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Could we a have a horizontal line representing your average on the reputation graph as well as / instead of a horizontal line indicating the position of the value 200?

I don't think any of us have too much trouble figuring out where 200 lies on an axis marked in increments of 50/100. I think the average (possibly the mode) would be much more interesting.


Note:

Whether to use a median, mode or mean is up for debate, but to clarify, when I suggest using the mode I don't mean highest frequency calculated from raw data, which is just coincidental. What I mean is frequency calculated from rounded-to-nearest x values of reputation, where x is 50, 100 or some such interval.

Here is a sample of normalized-rep (rounded to 50) frequencies from my history for December. As you can see, the mode is 250, which is a pretty good indication of my scores for the month.

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1 Answer 1

I like having the 200 there - that line should stay anyway. Not all of us break the 200 mark on a regular basis, and for me it's a big deal when it happens!


You tagged it discussion; here are my thoughts, all prepended with "If this is implemented, then....":

The mode is likely to give strange and unrepresentative answers unless you group the data, because it might happen that 120 is your mode rep but typically you get non-multiples of 10 between 210 and 290. (Humans are better at approximate frequency analysis from the graph than at correcly interpreting the mode.)

Median would be more realistic than mode, and upper and lower quartiles would tell you where the middle 50% of your answers lie.

Mean is OK but will be skewed by very high or very low rep days, so is less representative of the typical day.

It would perhaps make sense to have these as rolling over the period of the visible graph rather than all time, so that dormant users who become active get to see some change.


Here's a list of interval sizes versus mode (mode abbreviated to the central value in the group, so for example interval 11, mode 132 means the mode group is an interval of width 11, centre 132, so in more usual notation, I would call it 126.5 - 137.5), based on all your rep ever up to about 14:00 UTC on 2012.12.11.

   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20
 120 120 336 336 120 324 133 320 126 130 132  96 130 126 120 128  85 126 133 100
  21  22  23  24  25  26  27  28  29  30      49  50  51
 126 132 138 240 125 130 135 140  87  90     147 150 102

I hope this brings clear why mode is not a very good measure for reputation.

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Right, but since you don't break the 200 mark often, wouldn't a comparison against your average be more useful? I agree with your points about implementation though. –  Asad Dec 11 '12 at 12:02
    
@Asad The 200 line is a nice easy visual point of reference for me, giving an absolute scale mark right across the rather wide graph. That's why I want to keep it. (And for me 200 is a very significant number.) –  AndrewC Dec 11 '12 at 12:06
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I guess we could keep the 200 line as well, but this might clutter up the graph. Perhaps there could be options for which markers to show. –  Asad Dec 11 '12 at 12:10
    
@Asad comparison against my median, maybe, and for the reasons I said above, but my mean isn't a great measure, neither's my mode. Your mode is 120. That's not a sensible number to measure yourself by, and when you change the grouping interval you use for the mode, your mode leaps all over the place (90,324,130). Your mean is about 188. Your (min,lower quartile,median,upper quartile,max) is (20,120,177,260,427) for all time and (20,142,246,289,427) for the last 31 days, so currently a good day for you is above 246. Your 31-day mean is about 224. I that's skewed by the outliers including today. –  AndrewC Dec 11 '12 at 12:22
    
@Asad Your 31-day mode is 90, which represents the least typical days for you. –  AndrewC Dec 11 '12 at 12:24
    
@Asad No, mode's still the wrong measure, and very sensitive to interval. –  AndrewC Dec 11 '12 at 12:48
    
@Asad I've added a table of interval width and modes. It jumps all over the place. If I also alter where the midpoints of the modes lie, I'm sure that will also alter the results dramatically. –  AndrewC Dec 11 '12 at 13:00
    
@Asad Well done, by the way. –  AndrewC Dec 11 '12 at 13:03
    
You're misinterpreting interval size as interval over the x axis. I'm talking about intervals on the y-axis, which would normalise data to one of six (seven if you earn over 300 a day) values. You would measure the frequency of these, not the raw data. –  Asad Dec 11 '12 at 13:04
    
Thanks, what for? –  Asad Dec 11 '12 at 13:05
    
@Asad, no my intervals are reputation intervals, which is on the y-axis on the graph. x-axis intervals would be rolling means, which we haven't discussed. –  AndrewC Dec 11 '12 at 13:14
    
@Asad The "Well done" is for your contribution on Stack Overflow. –  AndrewC Dec 11 '12 at 13:14
    
That can't be right, since your mode would then be a range, not a number. i.e. 100-150, 100-150, 300-350 ... –  Asad Dec 11 '12 at 13:27
    
@Asad Sorry, I hadn't explained the table very clearly. I've edited the preamble to the table; does that clarify? –  AndrewC Dec 11 '12 at 13:32
    
I've been trying to figure out what I'm doing wrong, but I keep getting different results from you. See: sqlfiddle.com/#!2/304d2/10 for a frequency distribution for December. Your say my 31 day mode is 90, whereas my calculation indicates a normalised mode of 250. Am I missing something here? –  Asad Dec 11 '12 at 13:51

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