If a variable takes the discrete values α+4, α-(7/2), α-(5/2), α-3, α-2, α+(1/2), α-(1/2) , α+5(α0), then the median is

Question

If a variable takes the discrete values α+4, α-(7/2), α-(5/2), α-3, α-2, α+(1/2), α-(1/2) , α+5(α>0), then the median is (A) α-(5/4) (B) α-(1/2) (C) α-2 (D) α+(5/4)

Tardigrade Admin · Accepted Answer

Since, α>0 (given) arrange the data in ascending order, α-(7/2), α-3, α-(5/2), α-2, α-(1/2), α+(1/2) ,α+4, α+5 Median =(α-2+α-(1/2)/2)=(2 α-(5/2)/2)=α-(5/4)

Q. If a variable takes the discrete values $α + 4, α - \frac{7}{2}, α - \frac{5}{2}, α - 3, α - 2, α + \frac{1}{2}, α - \frac{1}{2}, α + 5 (α > 0)$ , then the median is

$α - \frac{5}{4}$

$α - \frac{1}{2}$

$α - 2$

$α + \frac{5}{4}$

$α + \frac{1}{2}$

Since, $α > 0$ (given) arrange the data in ascending order,
$α - \frac{7}{2}, α - 3, α - \frac{5}{2}, α - 2, α - \frac{1}{2}, α + \frac{1}{2}, α + 4, α + 5$
Median $= \frac{α - 2 + α - \frac{1}{2}}{2} = \frac{2 α - \frac{5}{2}}{2} = α - \frac{5}{4}$

Q. If a variable takes the discrete values α+4,α−27​,α−25​,α−3,α−2,α+21​,α−21​,α+5(α>0), then the median is

α−45​

α−21​

α−2

α+45​

α+21​

Since, α>0 (given) arrange the data in ascending order, α−27​,α−3,α−25​,α−2,α−21​,α+21​,α+4,α+5 Median =2α−2+α−21​​=22α−25​​=α−45​