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JEE Mains · Maths · STD 11 - 13. statistics
If the median and the range of four numbers \(\{x, y, 2x + y, x-y \}\) , where \(0 < y < x < 2y\) , are \(10\) and \(28\) respectively, then the mean of the numbers is
- A \(18\)
- B \(10\)
- C \(5\)
- D \(14\)
Answer & Solution
Correct Answer
(D) \(14\)
Step-by-step Solution
Detailed explanation
Since \(0 < y < x < 2y\) \(\therefore y > \frac{x}{2} \Rightarrow x - y < \frac{x}{2}\) \(\therefore x - y < y < x < 2x + y\) Hence median \( = \frac{{y + x}}{2} = 10\) \( \Rightarrow x + y = 20\,\,\,\,\,\,\,\,....\left( i \right)\) And range…
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