I am little bit confusing how to calculate $δβ/δρ$ value if I have set of values like this.
I have the values of $β$ and $ρ$ like this. $$ \begin{array}{l|l} β & ρ\\ \hline 0,324 & 0,687\\ 0,322 & 0,695\\ 0,319 & 0,721\\ 0,317 & 0,759\\ 0,316 & 0,798 \end{array} $$ from the above set of values i need to calculate this "$δβ/δρ$" $=$ ?
Can anyone explain me how to calculate it in microsoft excel or normal method?
On
Adding to @Ross Millikan's excellent answer, to compute in Excel, suppose your data is in columns A,B, in rows 2-6 (row 1 is the header row). Into entry C2 put "=A2-A3", then copy this into C3-C5 (Excel will update the references as needed). Into entry D2 put "=B2-B3", then copy this into D3-D5. (the previous two steps can be combined). Into entry E2 put "=C2/D2", then copy this into E3-E5.
$\frac {\delta \beta}{\delta \rho}$ is the change in $\beta$ between two lines divided by the difference in $\rho$ in the same two lines. So for the first two, you would have $\frac {\delta \beta}{\delta \rho}=\frac{0.324-0.322}{0.687-0.695}=\frac{0.002}{-0.008}=\frac {-1}4$ If these are measured values, the error is quite large because of the subtraction.