Talk:Average
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[edit] No more redirect,
Good, glad to see that this is no longer a redirect. It should never have been a redirect to arithmetic mean. At the least it should discuss the median, the mode and the subtle misuse of averages of "convenient" types in advertising and propaganda. -- Derek Ross
- Yip, I'll be sure to cite How to lie with statistics in the further information section. ;-) --snoyes 02:53 Mar 1, 2003 (UTC)
- Excellent! My favourite book on arithmetic! -- Derek Ross
A mean is only one particular type of average. A weighted average could refer to a weighted median as well, so I don't think that a redirect is the right solution to use for the weighted average article. -- Derek Ross
[edit] Properties of Median
"Also note that 1/2 of the scores, namely{1,2,2}, have values <= median and the other half, namely{2,3,9}, have values >= median"
This is not true, 1,2,2,2 (4 values) are <= median and 2,2,2,3,9 (5 values) have values >= median. This means that 2/3 of the population are <= median, and 5/6 are >= median. Not 50/50. -- PRB
- There are six values (1,2,2,2,3,9) in the sorted list. The list can be split in half giving two sorted lists of three values (1,2,2) and (2,3,9). The median is the mean of the largest value in the smaller list and of the smallest number in the larger list. When there are an odd number of values in the original list, the median will be the centremost number in the sorted list. -- Derek Ross | Talk
I always thought the median was ((highest-lowest)/2)+lowest, i.e. halfway between the lowest and the highest. So the median of {1,2,2,2,3,9} would be 5. If that's not the median, what is it? - Montréalais 09:37, 14 March 2006 (UTC)
- I'm not sure that there is a name for ((highest-lowest)/2)+lowest but perhaps that's just ignorance on my part. The median of {1,2,2,2,3,9} is definitely 2 though. And in fact the median of {1,2,2,2,3,9 000 000} comes to 2 too ! -- Derek Ross | Talk 15:41, 14 March 2006 (UTC)
I think the definition of median is very vague and should be more precise. "middle", "higher half" and "lower half" are very vague terms. For example, one might think in a sequence of 1,23,24,25...40 the median is 23, because it is the number that separates the "lower half" (values <= 20 by some definition) from the "higher half." For folks looking for concise definitions of terms, the language is confusing.
- "Median - the middle value that separates the higher half from the lower half of the data set"
[edit] Merge with central tendency
It looks like average and central tendency mean the same thing. If thats the case, they should be merged. The article on central tendency is so small that it would be an easy merge. Anyone agree? Fresheneesz 23:31, 18 March 2006 (UTC)
- Go for it. -- Derek Ross | Talk 23:45, 18 March 2006 (UTC)
[edit] Relationship between different types of mean
It would be worth noting the relationship between averages:
H^2=AG (or perhaps HA=G^2)
and
G=A-V/2 (approximately)
where:
H=harmonic mean
A=arithmetic mean
G=geometric mean
V=variance
I think there is another relationship:
V=(A^2-G^2) or perhaps SD=(A^2-G^2)
The last relationship was alluded to in a footnote to Corporate Finance by (from memory) Brierly and Miers. I spent a lot of time trying to figure out the relationship, as I wanted to be able to calculate the variance for published time series where the monthly daily A and G means are published, but not V.
I do not know how to do the fancy mathematical format stuff - please could someone else do it for me?
The above means you can calculate different kinds of average even when you do not have access to the original data.
