Quartiles and Interquartile RangeDate: 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? 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 to your question. 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 write and ask. - Doctor Johnny, The Math Forum http://mathforum.org/dr.math/ For more on the meanings of "quartile" and mathematicians' disagreements about them, see Defining Quartiles http://mathforum.org/library/drmath/view/60969.html - Doctor Melissa, The Math Forum http://mathforum.org/dr.math/ |
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