Nutrition: animals. The mouse weights (in grams) of a random sample of 100 mice involved in a nutrition experiment are:
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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 $\boxed{{\displaystyle 50.22}}$ grams.