JEE Mains · Maths · STD 11 - 13. statistics
If the mean deviation about median for the number \(3,5,7,2\,k , 12,16,21,24\) arranged in the ascending order, is \(6\) then the median is
- A \(11.5\)
- B \(10.5\)
- C \(12\)
- D \(11\)
Answer & Solution
Correct Answer
(D) \(11\)
Step-by-step Solution
Detailed explanation
Median \(=\frac{2 k+12}{2}=k+6\) Mean deviation \(=\sum \frac{\left|x_{i}-M\right|}{n}=6\) \((k+3)+(k+1)+(k-1)+(6-k)+(6-k)\) \(\frac{+(10-k)+(15-k)+(18-k)}{8}\) \(\therefore \quad \frac{58-2 k}{8}=6\) \(k=5\) Median \(=\frac{2 \times 5+12}{2}=11\)
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