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

Question

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

Dr. Abubacker · Accepted Answer

(a)
Arranging the given values in ascending order of magnitude
$x - \frac{7}{2},x - 3,\ x - \frac{5}{2},\ x - 2,\ x + \frac{1}{2},\ x + 4,\ x + 5$
There are 8 observations in the series, therefore
$median = \frac{Value\ of\ 4th\ term + Value\ of\ 5th\ term}{2}$
$= \frac{x - 2 + x - \frac{1}{2}}{2} = x - \frac{5}{4}$

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

Explanation

Reviewed by Dr. Abubacker

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