Nutrition: animals. The mouse weights (in grams) of a random sample of 100 mice involved in a nutrition experiment are:
\begin{tabular}{l|l|l|l|l|l|l}
Interval & $41.5-43.5$ & $43.5-45.5$ & $45.5-47.5$ & $47.5-49.5$ & $49.5-51.5$ \\
\hline Frequency & 2 & 5 & 11 & 30 & 17
\end{tabular}
\begin{tabular}{l|l|l|l|l|}
Interval & $51.5-53.5$ & $53.5-55.5$ & $55.5-57.5$ & $57.5-59.5$ \\
\hline Frequency & 16 & 13 & 5 & 1
\end{tabular}
a. Find the mean of the weight of the mice. gms
(Type an integer or a decimal. Round to two decimal places.)

Step 1 ：Given the weight intervals and their corresponding frequencies, we can calculate the mean weight of the mice by using the formula for the mean of a frequency distribution. This involves multiplying each value by its frequency, summing these products, and then dividing by the total number of values.

Step 2 ：First, we find the midpoints of each interval. These are: \([42.5, 44.5, 46.5, 48.5, 50.5, 52.5, 54.5, 56.5, 58.5]\).

Step 3 ：The frequencies for each interval are: \([2, 5, 11, 30, 17, 16, 13, 5, 1]\).

Step 4 ：We then multiply each midpoint by its corresponding frequency and sum these products.

Step 5 ：Finally, we divide this sum by the total number of values, which is the sum of the frequencies.

Step 6 ：Doing these calculations, we find that the mean weight of the mice is \(\boxed{50.22}\) grams.