Talk:Mode (statistics)

From Wikipedia, the free encyclopedia

Contents 1 If the highest frequency is one... 2 Commute with 3 Sample from a continuous distribution 4 I have a similar question to the first one above

[edit] If the highest frequency is one...

Question: Let's say the set is 1,2,3,4.

Is the mode all of them, since the highest frequency is one, or is there no mode whatsoever?

I brought this to question since the definition uses "frequency," and it would appear that they are all equally frequent and thus all modes? I'm not sure of the official accepted interpretation.

DOES ANYONE KNOW THE ANSWER?

The mode cannot be calculated in such a varied set of data and thus should not be used. - Ferret 03:27, 23 March 2006 (UTC)

This was a multiple choice question on a standardized test, so would I say 4 modes or no modes?--Dch111 21:02, 16 May 2006 (UTC)

No modes, according to my programming teacher who worked for NASA. —The preceding unsigned comment was added by 75.8.96.7 (talk) 04:42, 11 December 2006 (UTC).

[edit] Commute with

Do we really need to say commute with when discussing the linearity of mean, mode, and median? It does mean what we want to say, but it will convey it only to readers who don't need this article. Septentrionalis 21:23, 5 May 2006 (UTC)

In both places where it is used, it is immediately explained. Doesn't that work? I can't judge, because I don't need this article. Lambiam^Talk 01:28, 6 May 2006 (UTC)

That's the problem. Nobody who is editing it does. (And linear or independent might be just as bad.) Septentrionalis 01:51, 6 May 2006 (UTC)

I have reverted the addition of a wikilink to Commutative operation because it does not really cover the concept meant here. Commutative diagram is more to the point, but even I :) can see that that is a bridge too far. Lambiam^Talk 02:13, 6 May 2006 (UTC)

Well it would be nice if commutative operation really brought out the idea of commutative diagrams; it is in there, it's just not going to be obvious to the audience here.... Septentrionalis 03:25, 6 May 2006 (UTC)

The way I see it is as follows. For "commutative" in the sense of commutative diagram, reducing everything to the simplest case, operations f and g commute if:

f o g = g o f.

There is no universal quantification here, and the commuting operations are a pair of unary operations (although generalizations are possible and usual).

For "commutative" in the sense of commutative operation, operation ⊕ is commutative if,

x ⊕ y = y ⊕ x for all x and y in the domain.

Here the universal quantification is essential, and there is one operation which is binary.

I expect that attempts to unify the two notions will produced strained and non-natural results. Lambiam^Talk 18:51, 6 May 2006 (UTC)

Rather than try to explain the usage, I kept the idea. See what you think; I wouldn't put Commutative diagram under the See also, but go ahead if you like. Perhaps a general article on Commutativity? Septentrionalis 01:58, 7 May 2006 (UTC)

[edit] Sample from a continuous distribution

I don't understand why in "a sample from a continuous distribution [...] each value will occur precisely once." I'm not particularly familiar with statistics (I didn't know what a 'mode' was before reading this article), so this may just reflect confusion on my part, but I don't see why sample from a continuous distribution will contain every element only once (although it seems to me that it would do so with probabililty 1, i.e., almost certainly). Could someone explain? Benja 13:23, 15 May 2006 (UTC)

Indeed, more precisely formulated, the probability of any duplicate elements is 0. So if you were to repeat this for the rest of the life of the universe, you'd never expect a duplicate. Isn't that good enough for "will occur precisely once"? More strongly, though, the values have to be represented somehow, and one imaginable way is a random-value producing apparatus that keeps producing a stream of digits making up the decimal expansion of the values for the random variables. So imagine that after several eons of steady production we have that one stream is "0.7785[seventeen umptyzillion and four digits omitted]459(to be continued)" and so is another. Are the two values duplicates of each other? Perhaps, but most likely not. They may diverge at every next digit. But even if they are, we'll never know, since the streams will never be complete. So actually, the probability of any duplicate elements is 0, and, moreover, even if duplicacy (is that an English word?) occurs, it remains forever unknowable. Might as well say: can't happen. --Lambiam^Talk 13:50, 15 May 2006 (UTC)

Huh. Seems like I understood alright, but you guys have a seriously different way of looking at these things. :-) (I was assuming that we were using the language of theory, since continuous distributions are a theoretical/modelling tool rather than something you'd deal with in practice.) Although, if we look at this from a practical point of view, wouldn't it be more helpful to talk about the practical situation where you get, say, temperature readings with +/- .01 degrees accuracy and it's quite possible, but unlikely, that you'll get the same reading twice, rendering the mode meaningless and requiring the technique described? -- In any case, thanks for explaining! Benja 14:30, 15 May 2006 (UTC)

"You guys"? I'm just one editor with one viewpoint (who happened to have written the relevant paragraph). The above was all very theoretical and only thought experimental; actual random-value producing apparatus doesn't last that long. For practical application, the article tells you to discretize the data, as for a histogram, so that you will actually get (still in practice) frequencies greather than 1. --Lambiam^Talk

[edit] I have a similar question to the first one above

My question is I have a set of 10 numbers with 44 and 93 appearing twice. Is the mode "44 and 93" or is it the average of the two, as calculated with "median" involving even numbers?

Thanks! LandOfIsrael 18:26, 15 August 2006 (UTC)

The article gives the example of a data sample [1, 1, 2, 4, 4] and states: "the mode is not unique". That is about all that can be said about it. Depending on your needs, predilections, and local customs, you can pick your choice between: (a) for this sample the mode is undefined; (b) this sample actually has two modes: 1 and 4; and (c) the mode is indeterminate (whatever that means). I would not take the average except when you have a histogram peaking in two adjacent slots, because that could be severely misleading. Now here is a question: what is the mode of an empty data sample? --Lambiam^Talk 01:22, 16 August 2006 (UTC)

Thank you so much!!! I appreciate your taking the time to help me. I didn't see that example in the article even though it was staring me in the face. Oops! :) In this case I think I'll write that the mode is "44 and 93" and see how that works. Again, thank you!!! (Thanks as well to whoever moved my question to the bottom -- I wasn't aware of the wiki custom of oldest on the top/newest at the bottom!) LandOfIsrael 10:52, 16 August 2006 (UTC)