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If the mean deviation about the median of the numbers a, 2a, …, 50a is 50, then |a| equals (1) 3 (2) 4 (3) 5 (4) 2

If the mean deviation about the median of the numbers a, 2a, …, 50a is 50, then |a| equals
(1) 3
(2) 4
(3) 5
(4) 2

Grade:12

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
The given numbers area, 2a, …, 50a.
since the numer of terms is even, hence the median is given by
(25 + 26)/ 2 . a = 25.5 a
hence, the mean deviation about median is gievn by
2 ( | 0.5 + 1.5 + 2.5 + ….. + 24.5 |) / 50 . |a| = 50.
Hence 625 |a| = 2500
This gives |a| = 2500/625 = 4
Hence, |a| = 4.
Thanks & Regards
Latika Leekha
askIITians Faculty

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