The cost per load (in cents) of 35 laundry detergents tested by Consumer Reports is shown here. \begin{tabular}{cc} Class & Frequency \\ \hline $13-19$ & 3 \\ $20-26$ & 5 \\ $27-33$ & 3 \\ $34-40$ & 5 \\ $41-47$ & 2 \\ $48-54$ & 4 \\ $55-61$ & 7 \\ $62-68$ & 6 \\ \hline \end{tabular} Find the mean of the data set. If necessary, round to the nearest whole number. The mean cost per load was cents.

Step 1 ：The cost per load (in cents) of 35 laundry detergents tested by Consumer Reports is shown in the table. The table shows the frequency of each cost range.

Step 2 ：To find the mean of the data set, we need to calculate the sum of all the values in the set and then divide by the number of values. However, in this case, we have a frequency distribution. So, we need to multiply each class midpoint by its frequency, sum these products, and then divide by the total frequency. The class midpoint is the average of the lower and upper bounds of the class.

Step 3 ：The class midpoints are \(16, 23, 30, 37, 44, 51, 58, 65\) and the corresponding frequencies are \(3, 5, 3, 5, 2, 4, 7, 6\).

Step 4 ：Multiplying each class midpoint by its frequency and summing these products gives us the total sum.

Step 5 ：Dividing this total sum by the total frequency gives us the mean cost per load.

Step 6 ：Final Answer: The mean cost per load was \(\boxed{44}\) cents.