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 \(\boxed{1.5}\).