Perhaps I misunderstand the question - but I do not not believe there is any theoretical justification because all this formula does is get you to the exact middle of the distribution. You can get there from either direction with just a few twists of the formula. I see this formula as a heuristic, not a formula that invokes any theory (and, most days, needless worry - but that's another matter!). If you have the distribution (* = median)
4 5 6 6 9
*
and choose to worry about the fact that you have "tied scores" in the
interval that contains the median, the formula will give you 5.5 + [(2.5-2)/2]
= 5.5 + .25 = 5.75 going from bottom to top. But if you wanted to count
from top to bottom, change f(cum) to f(above) and subtract from the upper
limit of the interval, as in Median = Upper limit - w[(n/2 - f(above))/f(m)]
and it'll be 6.5 - [(2.5-1)/2)] = 6.5 - .75 = 5.75 (hopefully I didn't
make any mistakes). Just that you can get the _that spot_ (a quarter of
the way through the interval starting at the bottom, or three-quarters
of the way down from the top) either way.
"R.C. Intrieri" wrote:
Dear Tipsters,I am attempting to explain the formula to calculate the Median from Grouped data.
The formula for this is the followingMd = Lm + w [(n/2 � fcum)/fm]
Lm = lower limit of the interval that contains the median.
W = width of the interval
fm = is the frequency
fcum = the number of observations falling below this interval.The formula comes from Glass & Hopkins (3rd edition) Statistical methods in education and psychology
EQ 4.1 P.52The question that I have (and I need a reference if possible) is what is the justification from a theoretical point of view for using "the number of observations falling below the interval" as opposed to using the number of observations falling above the interval? Any help would be greatly appreciated. Thanks.
Bob Intrieri
Robert C. Intrieri, PhDOffice (309) 298-1336
Department of PsychologyFax (309) 298-2179
Western Illinois UniversityE-mail [EMAIL PROTECTED]
1 University Circle
Macomb IL 61455-1390---
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John W. Kulig
[EMAIL PROTECTED]
Department of Psychology
http://oz.plymouth.edu/~kulig
Plymouth State College
tel: (603) 535-2468
Plymouth NH USA 03264
fax: (603) 535-2412
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