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\textit{To get an estimate of your uncertainty, compute the standard deviation.

My 4 distances are 150, 120,

100 and 100 parsecs (pc)}

The average of my 4 distances is

\[

\bar {x}=\frac{\sum\limits_{i=1}^n {x_i } }{n}

\]

\[

\bar {x}=\frac{150pc+120pc+100pc+100pc}{4}=117.5pc

\]

The average = $ 120pc$

\textit{The standard deviation is }

\[

\sigma =\sqrt {\frac{\sum\limits_{i=1}^n {\left( {x_i -\bar {x}} \right)^2}

}{n-1}}

\]

\[

\sigma =\sqrt {\frac{\left( {150-120} \right)^2+\left( {120-120}

\right)^2+\left( {100-120} \right)^2+\left( {100-120} \right)^2}{n-1}}

=23.805

[/tex]

I've computed it but what does it mean? How do I estimate my uncertainty from this number? The book doesn't explain this.

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# Homework Help: Standard deviation

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