If the mean deviation about the median of numbers a, 2a, …. , 50a is 50, then |a| is equal to

Solution :

Median of a, 2a, 3a, 4a, ….. . 50a is

\(25a + 26a\over 2\) = 25.5a

Mean deviation = \(\sum{|x_i – Median|}\over N\)

\(\implies\)  50 = \(1\over 50\) {2|a|.(0.5 + 1.5 + …… + 24.5)]

\(\implies\) 2500 = 2|a|. \(25\over 2\) (25)

\(\implies\) |a| = 4


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