Find the mean and standard deviation of the frequency distribution.
\begin{tabular}{l|l|}
\hline $\mathbf{x}$ & $\mathbf{f}$ \\
\hline 4 & 3 \\
5 & 4 \\
6 & 0 \\
7 & 1 \\
8 & 2
\end{tabular}

Step 1 ：Given the frequency distribution table, we have the values of x as [4, 5, 6, 7, 8] and their corresponding frequencies as [3, 4, 0, 1, 2].

Step 2 ：To find the mean of the frequency distribution, we multiply each value of x by its corresponding frequency, sum these products, and then divide by the total frequency. This gives us a mean of \(5.5\).

Step 3 ：To find the standard deviation, we first calculate the variance. This involves subtracting the mean from each x value, squaring the result, multiplying by the corresponding frequency, summing these products, and dividing by the total frequency. This gives us a variance of \(2.25\).

Step 4 ：The standard deviation is then the square root of the variance, which gives us \(1.5\).

Step 5 ：Final Answer: The mean of the frequency distribution is \(\boxed{5.5}\) and the standard deviation is \(\boxed{1.5}\).