Median, QuartilesDate: 1/09/98 at 16:26:05 From: Dano Subject: Find median, upper and lower quartiles 22,18,9,26,14,15,6,19,28 Date: 01/22/98 at 17:07:13 From: Doctor Sonya Subject: Re: Find median, upper and lower quartiles Hi there, Dano. To find the median of a group of values, e.g., 1 3 4 55 6 82 2 begin by sorting the values in increasing order: 1 2 3 4 6 55 82 If you start pairing up the values, starting at the extremes, one of two things will happen. First, you might end up with one unpaired value in the middle: 1 2 3 4 6 55 82 | | |___| | | | |________| | median = 4 |_____________| In this case, the median is just the unpaired value. Second, you might end up with all the values paired: 1 2 3 4 5 6 55 82 | | | |_| | | | | | |_____| | | median = (4+5)/2 = 4.5 | |__________| | |_______________| In this case, the median is the mean of the innermost pair. Note that in this case, the median is not actually an element of the data set! Now, if you know how to find a median, then you also know how to find a quartile, because: The lower quartile is the median of the lower half of the data set. The upper quartile is the median of the upper half of the data set. In case like the first one above - where we have an odd number of elements in the data set - we include the median value in both halves: 1 2 3 4 <--> 4 6 55 82 | |_| | | |__| | |_____| |_______| 2+3 6+55 Q = --- Q = ---- 2 2 In cases where we have an even number of elements in the data set, the median isn't included in either half: 1 2 3 4 5 6 9 11 55 82 | |___| | | |_____| | |_______| |__________| Q = 3 Q = 11 You might also want to take a look at Box and Whisker Plots http://mathforum.org/library/drmath/view/52792.html for another point of view. -Doctors Sonya, Celko, and Ian, 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/ |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994-2015 The Math Forum
http://mathforum.org/dr.math/