JEE Mains · Maths · STD 11 - 13. statistics
Suppose that the mean and median of the non-negative numbers \(21, 8, 17, a, 51, 103, b, 13, 67, (a > b)\), are \(40\) and \(21\), respectively. If the mean deviation about the median is \(26\), then \(2a\) is equal to:
- A \(109\)
- B \(117\)
- C \(161\)
- D \(131\)
Answer & Solution
Correct Answer
(D) \(131\)
Step-by-step Solution
Detailed explanation
The given numbers are \(21, 8, 17, a, 51, 103, b, 13, 67\). There are \(9\) numbers in total. Given that the mean is \(40\), the sum of the numbers is: \(\sum x_i = 9 \times 40 = 360\) The sum of the known numbers is: \(21 + 8 + 17 + 51 + 103 + 13 + 67 = 280\) Therefore, the sum…
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