If the mean deviation about the median of the numbers $$a,$$ 2$$a,$$ . . . . . , 50$$a$$ is 50, then $$\left| a \right|$$ equals
A.
3
B.
4
C.
5
D.
2
Answer :
4
Solution :
Median is the mean of $${25^{th}}$$ and $${26^{th}}$$ observation
$$\eqalign{
& \therefore \,\,M = \frac{{25a + 26a}}{2} = 25.5a \cr
& M.D\left( M \right) = \frac{{\sum {\left| {{x_i} - M} \right|} }}{N} \cr
& \Rightarrow \,\,50 = \frac{1}{{50}}\left[ {2 \times \left| a \right| \times \left( {0.5 + 1.5 + 2.5 + .....24.5} \right)} \right] \cr
& \Rightarrow \,\,2500 = 2\left| a \right| \times \frac{{25}}{2}\left( {25} \right) \cr
& \Rightarrow \,\,\left| a \right| = 4 \cr} $$
Releted MCQ Question on Statistics and Probability >> Statistics
Releted Question 1
Select the correct alternative in each of the following. Indicate your choice by the appropriate letter only.
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