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Thread: Standard deviation from graph

  1. #1
    Mar 2016

    Unhappy Standard deviation from graph

    Sorry if this is a stupid question but please give me some help
    How would you know the standard deviation of a graph just from looking at it, I get that the mean is 10 but how is the standard deviation 4/3?
    Attached Thumbnails Attached Thumbnails Standard deviation from graph-screen-shot-2017-08-28-5.34.45-pm.png  
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  2. #2
    Junior Member
    Aug 2017

    Re: Standard deviation from graph

    I guess there is no actual method to deduct the standard deviation just by observing the graph IMO. However, you can use following trick to roughly estimate the SD from a Normal distribution.
    It is known that $\displaystyle \text{Pr}(x\in[\mu-3\sigma,\mu+3\sigma])\approx 0.95$ where $\displaystyle \mu$ and $\displaystyle \sigma$ are the mean and SD.
    Basically, if you could guess where the tail almost become zero from the figure, it helps you to make a rough estimation.
    In you figure, $\displaystyle \mu=10$ and tails almost disappear at $\displaystyle x<6$ and $\displaystyle x>14$. Therefore, $10+3\sigma=14$ and $10-3\sigma=6$ need to satisfied.
    That says $\sigma \approx 4/3$.
    Thanks from HallsofIvy and ChanelSapphire
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