Question

what is the median of this data set?[29,22,23,31,29,29,22,23]

Answer 1

Given the dataset:

$\mleft\lbrace29,22,23,31,29,29,22,23\mright\rbrace$

First of all, we order it:

$\mleft\lbrace22,22,23,23,29,29,29,31\mright\rbrace$

There are 8 elements, so, for the median we have:

$i=\frac{n}{2}$

Where n is the number of elements. Now, for n = 8:

$i=\frac{8}{2}=4$

This is a whole number, so the median is the semi-sum between the elements at positions i and (i + 1). That is, the fourth and fifth elements of the ordered dataset:

$Q_{50}=\frac{23+29}{2}=26$