# 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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