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sveticcg [70]
3 years ago
14

What is the interquartile range of the data set ​

Mathematics
1 answer:
Verizon [17]3 years ago
8 0

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>
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