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I have an array of numbers. Each of them represents item cost, as a percentage of total cost, where total cost is 100:

0.1 // this item represents 0.1% of total cost
0.4
0.6
0.8
0.8
0.8
0.8
0.9
1
1.1
1.3
1.4
1.7
2.1
2.8
3.2
4
5.7
6.1
8.4
19.1
37.1 // this item represents 37.1% of total cost

I would like to group the members of that array in four batches, relative to their distance to average: low cost, average cost, high cost, very high cost. I need help in defining the ranges for those groups. I though about using percentiles, in a way that everything up to 40th percentile would be low cost, up to 60th would be average cost, up to 80th = high cost, and rest = very high cost. But as you can see these ranges are provisional, they are not based on any meaningful calculus. Is there a more statistically accurate way to determine these ranges? Maybe something that includes standard deviation?

bonus question: what is the word for a value that is provisional, determined without calculation, but based on personal estimate (such as my ranges above) (update: found the word - arbitrary)

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1 Answer 1

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I would think the reason to make this classification is that you will treat the items in each group alike but distinguish the groups. As such, I would try to make groups that add up to $25\%$ of the total cost each. This would put the last two items in groups by themselves. Depending on how you treat the fact that you can't get exactly $25\%$ in each group the next group would have three or four and the low cost group would have everything else.

This sounds silly, but it really makes sense. You will spend most of your time discussing the high cost items, which are the ones that can influence the total cost. If one of the $0.8$s doubles in cost, you don't care much. If it gets cut in half you also don't care. If the $37.1$ changes by $10\%$ it has much more effect.

There is no mathematical magic here. You just have to group the items in a useful way and explain the reasoning. If somebody wants a different grouping, let them say so and why.

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  • $\begingroup$ That sounds reasonable and logical. Thanks Ross! $\endgroup$
    – srgb
    Commented Jun 6, 2018 at 3:57

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