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 _10(n). k = 1 + 3.322 _10(31) ≈ 1 + 3.322 × 1.491 ≈ 1 + 4.956 ≈ 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 RangeNumber of classes. w = (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 · x. | Class Interval | Tally | Frequency (f) | Midpoint (x) | f · 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 (x) of grouped data is: x = ( (f · x))/( f) From the table, we have: (f · x) = 402 f = 31 Substitute these values into the formula: x = (402)/(31) x ≈ 12.9677419 Rounding to two decimal places: x ≈ 12.97 The grouped frequency distribution table is shown above. The computed mean is 12.97.