A set of data is given. It is required to find the first, second, and third quartile.
The given data is:
[tex]2,8,9,10,14,15,16,16,17,17,20[/tex]
Recall that the lower quartile Q₁, or the first quartile, is the median of the lower half of the data in a set.
The lower half is:
[tex]2,8,9,10,14[/tex]
Find the median of the lower half to get the first quartile, Q₁:
Hence, Q₁=9.
Recall that the second quartile Q₂ is the same as the median of the data.
The median is the middle element or the mean of two middle elements in a numerical data set with the elements ordered by their value.
Notice that the middle number is 15.
Hence, second quartile Q₂=15.
The upper quartile Q₃, or the third quartile, is the median of the upper half of the data in a set.
The upper half of the data is:
[tex]16,16,17,17,20[/tex]
Calculate the median to find the third quartile, Q₃:
It follows that Q₃=17
The complete table is shown below:
