ZombieHorde
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Sun Oct-03-10 08:07 PM
Original message |
Math ordinal grammar question. |
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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?
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Geoff R. Casavant
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Sun Oct-03-10 08:10 PM
Response to Original message |
1. I don't think there are any non-integer ordinal numbers. |
ZombieHorde
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Sun Oct-03-10 08:21 PM
Response to Reply #1 |
4. You seem to be right, but my math professor wants me to use them. |
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I guess I will just have to make something up and hope for the best.
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Orsino
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Mon Oct-04-10 11:46 AM
Response to Reply #4 |
ZombieHorde
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Mon Oct-04-10 02:11 PM
Response to Reply #15 |
18. For describing the placement in a median. |
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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.
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Orsino
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Tue Oct-05-10 07:20 AM
Response to Reply #18 |
25. But if there isn't anything between the second and third members... |
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...why speak of that as a "place"? The median isn't actually a member of the set.
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ZombieHorde
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Tue Oct-05-10 02:44 PM
Response to Reply #25 |
27. You are suposed to average the numbers on either side of the place. |
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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.
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Orsino
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Wed Oct-06-10 08:56 AM
Response to Reply #27 |
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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.
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tabatha
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Sun Oct-03-10 08:15 PM
Response to Original message |
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"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."
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ZombieHorde
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Sun Oct-03-10 08:20 PM
Response to Reply #2 |
3. Shit, my professor wants me to use ordinal numbers with decimals. |
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Edited on Sun Oct-03-10 08:25 PM by ZombieHorde
Hopefully, she will just except whatever.
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tabatha
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Sun Oct-03-10 08:28 PM
Response to Reply #3 |
5. Your math professor ... hmmm |
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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.
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ZombieHorde
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Sun Oct-03-10 08:41 PM
Response to Reply #5 |
6. The formula for finding the median in a number set is (n+1)/2. |
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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.
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Jim__
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Mon Oct-04-10 09:45 AM
Response to Reply #6 |
14. A set is a collection of *distinct* objects. |
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Edited on Mon Oct-04-10 09:46 AM by Jim__
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.
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ZombieHorde
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Mon Oct-04-10 02:06 PM
Response to Reply #14 |
16. "the median is the middle value" = (n+1)/2 |
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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?
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Jim__
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Tue Oct-05-10 09:54 AM
Response to Reply #16 |
26. I'm curious about your set. |
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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. .
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ZombieHorde
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Tue Oct-05-10 02:50 PM
Response to Reply #26 |
28. The median is only a fraction if the set contains an even number of objects. |
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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.
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notesdev
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Mon Oct-04-10 12:07 AM
Response to Reply #3 |
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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!
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Sancho
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Sun Oct-03-10 09:17 PM
Response to Original message |
7. See the section on ordinal measures.. |
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http://en.wikipedia.org/wiki/Level_of_measurementProbably, any transformation (decimals for example) don't change the rank...
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tabatha
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Sun Oct-03-10 09:30 PM
Response to Reply #7 |
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"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
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BadgerKid
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Sun Oct-03-10 11:18 PM
Response to Original message |
9. Smells like a "countability" issue. |
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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.
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laconicsax
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Mon Oct-04-10 01:06 AM
Response to Original message |
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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.).
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Festivito
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Mon Oct-04-10 05:41 AM
Response to Original message |
12. I'd suggest that the rule should follow the last digit as usual. |
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As in, he passed the 123.4th mile marker.
Fractionalized ordinals. Yikes. Is nothing sacred.
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ZombieHorde
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Mon Oct-04-10 02:07 PM
Response to Reply #12 |
17. I asked my proffesor today and she told me to use the method you suggested. |
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So the place, 3.5, should be written 3.5th place.
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muriel_volestrangler
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Mon Oct-04-10 05:43 PM
Response to Reply #17 |
21. I'd tell her the median is not a member of the set |
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It's an attribute of the set, not a member, and thus does not have a 'place' in it.
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ZombieHorde
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Mon Oct-04-10 06:00 PM
Response to Reply #21 |
22. I did not mean to say the median has a place, the median is the place. |
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The 3.5th place is the address of the median of a number set.
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muriel_volestrangler
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Mon Oct-04-10 06:25 PM
Response to Reply #22 |
23. A median does not have an address, or a place, or an ordinal |
ZombieHorde
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Mon Oct-04-10 07:26 PM
Response to Reply #23 |
24. Yes, the median is a value, but you must find the placement to find the value. nt |
muriel_volestrangler
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Mon Oct-04-10 05:48 AM
Response to Original message |
13. The usual thing to do is use the qualifier 'equal' |
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ie 1st 2nd 3rd equal, and 3rd equal 5th 6th and so on.
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Terry in Austin
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Mon Oct-04-10 02:35 PM
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19. In a town with non-integer streets |
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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.
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ZombieHorde
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Mon Oct-04-10 05:00 PM
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