startinallover
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I'm doing a report on a set of lab data and am supposed to find the mean and mean's standard deviation
[tex]\bar{x} + \sigma_{\bar{x}}[/tex]
The mean is given by
[tex]\displaystyle{ \bar{x} = \sum_{i=1}^{N} w_{i} x_{i} }[/tex]
Where
[tex]\displaystyle{ w_{i} = \left( \frac{\sigma}{\sigma_{i}} \right)^2 }[/tex]
and for the error (mean's standard deviation)
[tex]\displaystyle{ \sigma_{\bar{x}} = \sigma = \frac{1}{ \sqrt{ \sum_{i=1}^{N} \frac{1}{\sigma_{i}^{2} } } } }[/tex]The problem is I can't quite figure it out what the σi would be, is it the standard deviation? This might sound very silly but it's been a long time I've dealt with this.
Any help is appreciated.
[tex]\bar{x} + \sigma_{\bar{x}}[/tex]
The mean is given by
[tex]\displaystyle{ \bar{x} = \sum_{i=1}^{N} w_{i} x_{i} }[/tex]
Where
[tex]\displaystyle{ w_{i} = \left( \frac{\sigma}{\sigma_{i}} \right)^2 }[/tex]
and for the error (mean's standard deviation)
[tex]\displaystyle{ \sigma_{\bar{x}} = \sigma = \frac{1}{ \sqrt{ \sum_{i=1}^{N} \frac{1}{\sigma_{i}^{2} } } } }[/tex]The problem is I can't quite figure it out what the σi would be, is it the standard deviation? This might sound very silly but it's been a long time I've dealt with this.
Any help is appreciated.