There are many methods of doing this. This one finds the median; however, instead of halving, you can use quarters instead.
First order the data, ascendingly:
10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30
Find the median:
For an even number of values: The number of values / 2
For an odd number of values: The number of values + 1 / 2
11 is odd.
11 + 1 / 2
12 / 2 = 6
The median is at the 6th position.
10, 17, 18, 18, 18, 20, 20, 25, 25, 30, 30
The median is 20.
<em>Other method:</em>
<em>You don't need this step.</em>
Using the values lower than the median, exclusive, find the median of the lower values;
For an odd number of values: <u>The number of values + 1 / 2</u>
10, 17, 18, 18, 18
5 + 1 / 2 = 6 / 2 = 3
The median of the lower values is at position 3.
This is the lower quartile.
10, 17, 18, 18, 18
<em>Other method:</em>
<em>For an odd number of values: </em><u><em>The number of values + 1 / 4</em></u>
<em>11 + 1 / 4 = 12 / 4 = 3</em>
<em>10, 17, </em><em>18,</em><em> 18, 18, 20, 20, 25, 25, 30, 30</em>
<em />
Using the values greater than the median, exclusive, find the median:
For an odd number of values: <u>The number of values + 1 / 2</u>
20, 25, 25, 30, 30
5 + 1 / 2 = 6 / 2 = 3
The median of the upper values is at position 3.
20, 25, 25, 30, 30
This is 25.
This is the upper quartile.
<em>Other method:</em>
<em>For an odd number of values: </em><u><em>(The number of values + 1 / 4) * 3</em></u>
<em>(11 + 1 / 4) * 3 = (12 / 4) * 3 = 3 * 3 = 9</em>
<em>10, 17, 18</em><em>,</em><em> 18, 18, 20, 20, 25, </em><em>25</em><em>, 30, 30</em>
Your interquartile range is 3 - 25
25 - 3 = 21
<h2>21</h2>
) to solve for the area.