Average time

[maradnu]

I find myself wondering how the 'average' time is calculated. I've seen several puzzles in which it would seem not to be an average of all the solution times. The average time on the puzzle with the following was 12 seconds.

1. Deanna48 August 5, 2023 9 sec.
2. claire0556 October 15, 2023 9 sec.
3. ecottontail August 21, 2023 10 sec.
4. Zhu September 28, 2023 11 sec.
5. M. Cheese September 30, 2023 11 sec.
6. AnotherPenguin June 28, 2023 13 sec.
7. Fudi September 30, 2023 19 sec.
8. didit Premium Member September 18, 2023 27 sec.
9. judy100 September 21, 2023 32 sec.
10. lspiegel August 31, 2023 93 sec.
11. eular magee November 16, 2023 426 sec.

[kb83]

Agree, maradnu, that average does not compute. It should generally be way larger than the 20 fastest times. I would have thought that the site simply adds each new solve time into a running total, and divides by the number of solutions. Very simple, which is why it is used in lieu of the (statistically more preferable) median solve time, which would require keeping a log of all of the solve times, which would be totally unfeasible (or would it?!). But I haven't the foggiest why you saw an average of 12 sec for your puzzle.

[kb83]

Actually, 13 is the MEDIAN of the times that were listed, I almost wonder if at the beginning of the life of a puzzle, they substitute the median... oh well, just a thought.

[Fudi]

I wonder if there are only stats showing for 11 users in the example above because this is one of the new puzzles and at the time maradnu saw it, only 11 solvers had solved it. (As opposed to the possibility that maradnu didn't include the full stats ... just an abbreviated list of these first 11 of them.) This would make sense if "averages" that we see are really medians ... and if the median of this set were 12 rather than 13 ... but I dunno.

[kb83]

Fudi, you've opened my eyes-- since they present the overall distribution of the solve times (at least with the curve), it suggests that the site maintains the ENTIRE set of solve times in memory for each puzzle. This is a large amount of data (!), but not out of the realm of possibility. Of course, if this is true, then in principle, they could also compute the median of each solver's solve times, by sorting by username. I've always wished that my solve times could be summarized by a median rather than a mean, which would liberate me to solve some of the ones that I reluctantly give up on in order to preserve my average.

[kb83]

Okay, I inspected the curve, which is a bell-shaped curve. But the curve is not based on the literal distribution of solve times, but rather it is a mapping of the quantiles to the corresponding normal quantiles. And indeed the "middle value" is the median, and it corresponds to what they are calling the "average." This is a misnomer, i.e. in statistics, we don't refer to the median as an "average." Rather the median is the value such that 50% of the values of the distribution fall above and below that value. The "average" is the arithmetic sum of the values divided by the number of values, and it corresponds to the common understanding of "average." However, I know very well that in the personal summaries, the "average" solve time IS INDEED the numerical average in the common understanding, and NOT the median. So, the "average" solve time for a particular quote is the MEDIAN (the 50% point), but the "average" for an individual in a month (or in a career) is the mean or "average" as we commonly use the term.

[maradnu]

This one had an average time of 13 seconds


1.
Toeprint August 12, 2023 8 sec.
2.
eraserheadbaby September 18, 2023 10 sec.
3.
M. Cheese October 6, 2023 10 sec.
4.
kb83 July 8, 2023 11 sec.
5.
Doar November 7, 2023 12 sec.
6.
WhyteChedda1415 October 17, 2023 14 sec.
7.
didit Premium Member November 19, 2023 17 sec.
8.
Koboi September 11, 2023 21 sec.
9.
judy100 September 12, 2023 28 sec.
10.
Ian123 August 7, 2023 31 sec.
11.
Codepig127 Premium Member September 18, 2023 58 sec.
12.
m1j9s48 November 10, 2023 40661 sec.

[kb83]

This bears out the fact that the "average" that is posted for a given puzzle is the median (middle value), NOT the arithmetic average.

[hrossa]

I get 13 as the median for that most recent list only by dropping the largest two values. I can see dropping 40661 as an outlier, but why 58? Would you like to weigh in, Admin?

[hrossa]

And 12 if the median of the list from Dec 10 if you drop the largest value.