Find the interquartile range for the following set of data: 7, 0, 5, 1, 6, 8, 12, 6, 3, 15, 11 and 4.

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:

$$0, 1, 3, 4, 5, 6, 6, 7, 8, 11, 12, 15$$

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.

$$Q_2 = \frac{6+6}{2} = \frac{12}{2} = 6$$

$Q_1$ 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.

$$Q_1 = \frac{3+4}{2} = \frac{7}{2} = 3.5$$

$Q_3$ 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.

$$Q_3 = \frac{8+11}{2} = \frac{19}{2} = 9.5$$

The interquartile range is the difference between the third quartile and the first quartile.

$$IQR = Q_3 - Q_1$$ $$IQR = 9.5 - 3.5$$ $$IQR = 6$$