When does it make sense to calculate the average value of some data and call it a representative of that data? For the purpose of this post, I'm using the following definition of the term
Average (from Wikipedia):
In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "expected" value of the data set. There are many different
descriptive statistics that can be chosen as a measurement of the central tendency of the data items.
An average is a single value that is meant to typify a list of values. If all the numbers in the list are the same, then this number should be used. If the numbers are not all the same, an easy way to get a representative value from a list is to randomly pick any number from the list. However, the word 'average' is usually reserved for more sophisticated methods that are generally found to be more useful.
The most common method is the arithmetic mean. There are many other types of averages, such as median (used most often to describe house prices and incomes). The average is calculated by combining the measurements related to a set and to compute a number as being the average of the set.
Can the probability distribution indicate if averaging makes sense? And what kind of average makes sense? For example, if we have a normal distribution, arithmetic mean clearly makes sense as an average (stating the standard deviation also might make it more representative, but that is for another discussion). But if we have a polynomial distribution (like a
Power Law Distribution) or an exponential distribution (like a
Poisson Distribution), what, if anything, makes sense?
If this question seems too basic, please excuse me — it obviously arises from a lack of clarity in understanding the concepts. I'd really appreciate if anyone can throw any light on this. Thanks in advance.
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Last Edit: January 07, 2009, 03:43:38 am by sids »
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