Math ordinal grammar question.

[ZombieHorde]

Ordinal numbers = 1st, 2nd, 3rd, 4th, etc.

How would you write 3.5? 3.5th, 3rd.5th, 3rd.5? How do decimals work with ordinal numbers?

[Geoff R. Casavant]

1. I don't think there are any non-integer ordinal numbers.

[ZombieHorde]

4. You seem to be right, but my math professor wants me to use them.

I guess I will just have to make something up and hope for the best.

[Orsino]

15. Why and how? n/t

[ZombieHorde]

18. For describing the placement in a median.

Consider the set; {1,2,3,4}. The "1" is in the first place, the "2" is in the second place, the "3" is in the third place, and the "4" is in the fourth place. The median is the middle value; (n+1)/2. The middle value for this set is between the second place and the third place. (4+1)/2=2.5th place.

[Orsino]

25. But if there isn't anything between the second and third members...

...why speak of that as a "place"? The median isn't actually a member of the set.

[ZombieHorde]

27. You are suposed to average the numbers on either side of the place.

If the set is {2,2,3,6,7,8,8,9}, then the place is in between 6 and 7, the median would be 6.5.

[Orsino]

29. Ah.

That's a different sort of "place" from those occupied by the actual members of the set...but I can see why you'd need a term for that, uh, place.

[tabatha]

2. from wiki

"Ordinals are an extension of the natural numbers different from integers and from cardinals. Like other kinds of numbers, ordinals can be added, multiplied, and exponentiated."

"In mathematics, natural numbers are the ordinary counting numbers 1, 2, 3, ... (sometimes zero is also included). Since the development of set theory by Georg Cantor, it has become customary to view such numbers as a set. There are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition; or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century."

[ZombieHorde]

3. Shit, my professor wants me to use ordinal numbers with decimals.

Hopefully, she will just except whatever.

[tabatha]

5. Your math professor ... hmmm

How does one order objects in decimal notation.

An object is either in first place, second place, etc.
Something can only be in, say, 2.5th place if it is half an object.

I'd be interested in hearing the outcome.

[ZombieHorde]

6. The formula for finding the median in a number set is (n+1)/2.

If a number set has six numbers {1,2,4,4,5,5}, then n=6.

6+1=7

7/2=3.5

She is a show-your-work-and-label-your-numbers nazi. She said the 3.5 has to be labeled as a "place", and she wants to see the 3.5 as a part of my shown work.

The median in my set is "4," but the place, an ordinal number, is 3.5.

The class is Social Statistics. I will have to ask her what she wants to see.

[Jim__]

14. A set is a collection of *distinct* objects.

It depends on what you are interested in in this set. But, if your interest is really just in the set of numbers, I would think this set is {1, 2, 4, 5} and your median would be 3. Of course, if those numbers are only values representing something else, e.g. the counts of individual in 5 different classes that you are intesrested in; then you could have duplicate numbers because the actual distinct objects would be the counts of the 5 separate classes.

Also, your definition of median is unusual. Normally, the median is the middle value - and when the set has an even number of objects, it is the average of the 2 middle terms - in this case, 3.

[ZombieHorde]

16. "the median is the middle value" = (n+1)/2

You don't need a formula to know half of 5 is 2.5; you have this memorized already. If you did not have this memorized, you would need to either use a formula or start counting fingers.

In your set, {1,2,4,5}, the placement of the median is between the 2nd (the number 2) and 3rd place (the number 4), what place is between 2nd and 3rd? 3.5th?

[Jim__]

26. I'm curious about your set.

Your set is: {1, 2, 4, 4, 5, 5} Does that mean that there was a tie for 3rd place and the tie is denoted by 2 occurrences of 4? And also a tie for 5th place and that is denoted by 2 occurences of 5 - although I would expect either 2 occurences of 3 and 2 occurrences of 5: or 2 occurences of 4 and 2 occurences of 6.

Based on what you're saying, I guess the median's place is 3.5. It seems like this is determined by whatever rules you're following and if your teacher says it's the 3.5 place, then that's the determinant. Do you have a set of rules for this? Do you have a text that covers this? I've googled it and I can't find anything that talks about a median being in some type of fractional place - but that may be because I'm not using the right search criteria. .

[ZombieHorde]

28. The median is only a fraction if the set contains an even number of objects.

If a set has 3 objects, {3,5,7}, then the location of the median is a whole number. The location is 2, and the median is 5.

If a set has 4 objects, {3,5,7,9}, then the location of the median is a fraction. The location is 2.5, and the median is 6.

Does that mean that there was a tie for 3rd place and the tie is denoted by 2 occurrences of 4?

The set itself is not necessarily ordinal, the placement of the median within the set is ordinal.

[notesdev]

10. God help you

who knows what other nonsense she is teaching you if she can't wrap her mind around the concept of ordinal. By definition ordinals must be integers and therefore cannot have decimals!

[Sancho]

7. See the section on ordinal measures..

http://en.wikipedia.org/wiki/Level_of_measurement

Probably, any transformation (decimals for example) don't change the rank...

[tabatha]

8. I agree.

"When using an ordinal scale, the central tendency of a group of items can be described by using the group's mode (or most common item) or its median (the middle-ranked item), but the mean (or average) cannot be defined."

and more at that link

[BadgerKid]

9. Smells like a "countability" issue.

The idea is that a set is countable if the members can be put into 1-1 correspondence with the natural numbers. It's conceivable (to me) to reorder your ordinal labels 1st, 2nd, 3rd, when you have to insert a "3.5th". Now if you can have a 3.5th, why not a 3.51st? And then a 3.512nd? You could then concoct any string of decimal places ad infinitum. The real number are uncountable.

[laconicsax]

11. I like 3rd.5th

I'm inclined to agree with the statement upthread saying there are no non-integer ordinals.

If they have to be invented, it shouldn't matter what you pick, though precedent would indicate some variation on the number itself and a suffix. (three -> third, five -> fifth, etc.).

[Festivito]

12. I'd suggest that the rule should follow the last digit as usual.

As in, he passed the 123.4th mile marker.

Fractionalized ordinals. Yikes. Is nothing sacred.

[ZombieHorde]

17. I asked my proffesor today and she told me to use the method you suggested.

So the place, 3.5, should be written 3.5th place.

[muriel_volestrangler]

21. I'd tell her the median is not a member of the set

It's an attribute of the set, not a member, and thus does not have a 'place' in it.

[ZombieHorde]

22. I did not mean to say the median has a place, the median is the place.

The 3.5th place is the address of the median of a number set.

[muriel_volestrangler]

23. A median does not have an address, or a place, or an ordinal

It has a value.

[ZombieHorde]

24. Yes, the median is a value, but you must find the placement to find the value. nt

[muriel_volestrangler]

13. The usual thing to do is use the qualifier 'equal'

ie
1st
2nd
3rd equal, and 3rd equal
5th
6th
and so on.

[Terry in Austin]

19. In a town with non-integer streets

Austin has an odd custom of "1/2" streets scattered among numbered streets. Between 38th Street and 39th Street, for example, there's a 38 1/2 Street. It's a fairly major thoroughfare, so you hear it referred to a lot -- always as "thirty-eighth and a half street." Written, you never see any ordinal notation, however.

I'd be curious to know if there's any sort of standard answer for the OP's question.

[ZombieHorde]

20. Interesting. nt