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 Find the interquartile range of this dataset

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.

Find the interquartile range of this 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

Learn how to find the interquartile range (IQR) of 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. This guide covers key statistical concepts, including quartiles, interpolation, and IQR calculations, making it ideal for students in Grades 9-12.

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