What is the interquartile range for the data set? 4, 7, 7, 3, 5, 2, 6, 7, 9

Answer: 4

Explanation: The interquartile range (IQR) is calculated by finding the difference between the first quartile (Q1) and the third quartile (Q3) of a data set.

Steps:

1. Arrange the data in ascending order: 2, 3, 4, 5, 6, 7, 7, 7, 9.
2. Determine the median (Q2): The median is the middle value, which is 6.
3. Find Q1 (the median of the first half): The first half is 2, 3, 4, 5. The median of this set is \( \frac{3 + 4}{2} = 3.5 \).
4. Find Q3 (the median of the second half): The second half is 7, 7, 7, 9. The median of this set is \( \frac{7 + 7}{2} = 7 \).
5. Calculate the IQR: \( IQR = Q3 - Q1 = 7 - 3.5 = 3.5 \).

Thus, the interquartile range is 3.5.