Talk:Mode (statistics)

message: 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)
replies: text: 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)
replies: text: 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)
replies: text: I got a proublem from my math class which implies there is a mode for a set of 5 numbers. (It's a hard proublem to explain so I won't right it out.) Lophoole 01:00, 26 January 2007 (UTC)
thread_title:  If the highest frequency is one... 

message: 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)
replies: text: 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. --LambiamTalk 13:50, 15 May 2006 (UTC)
replies: text: 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)
replies: text: "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. --LambiamTalk
observe the following data
1,3,4,5,7,9,12,13,15,15,15,15,15,16,17,19,22,24,24,25,25,26,26,27,30,30,31,32,32,33,33,34,35,35,36,36,37,,39,40,40,45,45,46,47,48,49,49.
class intervals     freq.
0-10                 6
10-20                10
20-30                8
30-40                14
40-50                9
according to the defination of the mode, 30-40 is the modal class. and the mode will lie in that interval. But if we look at the raw data then 15 is the mode. how do we resolve this contradiction ?   
Reeded 15:11, 28 March 2007 (UTC)

text: If the population distribution is continuous, the chance of observing two or more identical values is 0. If you discretize the data, then the result may (of course) depend on the details. If you have a distribution whose density function has a thin spike, it gets diluted when the intervals are much wider. The sample data show a thin spike at 15 and a robust mound around 35. The choice of intervals does actually not conform to the advice given in the article, but it is also possible to construct an example that does conform but still displays this phenomenon.  --LambiamTalk 23:01, 28 March 2007 (UTC)

text: Do you mean contiguous intervals? And isn't the data (if finite in size) always "discontinuous"? If the data comes from a discrete probability distribution, such as the Poisson distribution, then usually you don't use intervals but just tally the values: 3× a 0, 3× a 1, 4× a 2, 9× a 3, 5× a 4, 1× a 5, 2× a 6. If the frequencies are very low, you could lump groups of adjacent values together, making sure the groups have equal sizes. If the underlying distribution is continuous, like for the gamma distribution, then you must use intervals, and these intervals should partition the sample space into equi-sized parts. These intervals must be contiguous: together they must cover the whole space without gaps.  --LambiamTalk 12:27, 8 April 2007 (UTC)
thread_title:  Sample from a continuous distribution 

message: 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)
replies: text: 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? --LambiamTalk 01:22, 16 August 2006 (UTC)
replies: text: 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)
thread_title:  I have a similar question to the first one above 

message: I find it unfortunate that this table uses a different data set for each example, and that the clarity and usefulness would be greatly improved if the same data set was used for each entry.  I would like to edit it with the following data set: 1, 2, 2, 3, 4, 7, 9.  This would give a mean of 4, a median of 3, and a mode of 2.  --Pdcurry (talk) 23:31, 22 December 2009 (UTC)
thread_title:  Better Data Set for the '''''Comparison of common averages''''' table 

message: Why isn't there a criticism section???  —Preceding unsigned comment added by 129.98.192.217 (talk) 03:01, 25 October 2010 (UTC)
replies: text: Probably because there is no promotion section. The article, as far as i checked, provides factual and unbiased information on this statistic, and it is up to the reader to criticize it or not. If you feel some properties which make mode a bad statistic to use are missing you can probably edit the page adding them to the section where they belong. Plm203 (talk) 10:56, 29 October 2023 (UTC)
thread_title:  Criticism of the mode 

message: In the Wikipedia article we read "For samples, if it is known that they are drawn from a symmetric distribution, the sample mean can be used as an estimate of the population mode." I propose to change to: "For samples, if it is known that they are drawn from a symmetric unimodal distribution, the sample mean can be used as an estimate of the population mode." Otherwise, it fails for example for values 1, 2, 2, 2, 3, 4, 5, 5, 5, 6, having mean 3.5 which is not a good estimate of the two modes 2 and 5.  — Preceding unsigned comment added by 140.105.52.132 (talk) 22:22, 21 March 2012 (UTC)
thread_title:  Probably an error 

message: I texified the "Unimodal distributions" section under median, and found this similar section on this article. However, the two contradict each other. The media article claims that the difference between the mean and median are bounded by \sigma (3/5)^{1/2}, whereas this article claims that it is \sigma 3^{1/2}.
Which one is correct?
Tebello TheWHAT!!?? 21:34, 18 March 2012 (UTC)
replies: text: The correct statement is that the difference between the mean and the MEDIAN is \sigma (3/5)^{1/2} and that the difference between the mean and the MODE is \sigma 3^{1/2}. This is what is written in the articles.DrMicro (talk) 13:31, 7 July 2012 (UTC)
thread_title:  Unimodal distributions 

message: Substituted at 20:06, 1 May 2016 (UTC)
thread_title: Assessment comment

message: I plan to remove the section Confidence interval for the mode with a single data point unless I hear an objection. There are at least three problems with this section:
#Undue weight. It comprises well over 1/3 of the article, despite being about a very esoteric point (samples with only a single data point).
#At least part of it doesn't make sense (the first part of the subsection "Statistical tests").
#It assumes at the beginning that we know the mode, in order to form a confidence interval for the mode. Likewise, later in discussing symmetric distributions, the confidence interval for the mean/median/mode depends on the true value of the mean/median/mode. This renders it not useful in practice even if we did have a single-value sample.
Let me know if there is any objection to removing the entire section. Loraof (talk) 15:46, 24 June 2017 (UTC)
thread_title:  Proposed removal of section 

message: From the lead:
:"The mode of a continuous probability distribution is the value x at which its probability density function has a locally maximum value";
:"The mode is not necessarily unique to a given discrete distribution, since the probability mass function may take the same maximum value at several points".
Rather strange. A multimodal continuous case: several local maxima, possibly of different "heights". But multimodal discrete case: several local maxima of the same "height". Really so? Boris Tsirelson (talk) 18:55, 26 June 2017 (UTC)
replies: text: Strange, yes. But this seems to be how statisticians use these terms. References would be worthwhile. I'll add one for the discrete case. Loraof (talk) 14:39, 27 June 2017 (UTC)
thread_title:  Different treatment of discrete and continuous? 

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thread_title:  External links modified (February 2018) 

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thread_title:  "Math mode" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Why not talk of "a mode" when no uniqueness assumption is in effect ? I find the current presentation misleading and i don't think there would be any problem with using the indefinite article throughout. Thank you. Plm203 (talk) 11:00, 29 October 2023 (UTC)
thread_title:  Why use a definite article: "''the'' mode" ?