Math  /  Data & Statistics

Question15. Average monthly temperatures for the city of Hamilton, Ontario, from Januáry to December are shown. \begin{tabular}{|c|c|} \hline Month & Temperature (C)\left({ }^{\circ} \mathrm{C}\right) \\ \hline 1 & -4.8 \\ \hline 2 & -4.8 \\ \hline 3 & -0.2 \\ \hline 4 & 6.6 \\ \hline 5 & 12.7 \\ \hline 6 & 18.6 \\ \hline 7 & 21.9 \\ \hline 8 & 20.7 \\ \hline 9 & 16.4 \\ \hline 10 & 10.5 \\ \hline 11 & 3.6 \\ \hline 12 & -2.3 \\ \hline \end{tabular} a) Make a scatter plot of the data. b) Use the table and the graph to write a sinusoidal function to model the data. c) Graph your model on the same set of axes as your scatter plot. Comment on the accuracy of the fit.

Studdy Solution
The sinusoidal function that models the data is y=13.35cos(π6(x7))+8.55 y = 13.35\cos\left(\frac{\pi}{6}(x - 7)\right) + 8.55 and when graphed, it's a pretty good fit to the temperature data!

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