A texearcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the. standard deviation of the data. Round your answer to the nearest hundredth, if necessary. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{\begin{tabular}{c} Building \\ Toy Pieces \end{tabular}} \\ \hline 160 & 45 \\ \hline 265 & 350 \\ \hline 350 & 45 \\ \hline 104 & 296 \\ \hline 265 & 109 \\ \hline 170 & 480 \\ \hline \end{tabular}

Step 1 ：Given data = [160, 45, 265, 350, 350, 45, 104, 296, 265, 109, 170, 480]

Step 2 ：Calculate the mean of the data: \(\frac{160 + 45 + 265 + 350 + 350 + 45 + 104 + 296 + 265 + 109 + 170 + 480}{12} = 219.92\)

Step 3 ：For each number in the data, subtract the mean and square the result. For example, for the first number: \((160 - 219.92)^2\)

Step 4 ：Find the average of these squared differences. This is called the variance: \(\frac{\sum_{i=1}^{12} (x_i - 219.92)^2}{12} = 17029.41\)

Step 5 ：The standard deviation is the square root of the variance: \(\sqrt{17029.41} = 130.50\)

Step 6 ：Final Answer: The standard deviation of the data, rounded to the nearest hundredth, is \(\boxed{130.50}\)