Find the mean and standard deviation of the frequency distribution.
\begin{tabular}{c|c|}
\hline $\mathbf{x}$ & $\mathbf{f}$ \\
\hline 3 & 1 \\
4 & 1 \\
5 & 0 \\
6 & 3 \\
7 & 6 \\
8 & 4 \\
9 & 4
\end{tabular}

Step 1 ：Given the frequency distribution table, we have the values (x) as [3, 4, 5, 6, 7, 8, 9] and their corresponding frequencies (f) as [1, 1, 0, 3, 6, 4, 4].

Step 2 ：The mean of a frequency distribution is calculated by multiplying each value of the data set by its corresponding frequency, summing these products, and then dividing by the total number of data points.

Step 3 ：Using the above formula, the mean of the frequency distribution is calculated to be \(7.105263157894737\).

Step 4 ：The standard deviation is a measure of the dispersion of the data set and is calculated by taking the square root of the variance. The variance is calculated by subtracting the mean from each data point, squaring the result, multiplying by the corresponding frequency, summing these products, and then dividing by the total number of data points.

Step 5 ：Using the above formula, the variance of the frequency distribution is calculated to be \(2.5152354570637123\).

Step 6 ：The standard deviation is then calculated by taking the square root of the variance, which gives \(1.5859493866651964\).

Step 7 ：Final Answer: The mean of the frequency distribution is \(\boxed{7.105263157894737}\) and the standard deviation is \(\boxed{1.5859493866651964}\).