How many ball sets would it take to build a matched set?

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Cervisiae Amatorem
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How many ball sets would it take to build a matched set?

Postby Cervisiae Amatorem » Tue Dec 16, 2014 9:49 pm UTC

Here are the weights of my set of pool balls. How many sets would I have to buy in order to piece together a full set with a Coefficient of Variation of less than 1%?

The set doesn't have to be any particular weight, we can mix and match to build a set, but each set must have one of each numbered ball plus a cue ball. We can only order complete sets of 16, we can't order individual balls.

Code: Select all

1         169.4
2         170.3
3         178.7
4         169.3
5         173.0
6         176.9
7         167.2
8         160.8
9         166.2
10        177.0
11        172.8
12        176.2
13        173.2
14        168.3
15        179.9
cue       163.1
   
total    2742.3
average   171.39
std dev     5.38
CV          3.14%


My math is nowhere near strong enough to actually compute this. My intuition says that it will take around 5 sets, taking the best 3 matched balls from each set and getting lucky once. But I have nothing to back this up aside from some really dodgy math.

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jestingrabbit
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Re: How many ball sets would it take to build a matched set?

Postby jestingrabbit » Wed Dec 17, 2014 12:57 pm UTC

This is maths.
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Qaanol
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Re: How many ball sets would it take to build a matched set?

Postby Qaanol » Wed Dec 17, 2014 11:58 pm UTC

I don’t have time to work on this, but I’ll mention that the unbiased estimate for the population standard deviation, based on this sample, is 5.556. Consequently, the standard error of the mean is 1.389.
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