1. The problem is to find the mean (average) of the given list of numbers. 2. The formula for the mean of a set of numbers $x_1, x_2, \ldots, x_n$ is: $$\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}$$ where $n$ is the total number of values. 3. Count the number of values given. There are 41 numbers. 4. Sum all the numbers: $$24.1322314 + 22.65625 + 35.430839 + 22.82688093 + 21.484375 + 22.44801512 + 20.54569362 + 19.48696145 + 18.98871528 + 18.82711104 + 17.89802289 + 29.36576335 + 19.38214469 + 17.00680272 + 20.28650791 + 19.36849691 + 26.75 + 23.45679012 + 30.11600238 + 24.56747405 + 20.66115702 + 16.70620468 + 19.140625 + 21.2244898 + 15.43209877 + 16.54064272 + 32.76939491 + 20.39542144 + 19.07183725 + 17.31341037 + 21.25624402 + 23.58983547 + 22.03856749 + 19.06771066 + 38.96454612 + 31.11111111 + 32.84730011 + 21.2962963 + 20.39542144 + 29.05328798 + 19.97440779 + 24.22118581 = 841.927 $$ 5. Calculate the mean: $$\text{Mean} = \frac{841.927}{41} \approx 20.5365$$ 6. Therefore, the average of the given numbers is approximately $20.54$.