Step 1: Order the data from least to greatest. The given data set is $7, 0, 5, 1, 6, 8, 12, 6, 3, 15, 11, 4$. There are $n=12$ data points. Ordered data: $$0, 1, 3, 4, 5, 6, 6, 7, 8, 11, 12, 15$$ Step 2: Find the median ($Q_2$). Since there are 12 data points (an even number), the median is the average of the two middle values, which are the 6th and 7th values. The 6th value is $6$. The 7th value is $6$. $$Q_2 = \frac{6+6}{2} = \frac{12}{2} = 6$$ Step 3: Find the first quartile ($Q_1$). $Q_1$ is the median of the lower half of the data. The lower half consists of the first $n/2 = 12/2 = 6$ data points. Lower half: $0, 1, 3, 4, 5, 6$. The median of these 6 values is the average of the 3rd and 4th values. The 3rd value is $3$. The 4th value is $4$. $$Q_1 = \frac{3+4}{2} = \frac{7}{2} = 3.5$$ Step 4: Find the third quartile ($Q_3$). $Q_3$ is the median of the upper half of the data. The upper half consists of the last $n/2 = 12/2 = 6$ data points. Upper half: $6, 7, 8, 11, 12, 15$. The median of these 6 values is the average of the 3rd and 4th values. The 3rd value is $8$. The 4th value is $11$. $$Q_3 = \frac{8+11}{2} = \frac{19}{2} = 9.5$$ Step 5: Calculate the Interquartile Range (IQR). The interquartile range is the difference between the third quartile and the first quartile. $$IQR = Q_3 - Q_1$$ $$IQR = 9.5 - 3.5$$ $$IQR = 6$$ The interquartile range is $\boxed{\text{6}}$.