The first thing we need to do is arrange the numbers from smallest to largest.
35, 39, 40, 45, 60
The interquartile range, or IQR, is [tex]IQR=Q_{U}-Q_{L}[/tex]
[tex]Q_{U}[/tex] is the Upper Quartile
[tex]Q_{L}[/tex] is the Lower Quartile
So we need to find those first.
To identify what the upper and lower quartiles are we need to first find the median of the data set.
35, 39, 40, 45, 60
The median, or middle number, of this data set is 40.
The lower quartile is the median of the numbers LESS THAN the data set median.
35+39=74
74/2=37
[tex]Q_{L}=37[/tex]
The upper quartile is the median of the numbers GREATER THAN the data set median.
45+60=105
105/2=52.5
[tex]Q_{U}=52.5[/tex]
[tex]IQR=Q_{U}-Q_{L}[/tex]
IQR=52.5-37
IQR=15.5
