Given the data set: $4$, $7$, $7$, $10$, $12$, what is the median of the data?

• A. $8.5$
• B. $10$
• C. $8$
• D. $7$

Answer: (D)

Verified step by step guidance

1. Step 1: Arrange the data set in ascending order. The data given is 4, 7, 7, 10, 12, which is already sorted.
2. Step 2: Determine the number of data points, denoted as \(n\). Here, \(n = 5\).
3. Step 3: Since \(n\) is odd, the median is the middle value in the ordered data set. The position of the median is given by \(\frac{n + 1}{2}\).
4. Step 4: Calculate the median position: \(\frac{5 + 1}{2} = 3\). This means the median is the 3rd value in the ordered list.
5. Step 5: Identify the 3rd value in the data set, which is 7. Therefore, the median of the data set is 7.