ANSWER
A: 4.75
EXPLANATION
The given date set is
12, 14, 16, 17.5, 10, 18, 15, 15.5, 19
We arrange the data set in ascending order to get,
{10,12,14,15,15.5,16,17.5,18,19}
The median is,
[tex]15.5[/tex]
The first quartile is the median of the lower half of the ascending set.
{10,12,14,15}
[tex]Q_1= \frac{12 + 14}{2} = 13[/tex]
The third quartile is the median of the upper half of the ascending set.
{15.5,17.5,18,19}
[tex]Q_3= \frac{17.5+ 18}{2} = 17.75[/tex]
The inter- quartile range is
[tex]Q_3 - Q_1= 17.75 - 13 = 4.75[/tex]
