Prepare a grouped frequency distribution table and compute the mean for the given religious education test scores.

Step 1: Order the data and determine class intervals. First, arrange the given scores in ascending order: 0, 4, 5, 6, 7, 8, 9, 9, 10, 10, 10, 11, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 18, 19, 19, 20, 23, 24, 24

The total number of data points is $n = 31$. The minimum value is 0 and the maximum value is 24. The range is $24 - 0 = 24$.

To determine the number of classes, we can use Sturges' formula: $k = 1 + 3.322 \log_{10}(n)$. $k = 1 + 3.322 \log_{10}(31) \approx 1 + 3.322 \times 1.491 \approx 1 + 4.956 \approx 5.956$ We can choose 5 or 6 classes. Let's choose 5 classes for a clear distribution. The class width ($w$) is calculated as $\frac{Range}{Number of classes}$. $w = \frac{24}{5} = 4.8$ We round up to 5 to ensure all data points are covered and to have convenient integer class limits.

The class intervals will be: 0-4 5-9 10-14 15-19 20-24

Step 2: Prepare the grouped frequency distribution table. For each class interval, we count the frequency ($f$) of scores falling within it and calculate the midpoint ($x$). The midpoint is the average of the lower and upper class limits. Then, we calculate the product $f \cdot x$.

| Class Interval | Tally | Frequency ($f$) | Midpoint ($x$) | $f \cdot x$ | | :------------- | :---------------------------------- | :-------------- | :------------- | :---------- | | 0-4 | 0, 4 | 2 | 2 | 4 | | 5-9 | 5, 6, 7, 8, 9, 9 | 6 | 7 | 42 | | 10-14 | 10, 10, 10, 11, 12, 12, 12, 13, 13, 14, 14 | 11 | 12 | 132 | | 15-19 | 15, 15, 16, 16, 17, 18, 19, 19 | 8 | 17 | 136 | | 20-24 | 20, 23, 24, 24 | 4 | 22 | 88 | | Total | | 31 | | 402 |

Step 3: Compute the mean from the grouped frequency distribution table. The formula for the mean ($\bar{x}$) of grouped data is: $\bar{x} = \frac{\sum (f \cdot x)}{\sum f}$ From the table, we have: $\sum (f \cdot x) = 402$ $\sum f = 31$

Substitute these values into the formula: $\bar{x} = \frac{402}{31}$ $\bar{x} \approx 12.9677419$ Rounding to two decimal places: $\bar{x} \approx 12.97$

The grouped frequency distribution table is shown above. The computed mean is $\boxed{*12.97*}$.