Problem $2$:

Given the data set below, which type of interpolation would provide an interpolant function with the most accurate approximation for $?$ Provide details on the reasoning of your choice and the types of error that other methods might incur. In this case all of the data points must be used for this interpolation.

$1\mathrm{.}12\mathrm{.}5,3\mathrm{.}3,4\mathrm{.}45\mathrm{.}76\mathrm{.}5$

$2\mathrm{.}12\mathrm{.}252\mathrm{.}155\mathrm{.}25\mathrm{.}55\mathrm{.}4$