{N}{2} - C}{f}(L_{2} - L_{1})\)
IV. \(L_{2} + \frac{\frac{N}{2} - C}{f} \times i\)
Find the correct combination.
Answer: D
The formulas for the median of grouped data are I, II and III, so the keyed answer is the last option. Each of them is a form of the same rule: the median is the lower limit of the median class plus the distance into the class, found from the number of observations needed to reach N/2 and the frequency of the class, times the class interval. Formula IV starts from L2, the upper limit, and then adds the same amount, so it overshoots the class. It is not the median formula, and the options containing IV are rejected.
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