# SSMEDIAN

• From: Steven D'Aprano <steve pearwood info>
• To: gnumeric-list gnome org
• Subject: SSMEDIAN
• Date: Sat, 09 Apr 2011 11:34:07 +1000

```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?