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What is difference between averages and means? Can you explain?
I need to know about the difference between both.
The mean and the "average" (in the cubing sense) are both measures of central tendency. Outside of cubing, the word "average" almost always refers to the arithmetic mean (add everything up and divide), so "mean" and "average" have exactly the same meaning to laymen. The various measures of central tendency have different properties; the mean completely breaks down in the presence of outliers (e.g. a single DNF, even out of ten thousand solves, would make the entire mean a DNF), while the 5% trimmed mean (the cubing "average") can tolerate up to 5% of outliers, and the median can tolerate up to 50%.

There is nothing special, canonical, god-given about the 5% threshold we use in cubing. It was just decided as a community standard a long time ago, and now there's no real reason to change it. It could just as well have been 10% or 20%, if the powers that be had decided so back in the day, but they went with 5%, and now we're stuck with that for eternity. (There are a few voices here and there advocating for it to be 20% to match how ao5 drops the top and bottom. Give them exactly zero attention—they're just trying to make excuses for why they get bad solves so often.)

(I just really want to say this because I know many cubers are schoolkids and it would be extremely terrible if you get the idea that the cubing use of the word "average", as described by DGCubes, is universally recognised. It's not.)
 
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What is difference between averages and means? Can you explain?
I need to know about the difference between both.
There are different types of averages. Usually they are mean, mode and median. In cubing there is a new type for competitions. So what you ask is kind of muddled. They are all averages, just different types.
 
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How do I get my passion for cubing back?
Do whatever you like to do in your free time, if you're not interesting in cubing then you don't have to do it. It might come back if you just take a little break from it. Maybe you're done with cubing.
Maybe you want to explore another aspect of cubing to make it more interesting, like Blindfolded, FMC, Puzzle modding, and more. I can't tell you what to do, you'll have to decide for yourself.
 
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Does anyone understand exactly what standard deviation is?
I use blockkeeper as my main timer. http://dallasmcneil.com/projects/blockkeeper/
I think its pretty good but I don't get what one of the funtions means.
Standard deviation is a term that you see a lot of the time with statistics and such. Basically, it's the "average distance from the average," so the lower the standard deviation, the more consistent you are. Consider these sets of times:
{1, 3, 5, 7, 9} and {3, 4, 5, 6, 7}
The first one is a lot less consistent, and so has a higher standard deviation. The second, being more consistent, has a lower standard deviation.
 
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To calculate the standard deviation of those numbers:
  1. Work out the Mean (the simple average of the numbers)
  2. Then for each number: subtract the Mean and square the result.
  3. Then work out the mean of those squared differences.
  4. Take the square root of that and we are done!
 
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To add to the above, the reason you square the differences then take the square root is to eliminate any negative signs. If one result is 2 below the mean and one result is two above the mean, you want the function to give you an average difference of 2, not 0.
 
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I’ve been doing mastermorphix lately, but I’ve noticed a problem where on the last layer, I keep on getting impossible CP cases (I do LL beginners method, EO, EP, CP, CO), and it’s because every time I do a sune to permute the edges, it rotates the center 90 degress(click right here to see an example). Is there any sort of ang that can rotate the center 90 degrees or something?
 
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As an aside...If there is a good resource on how to determine probabilities on your own that would also be a nice reference tool.
1. Consider the exact types of symmetries where different puzzle states count as the "same" case. For example, for last layer algs, usually the reductions you care about are (what I call) pre-AUF and post-AUF (which are different things!). Depending on situation, you might also want to reduce by mirror symmetry and/or by inverting.
2. Count the number of cases without any symmetry reduction. (Usually this is just multiplying the number of possible corner orientations, possible corner permutations, etc. together. You might have to divide by 2 to account for corner permutation parity and edge permutation parity always being the same on a 3×3×3, but this doesn't apply to CxLL since you're completely ignoring edges.)
3. Classify the cases based on how symmetric they are. More symmetric cases are "less" likely after reducing by the relevant symmetries, e.g. a case with 4 symmetries will be 1/4 the probability of a case with only 1 symmetry, for the reason that the less symmetric case can show up in more different ways (each of which have the same probability). (Note that the solved state is the most symmetric under the usual symmetries, which is also why skips are typically the rarest possible case (e.g. 1/72 chance of PLL skip compared to 1/18 for most other PLLs).)

And finally,
4. Think very hard about why you want to calculate case probabilities. There almost always isn't a good reason to do this (beyond academic curiosity). It's meaningless to prioritise alg sets by case probability because (i) usually the people who think of doing this are trying to apply it to small alg sets like PLL or CMLL/COLL/CLL where prioritisation doesn't really matter and (ii) the vast majority of cases will have exactly the same probability (the highest possible: the one corresponding to trivial symmetry).

tl;dr 2/81 for every COLL case, except skip (1/162), diag (1/162), H permuted (1/81) and H diag (1/81).
 
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