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Arithmetic mean and standard deviation

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vaibhav.iit2002 Master | Next Rank: 500 Posts Default Avatar
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Arithmetic mean and standard deviation

Post Mon Oct 12, 2009 9:50 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
    10.5, 11, 11.5, 12, 12.5

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    maihuna Legendary Member Default Avatar
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    Post Mon Oct 12, 2009 9:55 am
    vaibhav.iit2002 wrote:
    Arithmetic mean and standard deviation of a certain normal distribution are 13.5 and 1.5. What value is exactly 2 standard deviations less than the mean?
    10.5, 11, 11.5, 12, 12.5
    10.5, one SD away means +/- SD so 2 less means: 13.5-3

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    papgust Community Manager
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    Post Mon Oct 12, 2009 10:06 pm
    maihuna wrote:
    10.5, one SD away means +/- SD so 2 less means: 13.5-3
    Can you help me understand how you get -3 in the calculation?

    sanjana Master | Next Rank: 500 Posts Default Avatar
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    Post Tue Oct 13, 2009 3:06 am
    Mean is 13.5
    SD = 1.5
    2sd = 2* 1.5 = 3

    We need to find the value exactly 2 sd less than the mean so we need to find 13.5-3
    If we had to find the value exactly 2 sd greater than the mean we would do 13.5+3

    In general :

    Points k Sd above the mean : x+k*SD
    points k sd below the mean : x-k*SD

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