1. **Problem Statement:** Given the data of student scores: 68, 84, 75, 82, 68, 90, 62, 88, 76, 93, 73, 79, 88, 73, 60, 93, 71, 59, 85, 75, 61, 65, 75, 87, 74, 62, 95, 78, 63, 72, 66, 78, 82, 75, 94, 77, 69, 74, 68, 60, 96, 78, 89, 61, 75, 95, 60, 79, 83, 71, 79, 62, 67, 97, 78, 85, 76, 65, 71, 75, 65, 80, 73, 57, 88, 78, 62, 76, 53, 74, 86, 67, 73, 81, 72, 63, 76, 75, 85, 77 We need to find: a. Frequency distribution table b. Mean c. Median d. Mode 2. **Frequency Distribution Table:** - Count the occurrences of each unique score. - For example, score 75 appears multiple times. 3. **Mean Formula:** $$\text{Mean} = \frac{\sum \text{all scores}}{\text{number of scores}}$$ 4. **Median:** - Sort the data in ascending order. - If number of data points $n$ is odd, median is the middle value. - If $n$ is even, median is average of two middle values. 5. **Mode:** - The score(s) that appear most frequently. --- **Step-by-step solution:** 1. Sort the data and count frequencies: | Score | Frequency | |-------|-----------| | 53 | 1 | | 57 | 1 | | 59 | 1 | | 60 | 4 | | 61 | 2 | | 62 | 5 | | 63 | 2 | | 65 | 3 | | 66 | 1 | | 67 | 2 | | 68 | 3 | | 69 | 1 | | 71 | 3 | | 72 | 2 | | 73 | 4 | | 74 | 4 | | 75 | 8 | | 76 | 4 | | 77 | 3 | | 78 | 5 | | 79 | 3 | | 80 | 1 | | 81 | 1 | | 82 | 2 | | 83 | 1 | | 84 | 1 | | 85 | 3 | | 86 | 1 | | 87 | 1 | | 88 | 3 | | 89 | 1 | | 90 | 1 | | 93 | 2 | | 94 | 1 | | 95 | 2 | | 96 | 1 | | 97 | 1 | 2. Calculate total number of scores: $$n = 80$$ 3. Calculate mean: $$\sum \text{scores} = 68+84+75+...+77 = 6103$$ $$\text{Mean} = \frac{6103}{80} = 76.29$$ 4. Find median: - Sorted data has 80 values (even). - Median is average of 40th and 41st values. - The 40th and 41st values in sorted data are both 75. - So, $$\text{Median} = \frac{75 + 75}{2} = 75$$ 5. Find mode: - The highest frequency is 8 for score 75. - So, $$\text{Mode} = 75$$ **Final answers:** a. Frequency distribution table as above. b. Mean = 76.29 c. Median = 75 d. Mode = 75