The given data set is: 3, 4, 2, 7, 9, 4, 5, 7, 4, 6. To find the median, we need to arrange the data in ascending order: 2, 3, 4, 4, 4, 5, 6, 7, 7, 9. Since the data set has an even number of values, the median is the average of the middle two values, which are 4 and 5. Adding them and dividing by 2 gives us 4.5. Therefore, the median of the given data set is 4.5.