JEE Mains · Maths · STD 11 - 13. statistics
A variable \(X\) takes values \(0, 0, 2, 6, 12, 20, \ldots, n(n-1)\) with frequencies \({}^nC_0, {}^nC_1, {}^nC_2, {}^nC_3, {}^nC_4, {}^nC_5, \ldots, {}^nC_n\), respectively. If the mean of this data is \(60\), then its median is :
- A \(56\)
- B \(42\)
- C \(72\)
- D \(90\)
Answer & Solution
Correct Answer
(A) \(56\)
Step-by-step Solution
Detailed explanation
The given variable \(X\) takes values \(x_r = r(r-1)\) with frequencies \(f_r = {}^{n}C_{r}\) for \(r = 0, 1, 2, \ldots, n\). The mean of the data is given by \(\bar{X} = \dfrac{\sum_{r=0}^{n} f_r x_r}{\sum_{r=0}^{n} f_r}\). We know that…
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