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what is a standard deviation anyway?

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  • 04-07-2012 9:52am
    #1
    im invisible
    Closed Accounts Posts: 4,372 ✭✭✭


    and what do you get when you have five of them?


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    #2
    alan4cult
    Registered Users Posts: 1,583 ✭✭✭alan4cult


    Standard Deviation is one measure of the spread of data. When people say 2 standard deviations, 3 standard deviations they are referring to the normal distribution.

    In the normal distribution:
    68.27% of data lie between 1 standard deviation either side of the mean
    e.g. if mean=2 and standard deviation=1.2 then 68.27% lies between 0.8 and 3.2

    5 standard deviations either side of the mean covers almost all possibilities (i.e. probability of lying outside this range is <0.001)

    Hopefully that explains it.


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    #3
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,847 Mod ✭✭✭✭Michael Collins


    I wonder is the post inspired by results from the LHC on the Higgs boson where they say they are near to a 5 sigma measurement result? Sigma being the Greek letter that is used in mathematics to represent the standard deviation.

    If so, what alan4cult says is of course true, but in the context of the Higgs boson they are talking about the probability of the results actually being the result of something other than the Higgs particle.

    Here they say that they are approaching a "5 sigma" result, which means you are out in the tails of the Normal/Gaussian Distribution (for example), and the chances that the measurements are due to something other than the Higgs boson is about 0.0000005733%. So quite unlikely I think you'll agree.

    Standard_deviation_diagram.svg

    This plot only shows out to "3 sigma" from the mean, but you can fairly clearly see, even at this sigma value, that the probability is already quite low when compared with the mean.

    See Wiki for more info

    http://en.wikipedia.org/wiki/Normal_distribution


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    #4
    SuperInfinity
    Banned (with Prison Access) Posts: 2,449 ✭✭✭SuperInfinity


    Didn't I hear something on the radio about how they were thinking later it mightn't be the Higgs Boson after all?

    http://news.discovery.com/space/might-the-higgs-boson-have-a-lookalike-imposter-120710.html

    I guess that 0.0000005733% not in a million trillion years chance may have come true... ;)


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    #5
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,847 Mod ✭✭✭✭Michael Collins


    SuperInfinity wrote: »
    Didn't I hear something on the radio about how they were thinking later it mightn't be the Higgs Boson after all?

    http://news.discovery.com/space/might-the-higgs-boson-have-a-lookalike-imposter-120710.html

    I guess that 0.0000005733% not in a million trillion years chance may have come true... ;)

    I don't think that I specified that original probability correctly. I think the chance that it isn't the Higgs boson is higher than that -- the chance that it isn't "a particle", and just some random data fluctuation, is what that percentage really means. Whether it follows the rules of the Higgs boson or not is, I guess, still to be determined.


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