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Average versus mean

  1. Oct 3, 2009 #1

    DaveC426913

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    I'm reading up on standard deviation.

    Wiki seems to use 'average' and 'mean' interchangeably.

    "find the arithmetic mean (average) of 3, 7, 7, and 19"

    Their answer is 9, which I would call the "average". The mean, to me is the middle value of the set, in this case, 7.
     
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  3. Oct 3, 2009 #2

    jamesrc

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    I've always used "arithmetic mean", "mean", and "average" interchangeably - arithmetic mean is probably the least ambiguous (there are different types of means and means are a type of average).

    The middle value (7 in your example) is the median, not the mean.
     
  4. Oct 4, 2009 #3

    statdad

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    The median, arithmetic mean, mode, and other, are all different ways to measure the "average" value of a set of data - or, in probability, the "average" of a distribution. The fact that average is such a vague term, one that doesn't describe any single characteristic of data or a distribution, is the source of the confusion.

    It's best to use the name of whichever measure you calculate: if you use the mean, say mean (and add arithmetic, geometric, harmonic, trimmed, etc., if there is any chance of confusion). If you use the median, say median, and so on.
     
  5. Oct 5, 2009 #4

    HallsofIvy

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    The definition of "mean", in statistics, is the arithmetic average. What you are calling "mean", the middle value, is the "median". In this example, 7 also happens to be the "mode", the value that occurs most often.
     
    Last edited: Oct 5, 2009
  6. Oct 5, 2009 #5
    IMHO, the average or mean descriptor is used very often where the median would provide more useful information, since the "rank" is weighted by the data in the mean and unweighted using the median.
     
  7. Oct 5, 2009 #6

    DaveC426913

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    What I'm hearing is what "average" is a generic term. That there are many ways for averaging a set of numbers. The key to clarity is to state what type of averaging one is using, such as mean or median.
     
  8. Oct 5, 2009 #7
    the mean of a distribution is its expected value. this is not generally an arithmetic average.
    the strong law of large numbers says that an arithmetic average of a very large independently chosen sample is close to the mean.
     
  9. Oct 6, 2009 #8

    statdad

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    "What I'm hearing is what "average" is a generic term. That there are many ways for averaging a set of numbers. The key to clarity is to state what type of averaging one is using, such as mean or median."

    Exactly. There is no universal rule for which measure to use, so being clear about the one you choose is important.
     
  10. Oct 6, 2009 #9
    an average and a mean are not the same. The mean is the weighted average - weighted by probabilities - this is not the same as an arithmetic average. In probability it is called the expected value. In practice averages and meas are identified because of the law of large numbers.
     
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