In a study of the time it takes an untrained mouse to run a maze, a researcher recorded these data in seconds.
\begin{tabular}{cc}
Class & Frequency \\
\hline $2.1-2.7$ & 6 \\
$2.8-3.4$ & 4 \\
$3.5-4.1$ & 5 \\
$4.2-4.8$ & 13 \\
$4.9-5.5$ & 7 \\
$5.6-6.2$ & 10
\end{tabular}

Find the mean of the data set. Round to one decimal place, if necessary.
The mean time for an untrained mouse to run a maze was $\square$ seconds.

Step 1 ：The mean of a data set is calculated by summing all the values and dividing by the number of values. However, in this case, we don't have the exact values, but we have classes (ranges of values) and their frequencies. So, we can estimate the mean by taking the midpoint of each class, multiplying it by the frequency of that class, summing these products, and then dividing by the total frequency.

Step 2 ：First, calculate the midpoints of each class. The midpoint of a class is the average of the lower and upper limits of the class. For example, the midpoint of the class $2.1-2.7$ is $(2.1+2.7)/2=2.4$.

Step 3 ：Next, multiply each midpoint by its corresponding frequency. For example, the product for the class $2.1-2.7$ is $2.4*6=14.4$.

Step 4 ：Sum all these products to get the numerator of the mean.

Step 5 ：Finally, divide this sum by the total frequency to get the mean. The total frequency is the sum of all frequencies, which is $6+4+5+13+7+10=45$.

Step 6 ：The mean time for an untrained mouse to run a maze was \(\boxed{4.4}\) seconds.