Forty new automobiles were tested for fuel efficiency by the EPA (in miles per gallon). This frequency distribution was obtained.
\begin{tabular}{|c|c|}
\hline Class & Frequency \\
\hline $8-12$ & 3 \\
\hline $13-17$ & 5 \\
\hline $18-22$ & 12 \\
\hline $23-27$ & 18 \\
\hline $28-32$ & 1 \\
\hline $33-37$ & 1 \\
\hline
\end{tabular}
What is the mean of the data set?
The mean of the data set is miles per gallon (answer to the nearest thousandth).

Step 1 ：Given a frequency distribution of fuel efficiency for 40 new automobiles tested by the EPA, we are asked to find the mean of the data set.

Step 2 ：The mean of a data set is calculated by summing all the values and dividing by the number of values. 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 (which is the total number of automobiles).

Step 3 ：The class midpoint is the average of the lower and upper bounds of each class. The class midpoints for the given data are \(10.0, 15.0, 20.0, 25.0, 30.0, 35.0\).

Step 4 ：The frequencies for each class are \(3, 5, 12, 18, 1, 1\).

Step 5 ：We multiply each class midpoint by its frequency and sum these products to get \(860.0\).

Step 6 ：The total frequency is the total number of automobiles, which is \(40\).

Step 7 ：We then divide the sum of the products by the total frequency to get the mean. So, the mean is \(\frac{860.0}{40} = 21.5\).

Step 8 ：Final Answer: The mean of the data set is \(\boxed{21.5}\) miles per gallon.