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I took statistics some 25 years ago, and remember that if students take a test, then the test scores actually form a bell curve.

But somebody claimed that for Pokemon IV: a random number from 0 to 15 is given to 3 properties: attack, defense, stamina, and the final concern is the percentage:

(attack + defense + stamina) / 45

For example, if attack is 12, defense is 15, and stamina is 11, then the final value of concern is

(12 + 15 + 11) / 45 = 84.4%

Somebody claimed that this distribution (of the percentage number) is actually a bell curve, is that true?

(for the distribution, what I mean is, say, if there are 100 or 1000 such Pokemons, then if you plot a graph with x-axis being the percentage 0% to 100%, and y-axis being the count of such Pokemons having this percentage, then is it a bell curve)

To extend the question a little bit:

  1. If the final concern is based only on one property that is a random number from 0 to 15, then it is a even distribution? (I think it would just be a horizontal line.)
  2. If it begins to be based on 2 or more properties, does it then begin to be a bell curve?
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    $\begingroup$ If you assume that the three IV are independant variables then yes the final value of concern tends toward a gaussian distribution according the the Central Limit Theorem (and the larger the number of variables the more bell-y the distribution). Another example is the distribution of the mean of independant variables that tends towards a gaussian distribution $\endgroup$
    – Riff
    Commented Feb 13, 2017 at 15:47
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    $\begingroup$ This question seems perfectly clear to me. $\endgroup$
    – gung - Reinstate Monica
    Commented Feb 13, 2017 at 16:02
  • $\begingroup$ For the case where the properties are continuous (vs. integer), there is a nice visualization of the convergence to a bell curve here (along with a detailed analysis). $\endgroup$
    – GeoMatt22
    Commented Feb 13, 2017 at 18:52

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You are right that one number only will have a Uniform distribution (or what you call "even"), however, it will be a discrete uniform distribution (if I understand correctly that the selected number is an integer) and therefore not a straight line parallel to the X-axis but a series of 16 dots parallel to the X-axis. Also - I don't think that the sum of 3 uniform distributions is close enough to the bell curve (the Normal or Gaussian distribution). I am not sure how many you need, but probably at least 10. Having read your question again, I believe you don't want the score to have an exact "bell curve" distribution but just a non-uniform distribution. If this is your question, then you are right - the distribution of the sum (or average) of 2 or 3 or more scores becomes a triangular distribution, which means smaller probabilities on both ends and higher probabilities towards the center.

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