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A doubt about basic statistics with rounding

To determine the number of classes that exists in a sequence of numbers I can use the Sturges Rule where k = 1 +3.33 log n or by rule of the square root of the numbers quantity in a sequence.

So, in a sequence that has 20 numbers, to determine the number of classes I need to get the square root of 20.

SQRT(20) = 4,47

SEQUENCE

8, 10, 10, 12, 12, 14, 14, 16, 16, 16, 18, 18, 20, 20, 20 ,20 ,20, 22, 24, 25

I can rounding the square of 20, or I have to consider that SQRT(20) is 4 ?

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Did you know that there is a statistics stackexchange site, called CrossValidated? –  Gerry Myerson Sep 25 '12 at 0:18
    
This seems to me to be more about arithmetic and mathematics than statistics. I am not sure where this question is best suited but given mathematics vs CV I would vote for mathematics. I tried to edit to improve the english and make it understandable. Unfortunateoly I don't know what "I can rounding the square of 20" means. It needs fixing but I don't know what is intended. –  Michael Chernick Sep 25 '12 at 1:35
    
Rounding numbers to the nearest integer is a mathematical rule. How rounding affects error in repeated application on a set of numbers with some sense of randomness can be statistical. But I am not sure this is a statistical question. I think this problem may be more a matter of when a number close to 4.5 is rounded either up or down the approximation is about as bad as rounding can be. –  Michael Chernick Sep 25 '12 at 1:40
    
Maybe the last sentence should read "Can I avoid rounding the square root of 20, or do I have to consider that $\: \sqrt{20} = 4 \:$? $\;\;$ (I think the answer in that case would be "No, you do have to consider that $\: \sqrt{20} = 4 \:$.) –  Ricky Demer Sep 25 '12 at 2:17
1  
Obviously the answer is an integer is the exact solution. The square root is an approximation. I think there are several questions here. Can an approximation that is not a solution be an answer? Should we take the approximation and round off giving 4 as an answer? Should we round up and say 5 is the answer. Or should we say that the answer is either 4 or 5. Finally we could actually make the answer statistical by assigning probabilities to the two answers. Is the approximation always accurate enough that it must actually be one of the two closest integers? –  Michael Chernick Sep 25 '12 at 12:19

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