To find the interquartile range (IQR) of a dataset, we follow these steps:

1. Arrange the data in ascending order: This step is already done for the dataset: $0.0, 0.0, 0.0, 0.0, 2.0, 5.0, 5.0, 5.0, 5.0, 10.0, 10.5, 48.5, 48.6, 50.4, 54.0, 57.4, 90.6, 99.6$

2. Identify Q1 and Q3:

   • Q1 (first quartile) is the value at the 25th percentile.
   • Q3 (third quartile) is the value at the 75th percentile.

3. Find the positions of Q1 and Q3:

   • The dataset has 18 values, so to find the positions of Q1 and Q3:
     • $Q1 = \frac{n+1}{4}$, where $n = 18$. Thus, $Q1$ is at the $\frac{18+1}{4} = 4.75$th position.
     • $Q3 = \frac{3(n+1)}{4}$, so $Q3$ is at the $\frac{3(18+1)}{4} = 14.25$th position.

4. Interpolate Q1 and Q3:

   • For Q1 (4.75th position), interpolate between the 4th and 5th values:

     • 4th value: 0.0
     • 5th value: 2.0
     • Interpolation: $0.0 + 0.75 \times (2.0 - 0.0) = 1.5$

   • For Q3 (14.25th position), interpolate between the 14th and 15th values:

     • 14th value: 50.4
     • 15th value: 54.0
     • Interpolation: $50.4 + 0.25 \times (54.0 - 50.4) = 51.3$

5. Calculate the IQR:

   • $IQR = Q3 - Q1 = 51.3 - 1.5 = 49.8$

Thus, the interquartile range (IQR) is 49.8.

Would you like more details or have any questions?

Here are some related questions:

1. How do you find the median of a dataset?
2. What is the difference between range and interquartile range?
3. How do you deal with outliers in a dataset using IQR?
4. How do quartiles relate to the box plot representation of data?
5. What are the advantages of using the interquartile range over standard deviation?

Tip: The interquartile range is useful for identifying outliers because it focuses on the middle 50% of the data, ignoring extreme values.