JEE Mains · Maths · STD 11 - 13. statistics
If the mean deviation about the median of the numbers \( k, 2k, 3k, \dots, 1000k \) is 500, then \( k^{2} \) is equal to :
- A 16
- B 4
- C 1
- D 9
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
\(\because\) median \(=\frac{1001 k }{2}= X _{ M }\) \(\therefore\) mean deviation about median \(=\frac{\sum\left| X _{ i }- X _{ M }\right|}{ n }\) \(=\frac{2\left(\frac{ k }{2}+\frac{3 k }{2}+\frac{5 k }{2}+\ldots 500 \text { terms }\right)}{1000}\)…
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