Common data set for Problems $1$ and $2$

The temperature in a region varies as in the following table:

$\backslash$table$[[$Depth$,2(m),0,0\mathrm{.}5,1\mathrm{.}0,1\mathrm{.}5,2\mathrm{.}0,2\mathrm{.}5,3\mathrm{.}0],[$Temperature $(C),70,68,55,22,13,11,10]]$

Problem $1($Regression$/$curve fitting$)$: The point at which the temperature$-$depth curve has zero curvature $($i$.$ e$.)\frac{d^{2}T}{w_2}{|}_z||=0$ is called the thermocline. Fit a cubic polynomial for this $($entire$)|||$ dataset and using the same, solve for $z_0($the thermocline depth$).$

Problem $2($Numerical Integration$)$: Determine the average temperature of the region defined as

$(T)=\frac{1}{3m}{\displaystyle \underset{x=0m}{\overset{x=3m}{}}}T(z)dz$

Use Simpspns's, $1/3$ rule. Do the integration using the data from the table directly $($use step length as per the data$).$