To calculate the interquartile range (IQR) of the given data, we follow these steps:

1. Arrange the data in ascending order:

$4, 7, 25, 25, 26, 27, 28, 32, 41, 45, 45, 49, 49, 49, 52$

2. Find the median (Q2), which divides the data into two equal halves:

Since there are 15 data points, the median is the 8th number in the ordered list: $\text{Median (Q2)} = 32$

3. Find the lower quartile (Q1), which is the median of the lower half of the data (values before 32):

The lower half is: $4, 7, 25, 25, 26, 27, 28$. Since there are 7 values, the median is the 4th number: $\text{Q1} = 25$

4. Find the upper quartile (Q3), which is the median of the upper half of the data (values after 32):

The upper half is: $41, 45, 45, 49, 49, 49, 52$. Again, there are 7 values, so the median is the 4th number: $\text{Q3} = 49$

5. Calculate the Interquartile Range (IQR):

$\text{IQR} = Q3 - Q1 = 49 - 25 = 24$

Thus, the Interquartile Range (IQR) of the data is 24.

---

Would you like further details or any clarifications? Here are some related questions you might find interesting:

1. How do outliers affect the IQR calculation?
2. What other measures of dispersion, like the range and standard deviation, can be calculated from the data?
3. How can you calculate the IQR for a large dataset?
4. What is the significance of the median and quartiles in data analysis?
5. How do you interpret the IQR in the context of a boxplot?

Tip: The IQR is useful for identifying outliers. Any data points that lie more than 1.5 times the IQR above Q3 or below Q1 are considered potential outliers.