Answer: arithmetic mean is greater than the median.

## Explanation Let's calculate the three measures of central tendency: **Data:** 8, 13, 3, 12, 8, 10 **1. Arithmetic Mean:** Sum = 8 + 13 + 3 + 12 + 8 + 10 = 54 Number of observations = 6 Mean = 54 ÷ 6 = 9 **2. Median:** First, arrange data in ascending order: 3, 8, 8, 10, 12, 13 Since there are 6 observations (even number), median is the average of the 3rd and 4th values: Median = (8 + 10) ÷ 2 = 18 ÷ 2 = 9 **3. Mode:** The value that appears most frequently: 8 (appears twice) **Comparison:** - Mean = 9 - Median = 9 - Mode = 8 **Analysis of options:** A. **median is greater than the mode** → 9 > 8 ✓ True B. **mode is greater than the arithmetic mean** → 8 > 9 ✗ False C. **arithmetic mean is greater than the median** → 9 > 9 ✗ False Wait, this reveals an issue. Let me recalculate carefully: **Recalculation:** Data: 3, 8, 8, 10, 12, 13 Mean = (3+8+8+10+12+13)/6 = 54/6 = 9 Median = (8+10)/2 = 9 Mode = 8 Actually, looking at the options: A. median (9) > mode (8) → TRUE B. mode (8) > mean (9) → FALSE C. mean (9) > median (9) → FALSE (they are equal) But the question asks for which statement is correct. Only option A is true. However, I need to check if there might be a trick. Let me recalculate the mean one more time: 3 + 8 = 11 11 + 8 = 19 19 + 10 = 29 29 + 12 = 41 41 + 13 = 54 54 ÷ 6 = 9 Yes, mean = 9, median = 9, mode = 8 So the correct answer should be A. But wait, the question format suggests only one correct answer among A, B, C. Let me check if I'm missing something. Actually, looking at the data again: 8, 13, 3, 12, 8, 10 Sorted: 3, 8, 8, 10, 12, 13 Maybe the question expects us to recognize that: - Mean = 9 - Median = 9 - Mode = 8 So: A. median (9) > mode (8) → TRUE B. mode (8) > mean (9) → FALSE C. mean (9) > median (9) → FALSE Therefore, the correct answer is **A**. **Final Answer: A**

Author: LeetQuiz .