Median Average

[rjohnson_8ball]

Occassionally someone sees me messing with a 3x3 at our local bar and I get asked, "How fast can you solve that thing?" I give a number X. The person says to his friend, "Let's bet. Do you want to bet his next solve will be over or under X?"

In my opinion, a "median" average is the best indicator of your expected solve time. Exactly half your solves are faster and half are slower. (Just record many solves into a list, sort them, and take the score in the middle of the list. Average the middle two if the list does not have an odd number of entries.)

The problem with Average 3 of 5 or Average 10 of 12 is you need to sum up the times (after discarding the fastest and worst) then divide by 3 or 10. This can be tough without a calculator. Also, the solve times are scattered a bit more on a logarithmic scale, with a more data points scattered closer to the fast end of the range and a few extraneous slow solves at the other end.

Finding the median is much simpler; just do about 11 solves and chose the time in the middle. With a short list, you can mentally or physically cross out your fastest and slowest times and determine the median solve.

I wonder why median is not used more often.

 

[Stefan]

I wonder why median is not used more often.

I like our normal average better, I think it gives a more representative value and I'd dislike ignoring all but one solve. And I have my computer calculate it anyway, so calculation difficulty is irrelevant.

 

[Ranzha]

rjohnson_8ball: Most newer scientific calculators have a stat function to make a table of your times. Then find the average with the "mean x" button.

 

[Dene]

ugh I hate medians. People talk about "robust" and all that crap but screw that.

 

[rjohnson_8ball]

My point is, median is the only way to settle an "under/over" question. If I tell a person I can solve a cube in 40.00 seconds and someone says "Prove it!", then the person expects half my solves to be less than 40.00 and half to be over 40.00.

I usually do the simple thing that other cubers do -- just let a computer figure my average 10 of 12.
But without a computer, calculator, or cell phone app, my "middle" solve time should be a good indicator.

 

[rjohnson_8ball]

@Stephan: If you do 5 solves but your cube pops on two occasions, you might avoid the 2nd DNF by fixing the cube and taking a very slow solve time. In my eyes, that slow time would affect the person's mean average unjustly. To me, the "median" would work better.

 

[amostay2004]

If a non-cuber asks you how fast you can solve the cube, the best number to give is something safely above your normal average.
1. 15, 20, or 30 seconds, they don't make much difference to a non-cuber.
2. When you say your best time is 15 seconds they almost always thing you can do it in 15 seconds (or 1-2sec slower)
3. You're usually outside, and not warmed up
4. You usually don't bring your main cube out.
5. Weather might be cold outside and it's really hard to cube.

I average 12 but if people ask me I'd just say 15-20 seconds

 

[hawkmp4]

@Stephan: If you do 5 solves but your cube pops on two occasions, you might avoid the 2nd DNF by fixing the cube and taking a very slow solve time. In my eyes, that slow time would affect the person's mean average unjustly. To me, the "median" would work better.

What about puzzles with parity? 1/2 the time, a person would get a median higher than their average, 1/2 the time lower. Which case it is is only determined by chance. That seems unfair.

 

[Joker]

ugh I hate medians.

Same here. I ALWAYS say to go with an average for numbers no matter what it is - cubing, time for 400m run, etc -
But I guess you could use median to be fairly accurate, if the average is of a high number (100 or something)

But I like 3 of 5/10 of 12/ 100/100 averages the best.
I just think they are more accurate, that's all.

 

[Dene]

My point is, median is the only way to settle an "under/over" question. If I tell a person I can solve a cube in 40.00 seconds and someone says "Prove it!", then the person expects half my solves to be less than 40.00 and half to be over 40.00.

Do they? If someone told me they averaged 40s at some activity I would assume that most of the times they attempted that activity it would take them around about 40s. I wouldn't think "ok so half of your attempts will be over 40s and half will be under". Just seems like a weird way to think to me.

 

[Ranzha]

If a non-cuber asks you how fast you can solve the cube, the best number to give is something safely above your normal average.
1. 15, 20, or 30 seconds, they don't make much difference to a non-cuber.
2. When you say your best time is 15 seconds they almost always thing you can do it in 15 seconds (or 1-2sec slower)
3. You're usually outside, and not warmed up
4. You usually don't bring your main cube out.
5. Weather might be cold outside and it's really hard to cube.

I average 12 but if people ask me I'd just say 15-20 seconds

1337th post, man! Grats!

 

[rjohnson_8ball]

@Stephan: If you do 5 solves but your cube pops on two occasions, you might avoid the 2nd DNF by fixing the cube and taking a very slow solve time. In my eyes, that slow time would affect the person's mean average unjustly. To me, the "median" would work better.

What about puzzles with parity? 1/2 the time, a person would get a median higher than their average, 1/2 the time lower. Which case it is is only determined by chance. That seems unfair.

You can be sure to do an even number of solves for puzzles with parity. Then I expect the median (average of middle 2 solves) and mean to both be reasonable.

 

[rjohnson_8ball]

If a non-cuber asks you how fast you can solve the cube, the best number to give is something safely above your normal average.
...

Yes, I do that. I usually carry a store bought Rubik's Cube in public, so people don't pop it. My solves are a little slower due to that and bad lighting and other reasons. And I like to succeed with the time I advertise.

 

[Joker]

My point is, median is the only way to settle an "under/over" question. If I tell a person I can solve a cube in 40.00 seconds and someone says "Prove it!", then the person expects half my solves to be less than 40.00 and half to be over 40.00.

Do they? If someone told me they averaged 40s at some activity I would assume that most of the times they attempted that activity it would take them around about 40s. I wouldn't think "ok so half of your attempts will be over 40s and half will be under". Just seems like a weird way to think to me.

Agreed again. If someone is consistent at something, I do not think they should use median by any means.

 

[hawkmp4]

@Stephan: If you do 5 solves but your cube pops on two occasions, you might avoid the 2nd DNF by fixing the cube and taking a very slow solve time. In my eyes, that slow time would affect the person's mean average unjustly. To me, the "median" would work better.

What about puzzles with parity? 1/2 the time, a person would get a median higher than their average, 1/2 the time lower. Which case it is is only determined by chance. That seems unfair.

You can be sure to do an even number of solves for puzzles with parity. Then I expect the median (average of middle 2 solves) and mean to both be reasonable.

So you're advocating a rule change that would invalidate all existing averages for Square 1, 4x4, and 6x6?

 

[Kynit]

I think that median gives a good idea of where you are without any difficult calculations, which might be useful for a few select situations. Other than that, mean all the way.

Besides, mean is much better for competition format

 

[rjohnson_8ball]

@Stephan: If you do 5 solves but your cube pops on two occasions, you might avoid the 2nd DNF by fixing the cube and taking a very slow solve time. In my eyes, that slow time would affect the person's mean average unjustly. To me, the "median" would work better.

What about puzzles with parity? 1/2 the time, a person would get a median higher than their average, 1/2 the time lower. Which case it is is only determined by chance. That seems unfair.

You can be sure to do an even number of solves for puzzles with parity. Then I expect the median (average of middle 2 solves) and mean to both be reasonable.

So you're advocating a rule change that would invalidate all existing averages for Square 1, 4x4, and 6x6?

No. I am not advocating any rule change at all. I am just suggesting people might find it useful or simple, and in specific situations "median" could be a better indicator than "mean".

 

[Owen]

I've considered this before. It just seems a little weird that an average would be based off of one solve.

 

[amostay2004]

If a non-cuber asks you how fast you can solve the cube, the best number to give is something safely above your normal average.
1. 15, 20, or 30 seconds, they don't make much difference to a non-cuber.
2. When you say your best time is 15 seconds they almost always thing you can do it in 15 seconds (or 1-2sec slower)
3. You're usually outside, and not warmed up
4. You usually don't bring your main cube out.
5. Weather might be cold outside and it's really hard to cube.

I average 12 but if people ask me I'd just say 15-20 seconds

1337th post, man! Grats!

Woah thanks for noticing :tu

 

[TMOY]

So you're advocating a rule change that would invalidate all existing averages for Square 1, 4x4, and 6x6?

Just want to point out that speaking of "puzzles with parity" doesn't make sense anyway. Having parity or not depends on your solving method, not on the puzzle. I don't have a parity fix step on my big cubes solves, should my times be invalidated because of what other people do ? That's absurd, period. So he's advocating a void rule change, I don't see the problem with that