Given the data set:
[tex]23,17,14,21,23,18,29,20,13[/tex]
a. 1. You need to order it from least to greatest:
[tex]13,14,17,18,20,21,23,23,29[/tex]
2. You can identify the Range. Therefore, the minimum point of the whisker must be on:
[tex]13[/tex]
And the maximum point on the whisker must be on:
[tex]29[/tex]
3. Determine the Median of the whole data set (the middle value in the data set). Since there 9 values in the set, you can determine that:
[tex]Median=20[/tex]
4. Find the Median of the bottom half part of the data:
[tex]Median_{bottom}=17[/tex]
5. And the Median of the top half is:
[tex]Median_{top}=23[/tex]
Knowing all that data, you can create the Box Plot:
b. By definition, the first quartile divides 25% of the data. Therefore, you can determine that the percentage of the data that is above the first quartile is:
[tex]75\text{\%}[/tex]
c. By definition, the second quartile divides 50% of the data. Therefore, the percentage of the data that is below it is:
[tex]50\text{ \%}[/tex]
Hence, the answers are:
a.
b.
[tex]75\text{\%}[/tex]
c.
[tex]50\text{\%}[/tex]
