SSMEDIAN

[Steven D'Aprano <steve pearwood info>]

Hello,

I'm trying to find out information about the SSMEDIAN statistical 
function in Gnumeric, and how it differs from MEDIAN.

I have read the description of the function:

"median for grouped data as commonly determined in the social sciences"

http://projects.gnome.org/gnumeric/doc/gnumeric-SSMEDIAN.shtml

and spent much time googling for more information, but for something 
described as "commonly", I haven't been able to find any information 
about it. Neither Wikipedia nor Mathworld has any reference that I can 
find to the social sciences using a different algorithm for finding the 
median of grouped data.

The example given in gnumeric's function wizard shows ssmedium(7, 8, 8) 
with the default interval of 1 as returning 7.75. How should I interpret 
this? This is my guess:

If the interval is 1, then the data point 7 actually means some value 
between 6.5 and 7.5;
Likewise the data point 8 means 7.5 through 8.5.

So we have grouped data:

Group        Frequency
6.5 - 7.5    1
7.5 - 8.5    2


If I apply the formula for grouped median found here:

http://www.duncanwil.co.uk/average4.html

median = L + i*(n/2 - CF)/f

where:

L = the lower limit of the class containing the median
i = the width of the class containing the median
n = the total number of frequencies
CF = the cumulative number of frequencies in the classes preceding the 
class containing the median
f = the frequency of the median class

I get:

median = 7.5 + 1*(3/2 - 1)/2 = 7.75

which matches. But of course, this could just be a coincidence. Can 
somebody please:

* confirm that the formula above is that used by SSMEDIAN?

* if not, what does SSMEDIAN actually do?

* point me at a more authoritative source for the formula given?



Thank you in advance!



--
Steven