Gabriel and Lucia took a road trip across the country. The room costs, in dollars, for their overnight stays are listed in the accompanying table. Find the standard deviation of the distribution.
Click the icon to view the room costs in dollars.

The standard deviation of the distribution is $\$ \square$.
(Type an integer or a decimal. Round to the nearest cent as needed.)
Room Costs (\$)
\begin{tabular}{|ccccccc|}
\hline 97 & 108 & 125 & 160 & 184 & 173 \\
118 & 246 & 135 & 131 & 126 & 263 & \\
\hline
\end{tabular}
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Step 1 ：First, we need to find the mean (average) of the room costs. This is done by adding all the room costs together and dividing by the total number of costs. The room costs are: 97, 108, 125, 160, 184, 173, 118, 246, 135, 131, 126, 263. The mean is calculated as \(\frac{97 + 108 + 125 + 160 + 184 + 173 + 118 + 246 + 135 + 131 + 126 + 263}{12} = 155.5\).

Step 2 ：Next, for each room cost, we subtract the mean and square the result. This gives us the squared differences: 3422.25, 2256.25, 930.25, 20.25, 812.25, 306.25, 1406.25, 8190.25, 420.25, 600.25, 870.25, 11556.25.

Step 3 ：We then find the mean of these squared differences. This is done by adding all the squared differences together and dividing by the total number of squared differences. The mean of the squared differences is calculated as \(\frac{3422.25 + 2256.25 + 930.25 + 20.25 + 812.25 + 306.25 + 1406.25 + 8190.25 + 420.25 + 600.25 + 870.25 + 11556.25}{12} = 2565.9166666666665\). This is also known as the variance.

Step 4 ：Finally, we take the square root of the variance to find the standard deviation. The standard deviation is calculated as \(\sqrt{2565.9166666666665} = 50.65487801452755\).

Step 5 ：We round the standard deviation to the nearest cent to get the final answer. The standard deviation of the room costs is \(\boxed{50.65}\).