求以下数据集的中位数：
7， 3， 9， 5， 11

Question

BlackTom AI · Accepted Answer

The median is the middle value of an ordered dataset. For an odd number of observations (n), the median is the value at position (n+1)/2 in the sorted list.

Relevant concepts:
- Median: middle value when data are sorted.
- For odd n, index = (n + 1) / 2.
- Sorting the data is required before selecting the middle value.

Step-by-step reasoning and calculations:
1. Count the data points. There are 5 numbers: 7, 3, 9, 5, 11. So n = 5 (odd).
2. Compute the median index: (n + 1) / 2 = (5 + 1) / 2 = 6 / 2 = 3. The median will be the 3rd value after sorting.
3. Sort the data in ascending order: 3, 5, 7, 9, 11.
4. Identify the 3rd (middle) value in the sorted list: the 1st is 3, 2nd is 5, 3rd is 7, 4th is 9, 5th is 11. Thus the median = 7.

Intermediate calculations shown:
- Sum for reference: 7 + 3 + 9 + 5 + 11 = 35; mean = 35 / 5 = 7. (Here mean equals median by coincidence, but median is obtained by ordering and picking the middle.)
- Median index: (5 + 1) / 2 = 3 → pick 3rd element of sorted list.

Why the correct answer is correct:
- Because with five ordered values, the median is the third entry, which is 7.

Why other possible choices would be incorrect:
- 3 and 11 are extremes (minimum and maximum), not the middle.
- 5 and 9 are adjacent to the middle but are the 2nd and 4th values, not the 3rd.
- Any average of two values is only used for even n, not applicable here.

Conclusion: The median of the dataset 7, 3, 9, 5, 11 is 7, which matches the provided answer.

求以下数据集的中位数： 7， 3， 9， 5， 11单项选择题

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