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### Quartiles and Interquartile Range

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Date: 10/27/1999 at 11:17:39
From: Newton
Subject: What is interquartile range?

What is interquartile range? How do I calculate Q1, Q2, and Q3?
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Date: 11/12/1999 at 13:16:28
From: Doctor Johnny
Subject: Re: What is interquartile range?

Newton,

I hope that I can give you some insight into your question. Let's
begin by looking at some definitions to help better explain the answer

Median (Q2): the number that divides the data into two equal halves.
The piece of data that is exactly in the middle, when arranged in
numerical order.

Lower Quartile (Q1): the number that divides the lower half of the
data into two equal halves.

Upper Quartile (Q3): the number that divides the upper half of the
data into two equal halves.

These three pieces are called quartiles because they divide the data
into four equal portions.

Interquartile range: the difference between the upper and lower
quartiles.

Let's look at a set of data and explain these four points of emphasis:

25, 26, 27, 28, 29, 30, 40, 41, 42

The median is to be found first. A general formula used to find the
piece that represents the median is (n+1)/2, where n is the number of
pieces of data that you have. Since there are nine pieces of data
listed, you would say (9+1)/2 = 5. This says that the 5th piece of
data is the median.

25, 26, 27, 28,     29,     30, 40, 41, 42
^
median

Now we find the upper and lower quartiles. These are actually the
medians of the upper and lower halves of data. Since there are
four pieces of data in the upper and lower halves, you can use
(4+1)/2 = 2.5. This means that the median is halfway between the
second and third pieces of data in each half.

Lower Quartile: 26 + 27 = 53/2 = 26.5
Upper Quartile: 40 + 41 = 81/2 = 40.5

25, 26,    (26.5)    27, 28,    29,    30, 40,    (40.5)  41, 42
^                  ^                   ^
Q1              median (Q2)            Q3

The interquartile range can be found by taking the difference between
the upper and lower quartiles (40.5 - 26.5 = 14.) This means that
there are fourteen units between the upper and lower quartiles.

I hope that this will help you better understand the concept of
interquartile range. If you have any further questions, feel free to

- Doctor Johnny, The Math Forum
http://mathforum.org/dr.math/
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For more on the meanings of "quartile" and mathematicians'

Defining Quartiles
http://mathforum.org/library/drmath/view/60969.html

- Doctor Melissa, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Statistics

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