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    Standard deviation

    Definition: measures the spread of data around it’s mean

    Formula: N-1 is used instead of N because it removes bias and was imposed by bessel.

    Example 1)
    There is a client who is considering selling his business and wants to know if it’s worth keeping.

    If the clients monthly income is 7200, 6500, 7500, 4020, 5300 for Jan, Feb, March, April and June respectively.

    The clients wants to know how likely it is for his business to make over 6000 a month based on this years earnings.
    Monthly Income---Mean – 6104, xi – mean:-----(xi-mean)2
    7200---------- 1096 ---------------------- 1201216
    6500---------- 396 ---------------------- 156816
    7500---------- 1396 ---------------------- 1948816
    4020---------- -2084 --------------------- 4343056
    5300---------- -804 ---------------------- 646416

    Standard deviation = 1440.17 and mean 6104
    Using normal distribution

    So P(X?6000)
    P(Z?(6000 – 6104)/1440.17) = P(Z?-0.07) = P(Z?0.07) = 52.79% (using table above)
    So there is a 52.79% chance of him earning over 6000 a month.

    IS THIS VALID!!! IM NOT SURE IF YOU ARE ALLOWED TO USE NORMAL DISTRIBUTION IN THIS CASE!!!

    For my method I am using bessels correction, which uses N-1 as opposed to N because this reduces bias in the final figure.
    Is this method valid to use?
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    Maths Forum !!!!!!!!!!!!!!!!!! !!!!!!!!!......You will recieve more help there , not in the University section.
 
 
 
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