First slide

Introduction to statistics

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

Moderate

A

$x - \frac{5}{4}$
B

$x - \frac{1}{2}$
C

$x - 2$
D

$x + \frac{5}{4}$

Solution

Arranging the given values in ascending order of magnitude, we get
$x - \frac{7}{2}, x - 3, x - \frac{5}{2}, x - 2, x - \frac{1}{2}, x + \frac{1}{2}, x + 4, x + 5$
There are 8 observations in this series
$∴$ Median= AM of 4th and 5th observation
$\Rightarrow$ Median = AM of (x - 2) and (x -1/2)
$\Rightarrow Median = \frac{x - 2 + x - \frac{1}{2}}{2} = x - \frac{5}{4}$

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