A dataset consists of . If 9 is replaced by 3, which of the following statements is true?
- The mean decreases, and the median increases.
- The mean increases, and the median stays the same.
- The mean decreases, and the median stays the same. (correct answer)
- The mean stays the same because the mode is unchanged.
- The mean decreases, and the median decreases.
Explanation: This question tests descriptive statistics by examining mean and median after replacing a value. Mean sensitive to changes, median to order; original {1,2,2,2,9} sum=16, mean=3.2, median 2. Replace 9 with 3: {1,2,2,2,3} sum=10, mean=2 (decreases), median 2 (same). Mean decreases, median stays same, as replacement lowers sum but middle unchanged. A tempting option is thinking median increases to 2.5 or something, but sorted it's 1,2,2,2,3, middle 2. Confusion with mode might suggest mean same, like D.