jmc

We want to find the fraction of people that chose ``Pop". To this end, we find the fraction of the circle that represents ``Pop", $\frac{251}{360}$, and multiply by the total number of people surveyed: $472\cdot \frac{251}{360}\approx 329.089$. Rounding to a whole number gives a possible answer of $329$ people.

This method doesn't prove that the answer is unique, but we can check that $328$ people would take up only $\frac{328}{472}\cdot 360\approx 250.169$ degrees of the pie chart, while $330$ people would take up $\frac{330}{472}\cdot 360\approx 251.695$ degrees. So, $\boxed{329}$ people are the only number whose share of the pie rounds to the nearest degree as $251^{\circ }$.