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The problem asks for the smallest possible value of \( n \) (the number of patients randomized in the first month) such that the median enrollment for the first five months is 7.

### Step-by-step approach:
1. The number of patients randomized in the first five months is \( n, 9, 7, 2, 3 \).
2. The **median** is the middle value when the data is ordered from least to greatest.
3. Currently, the data set is \( n, 9, 7, 2, 3 \). Sorting this (once \( n \) is determined) will help us determine the median.

Since there are 5 values, the median is the 3rd value in the ordered list.

4. The condition is that the median should be **7**. So, when the data is arranged in ascending order, the third value must be 7.

Let's determine the smallest possible value of \( n \) by testing different values and observing the order of the data.

### Test different values of \( n \):
- If \( n = 6 \): The data set becomes \( 6, 9, 7, 2, 3 \).
  - Sorting: \( 2, 3, 6, 7, 9 \). The median is 6, not 7.

- If \( n = 7 \): The data set becomes \( 7, 9, 7, 2, 3 \).
  - Sorting: \( 2, 3, 7, 7, 9 \). The median is 7, which satisfies the condition.

Thus, the smallest possible value of \( n \) is \( \boxed{6} \).

Would you like further explanation or have any questions?

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Here are 5 related questions for further practice:
1. What happens if the median is required to be 8 instead of 7?
2. How would the value of \( n \) change if there were 6 months of data?
3. What is the mean of the set \( n, 9, 7, 2, 3 \) for \( n = 7 \)?
4. How do you calculate the range of a data set?
5. What is the mode of the data set \( n, 9, 7, 2, 3 \) for \( n = 7 \)?

**Tip:** When dealing with medians, always sort the data set first to easily locate the middle value!

The table below shows the number of patients randomized in a clinical trial in each of the first five months of the study. If the median enrollment for the first five months was 7, what is the smallest (i.e., least) possible value for n?

Learn how to determine the smallest possible value for n in a median calculation problem involving patient enrollment in a clinical trial. The problem uses concepts from statistics, including median calculation and data sorting. Suitable for students in Grades 9-11.

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