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Is there any rule which tells when to use a particular measure of central tendency.

MrAP
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  • @Tahir, This is not a duplicate. I am asking how to determine what measure to use in a particular situation. – MrAP Dec 05 '16 at 00:24
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    This is a "possible" dublicate. If you scroll down on that question, you can see some examples in answers. Besides, what do you mean by particular situation? – T.E.G. Dec 05 '16 at 00:26
  • @Tahir, By particular situation,i mean to ask that whenever i want to determine the central tendency of a set of data, which one of the measures should i use? – MrAP Dec 05 '16 at 00:30
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    Again, I recommend that you check answers in that question. Once you understand the measures of central tendency, it will give a good idea (and with examples) about which one to use in a particular situation. If you have a specific problem about your data, it might be better to provide more information. Asked in this way, I think it is also a very broad question and you might find more information just by googling. – T.E.G. Dec 05 '16 at 00:46
  • At first pass, I think this is close enough to be considered a duplicate. What you primarily need is to understand them. Once you do, you determine which is best by knowing what they are & the particulars of the situation you are facing. As this is a generic question, you mostly need to understand the three. – gung - Reinstate Monica Dec 05 '16 at 00:52
  • Also, if this a question from a course or textbook, please add the `[self-study]` tag & read its [wiki](http://stats.stackexchange.com/tags/self-study/info). – gung - Reinstate Monica Dec 05 '16 at 00:57
  • No, its not from any textbook. – MrAP Dec 05 '16 at 01:05
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    There are a number of rules, and many more answers than you might expect. Depends what data you have, and what you want to do with it. – Carl Dec 05 '16 at 05:50

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In cases when it is possible to find the mean, median and mode then the usefulness follows from what is important to you.

If we are talking about utility (or money) then the mean is used quite commonly because the expected value (mean) of the money we get is an attractive thing to maximize.

However, the St Petersburg paradox is an example of where the mean is not useful, it involves a gambling game with a 50% chance of losing your money but the mean amount of profit is infinite. This game isn't attractive to most people and thats because they look at the median profit (which is a loss). If you aren't concerned with the absolute value of the profit but you care more about frequently getting above a certain profit then the median is a useful statistic

The mode is useful when you need to be exactly correct. Perhaps you are predicting peoples' ages and they give you a dollar if you are right. Here if you are wrong it doesn't matter if you are above or below the age you guessed, it also doesn't matter if you are wrong by 1 year or by 10 years because those mistakes have equal consequences.

Aside from the usefulness for your context there are a few statistical properties of the central tendencies. The median is a robust way to measure central tendency because outliers don't affect it greatly. On the other hand, the mean is the most efficient estimate of central tendency so the sample mean converges faster than the sample median.

Hugh
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    For the mode, another use case is when you want a "representative end-member", and the distribution is multi-modal. That is, of the three, the mode is the only value "guaranteed" to have a relatively high probability, and also the only one guaranteed to be a valid "instance". (For example consider a Bernoulli distribution over $\{0,1\}$, i.e. a coin flip can never give "half a head".) This can be particularly significant in the case of multi-dimensional distributions (e.g. a PDF over images, where the mean image may just be a blur, but the modal image will "retain sharpness"). – GeoMatt22 Dec 05 '16 at 01:54