Question

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

• A. 3
• B. 4
• C. 5
• D. 2

Answer 1

Answer: (B)

4

Answer 2

Median is the mean of 25th and 26th observation $\therefore \, M = \frac{25 a + 26a}{2} = 25.5 a$ $M.D (M) = \frac{\sum |x_i - M|}{N}$ $\Rightarrow \, 50 = \frac{1}{50} [ 2 \times |a | \times (0.5 + 1.5 + 2.5 + .... 24.5)]$ $\Rightarrow \, 2500 = 2 |a | \times \frac{25}{2} (25)$ $\Rightarrow \, |a | = 4$