If a variable takes the discrete values alpha | vedclass

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Question

(D) First,arrange the given $8$ values in ascending order:
$\alpha - 4, \alpha - 3.5, \alpha - 3, \alpha - 2.5, \alpha - 2, \alpha - 0.5, \alpha + 0.

Vedclass · Accepted Answer

$\alpha - \frac{9}{4}$

Vedclass · Answer

(D) First,arrange the given $8$ values in ascending order:
$\alpha - 4, \alpha - 3.5, \alpha - 3, \alpha - 2.5, \alpha - 2, \alpha - 0.5, \alpha + 0.5, \alpha + 5$
Since the number of observations $n = 8$ (which is even),the median is the average of the $4^{th}$ and $5^{th}$ terms.
$4^{th} 	ext{ term} = \alpha - 2.5 = \alpha - \frac{5}{2}$
$5^{th} 	ext{ term} = \alpha - 2$
$	ext{Median} = \frac{(\alpha - \frac{5}{2}) + (\alpha - 2)}{2}$
$	ext{Median} = \frac{2\alpha - 4.5}{2} = \alpha - 2.25 = \alpha - \frac{9}{4}$

$x_i$	$5$	$15$	$25$	$35$	$45$	$55$
$f_i$	$12$	$18$	$27$	$20$	$17$	$6$

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

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