Approximate the mean for following GFDT. \begin{tabular}{|c|c|} \hline Data & Frequency \\ \hline $30-34$ & 1 \\ \hline $35-39$ & 1 \\ \hline $40-44$ & 2 \\ \hline $45-49$ & 5 \\ \hline $50-54$ & 4 \\ \hline $55-59$ & 9 \\ \hline $60-64$ & 10 \\ \hline $65-69$ & 17 \\ \hline $70-74$ & 13 \\ \hline \end{tabular} mean $=$ Report answer accurate to one decimal place. Check Answer

Step 1 ：Given the frequency distribution table, we can calculate the mean by multiplying each data point by its frequency, summing these products, and then dividing by the total frequency.

Step 2 ：Since the data points are ranges, we'll use the midpoint of each range as the data point. The midpoints are \([32, 37, 42, 47, 52, 57, 62, 67, 72]\).

Step 3 ：The corresponding frequencies are \([1, 1, 2, 5, 4, 9, 10, 17, 13]\).

Step 4 ：Multiplying each midpoint by its corresponding frequency and summing these products, we get the total sum.

Step 5 ：Dividing this total sum by the total frequency, we get the mean of the frequency distribution.

Step 6 ：The mean of the frequency distribution is approximately \(61.354838709677416\).

Step 7 ：Rounding to one decimal place, the mean is \(\boxed{61.4}\).