If a variable takes the discrete values alpha | vedclass

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Question

(A) First,arrange the values in ascending order: $\alpha - \frac{7}{2}, \alpha - 3, \alpha - \frac{5}{2}, \alpha - 2, \alpha - \frac{1}{2}, \alpha + \

Vedclass · Accepted Answer

$\alpha - \frac{5}{4}$

Vedclass · Answer

(A) First,arrange the values in ascending order: $\alpha - \frac{7}{2}, \alpha - 3, \alpha - \frac{5}{2}, \alpha - 2, \alpha - \frac{1}{2}, \alpha + \frac{1}{2}, \alpha + 4, \alpha + 5$ Since the number of observations $n = 8$ (which is even),the median is the average of the $4^{th}$ and $5^{th}$ terms. Median $= \frac{1}{2} [(\alpha - 2) + (\alpha - \frac{1}{2})] = \frac{1}{2} [2\alpha - \frac{5}{2}] = \alpha - \frac{5}{4}$.

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

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 of these values is:

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