What is the median value of the data set: 1, 2, 4, 4, 5, 7, 8, 9, 9, 9, 10, 11, 12?

To find the median of a data set, you first need to arrange the numbers in order from smallest to largest, which is already done in this case: 1, 2, 4, 4, 5, 7, 8, 9, 9, 9, 10, 11, 12.

Next, determine the number of values in the data set. Here, there are 13 values. Since the count is odd, the median will be the middle number. The median is positioned at the ( \frac{n+1}{2} )th position, where ( n ) is the total number of values.

Calculating this gives ( \frac{13 + 1}{2} = 7 ). Thus, the median is the 7th value in the ordered list. Counting through the ordered set, we find that the 7th value is 8. Therefore, the median of this data set is 8.

This makes the choice of 8 the correct answer for the median of the given data set.