Final answer:
The interquartile range (IQR) is 4 for the given data set when arranged in ascending order and calculated as the difference between the median of the upper and lower halves of the data (Q3 - Q1).
Step-by-step explanation:
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a data set. In the provided data set (4,7,7,3,5,2,6,7,9), we must first arrange the numbers in ascending order: 2, 3, 4, 5, 6, 7, 7, 7, 9. The median (Q2) of this data set is 6. The lower half of the data set is 2, 3, 4, 5, and the median (Q1) is 3. The upper half is 7, 7, 7, 9, and the median (Q3) is 7. The IQR is then 7 minus 3, which is 4.
The IQR is important because it shows the range within which the central 50 percent of the data falls and is less affected by outliers than the range. An outlier in this context is a data point that is significantly higher or lower than most of the other data points. Therefore, the IQR is valuable for understanding the variability of a data set.