(Thinking question) The median of the following data is 26.25. Find the missing frequency \(x\).Class0–1010–2020–3030–4040–50Frequency5\(x\)20155

Answer: \(x = 10\)

N = 5 + x + 20 + 15 + 5 = 45 + x. The median 26.25 lies in the class 20–30, so that is the median class.

L = 20, f = 20, h = 10, cf (before median class) = 5 + x

\(\text{Median} = L + \left[ \dfrac{\frac{N}{2} - cf}{f} \right] \times h\)

\(26.25 = 20 + \left[ \dfrac{\frac{45 + x}{2} - (5 + x)}{20} \right] \times 10\)

\(6.25 = \dfrac{1}{2}\left[ \dfrac{45 + x - 10 - 2x}{2} \right] = \dfrac{35 - x}{4}\)

\(35 - x = 25 \Rightarrow x = 10\)

Check: N = 55, N/2 = 27.5; cumulative frequencies 5, 15, 35, … so 20–30 is indeed the median class, and median = \(20 + \dfrac{27.5 - 15}{20} \times 10 = 26.25\).