How to define mathematically the integer part of an average?

Question

Scenario: Suppose I have three numbers: 1, 3 and 4. The average of the three numbers are 2.67 (to 2 decimal places). It many real-world applications, there is the need to consider only the "whole number", that is, the integer part, hence the value 2 only.
Question: How do I define using mathematical expression this particular issue, that is, consider only the whole number result of the average expression?
Thank you.

Mathematics has the floor (and ceiling) operations, using "hooked" parentheses. See e.g. https://en.wikipedia.org/wiki/Floor_and_ceiling_functions . You'll need to take into account whether your average is positive or negative to use those operations. — , Jul 30 '15 at 08:45
I am looking for a "mathematical expression", describing that only the "integer part" of the result is being considered. — george24, Jul 30 '15 at 08:49
But the wikipedia link I gave shows how you can define truncation as well; applying that to average, you'd get something like \sgn(1/n \Sigma x_i) \lfloor | 1/n Sigma x_i | \rfloor . — , Jul 30 '15 at 08:56
It's not clear what you want. The floor and ceiling functions cause a number to become an integer, but you aren't liking that answer. You can say floor(8/3)=2, but you can't say 8/3 ∈ N, because that's false. ∈ N is a statement, not a conversion of one number to another. — Teepeemm, Jul 30 '15 at 12:58
I'm voting to close this question as off-topic because it is not about programming. — , Jul 30 '15 at 16:07
possible duplicate of What is the symbol to refer to the set of whole numbers — Martijn Pieters, Jul 30 '15 at 20:16

score 1 · Answer 1 · answered Jul 30 '15 at 08:44

1

You can define the integral part using Greatest integer function(represented as |_ _|).

So, greatest integer(2.67) = |_ 2.67 _| = 2.

And, in almost all of the programming languages there exists methods/functions defined in mathematical libraries to achieve the same.

In Java, you can achieve the same using double floor(double d) method.

Ex :- Math.floor(2.67) = 2.0 and then you can convert it into int using down-casting OR down promotion.

int res = (int)(Math.floor(2.67));

As mentioned by Evert, if you're performing operations with negative average, then you need to use smallest-integer function(ceil function).

int res = (int)(Math.ceil(2.67));

So, your code would be :-

if(avg>=0)
Math.floor(avg);
else
Math.ceil(avg);

answered Jul 30 '15 at 08:44

What about negative results? – Jul 30 '15 at 08:46
Not what I am looking for. – george24 Jul 30 '15 at 08:48
For that OP can have an if-else condition. Wait, I'm editing that in my answer. – Jul 30 '15 at 08:48
@Evert-Please check now... – Jul 30 '15 at 08:52
@george24-What do you want? A mathematical expression?? – Jul 30 '15 at 08:52

score 1 · Answer 2 · answered Jul 30 '15 at 08:49

1

Integers in Java don't use remainders, so if you were to add all values together and divide by N (the number of values), you should arrive at the greatest whole number.

This is in no way a highly accurate method of doing it, but it is definitely a fast solution that "works".

int a, b, c;
a = 1; b = 3; c = 4;
System.out.println((a + b + c) / 3); //Equals 2 [replace 3 with N]

answered Jul 30 '15 at 08:49

insidesin

111

This isn't necessarily Java. – Teepeemm Jul 30 '15 at 12:46
My bad. How do other languages compute Integers differently? – Jul 30 '15 at 13:01
Java, C, C++, and many others use integer division and this would work fine. Python (version 3+) and Javascript use floating point division. – Teepeemm Jul 30 '15 at 13:38
That's probably why I'm over-assuming, I'm not a scripting guy (yet) :P @Teepeemm – Jul 30 '15 at 13:40

score 1 · Answer 3 · 2015-07-31T08:46:21.957

1

$$ \text{sgn} \left( \frac{1}{n} \Sigma x_i \right) \left\lfloor \left\lvert \frac{1}{n} \Sigma x_i \right\rvert \right\rfloor $$

edited Jul 31 '15 at 08:46

answered Jul 30 '15 at 09:04

score -1 · Answer 4 · answered Jul 30 '15 at 08:48

-1

Mathematically, Avg(n1,n2,...nm) = p/q for lowest values (no more divisible) for all p belongs to natural number and q =1.

answered Jul 30 '15 at 08:48

AKS

101
1

Mathematically, that will only happen if the average is already an integer, making this question (whatever it is) moot. – Teepeemm Jul 30 '15 at 12:45
@Teepeee...Sorry but looks you don't aware about algos, it was just an psuedo. If you didn't understand, you may ask. – Jul 30 '15 at 12:51
@eorge24 , pls. accept answer if it solves your problem. Do you need programming solution , pseudo, algo. You may clarify if the answers are still acceptable. – Jul 30 '15 at 12:54
1

Avg(1,3,4) = 8/3 is lowest values, with p=8 and q=3≠1. What part of your algorithm am I misunderstanding? – Teepeemm Jul 30 '15 at 12:55
@Teepeemm, Oh that is not I am trying to explain. For "mathematical expression that is, consider only the whole number" , your 8/3 is not giving the whole number per the rule. To get and confirm if the whole number is achieved , the expression can be formulated. With the provided example, the output will not be fully whole number and we need a so called to trunk or floor or ceil the value. So it is a first step.if it fails/not fulfilled then user has confirmed that he need to use special functions (or he need alto) will be cleared after first step. – Jul 30 '15 at 13:03
@Teepeemm-It seems the author of this answer is unaware of all other answers posted here and himself written a crap and bewildering solution. You may better downvote and flag rather than make this intelligent person understand... – Jul 30 '15 at 13:09

How to define mathematically the integer part of an average?

4 Answers4