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    The masses, xkg of 50 bags of flour were measured and the results were summarised as follows:
    n=50\,\,\,\,\sum{(x-1.5)=1.4\,\,\,\,\,\,\,}\sum{{{(x-1.5)}^{2}}=0.05\,\,\,\,\,\,\,}

    Find Mean and sd of the masses of these bags of flour.

    I'm not sure where the 1.5 comes from or what to do with it and how to make use of the sum expressions.
    Apparently the answer is 1.528 for the mean and 0.0147 for the sd.
    Any advice would be welcome.
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    (Original post by xlaser31)
    The masses, xkg of 50 bags of flour were measured and the results were summarised as follows:
    n=50\,\,\,\,\sum{(x-1.5)=4\,\,\,\,\,\,\,}\sum{{{(x-1.5)}^{2}}=0.05\,\,\,\,\,\,\,}

    Find Mean and sd of the masses of these bags of flour.

    I'm not sure where the 1.5 comes from or what to do with it and how to make use of the sum expressions.
    Apparently the answer is 1.528 for the mean and 0.0147 for the sd.
    Any advice would be welcome.
    They've simply put the -1.5 in there to make life hard for you and to see if you know how to deal with removing the 1.5's.

    You're given \displaystyle \sum_{i=1}^{50} (x_i - 15)  = 4 you want to find the mean, which is \frac{1}{50}\sum_{i=1}^{50}x_i.

    How can you get the latter from the former? Well:

    \displaystyle

\begin{equation*} \sum_{i=1}^{50} (x_i-1.5) = \sum_{i=1}^{50}( x_i) - \sum_{i=1}^{50} (1.5) = 4\end{equation*}

    But: \sum_{i=1}^{50} (1.5) = 1.5 \times 50 = 75, so:

    \displaystyle

\begin{equation*}  \sum_{i=1}^{50}( x_i) - \sum_{i=1}^{50} (1.5) = \sum_{i=1}^{50} (x_i) - 75 = 4 \iff \sum_{i=1}^{50}x_i = 4 + 75\end{equation*}

    But you want \frac{1}{50}\sum_{i=1}^{50} x_i, so how do you get that? Can you now do something similar for variance?
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    Sorry the 4 should have been 1.4, but I get it now.
    Thanks
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    (Original post by xlaser31)
    ...
    If you've covered it, you may recognise this as an example of coding, which would make the calculations easier.
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    (Original post by xlaser31)
    Sorry the 4 should have been 1.4, but I get it now.
    Thanks
    As above, you might want to look up "coding" on examsolutions or such, but the way I've done it is basically by deriving the coding from first principles.

    You'er welcome.
 
 
 
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