Statistics And Probability Question 442
Question: If a variable takes the discrete values $ \alpha -4,,\alpha -\frac{7}{2},,\alpha -\frac{5}{2},,\alpha -3,,\alpha -2,,\alpha +\frac{1}{2},,\alpha -\frac{1}{2},,\alpha +5,(\alpha >0) $ , then the median is
[DCE 1997; Pb. CET 1988]
Options:
A) $ \alpha -\frac{5}{4} $
B) $ \alpha -\frac{1}{2} $
C) $ \alpha -2 $
D) $ \alpha +\frac{5}{4} $
Show Answer
Answer:
Correct Answer: A
Solution:
Arrange the data as $ \alpha -\frac{7}{2},\alpha -3,\alpha -\frac{5}{2},\alpha -2,\alpha -\frac{1}{2},\alpha +\frac{1}{2},\alpha +4,\alpha +5 $ Median $ =\frac{1}{2}[\text{value of }{4^{th}}item+\text{value of }{5^{th}}\text{item }] $ \ Median $ =\frac{\alpha -2+\alpha -\frac{1}{2}}{2} $ $ =\frac{2\alpha -\frac{5}{2}}{2} $ = $ \alpha -\frac{5}{4} $ .
BETA
