First slide

Introduction to statistics

Question

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

Easy

A

$α - \frac{5}{4}$
B

$α - \frac{1}{2}$
C

$α - 2$
D

$α + \frac{5}{4}$

Solution

Arrange the data as follows:
$\begin{array}{l} α - \frac{7}{2}, α - 3, α - \frac{5}{2}, α - 2, α - \frac{1}{2}, α + \frac{1}{2}, α + 4, α + 5 \\ Median = \frac{1}{2} [value of 4 th item + value of 5 th item] \\ ∴ Median = \frac{α - 2 + α - \frac{1}{2}}{2} = \frac{2 α - \frac{5}{2}}{2} = α - \frac{5}{4} \end{array}$

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