10.0	90.6	48.5	50.4	57.4	99.6	0.0	5.0	0.0	0.0
5.0	2.0	10.5	5.0	47.0	0.0	5.0	54.0	0.0	48.6 fine interquartile range

To calculate the **interquartile range (IQR)**, we need to follow these steps:

1. **Sort the data** in ascending order.
2. **Find the first quartile (Q1)**, which is the median of the lower half of the data.
3. **Find the third quartile (Q3)**, which is the median of the upper half of the data.
4. **Calculate the IQR** using the formula:
   \[
   IQR = Q3 - Q1
   \]

### Step 1: Sort the data
Here is the sorted version of your dataTo calculate the **interquartile range (IQR)**, we need to follow these steps:

1. **Sort the data** in ascending order.
2. **Find the first quartile (Q1)**, which is the median of the lower half of the data.
3. **Find the third quartile (Q3)**, which is the median of the upper half of the data.
4. **Calculate the IQR** using the formula:
   \[
   IQR = Q3 - Q1
   \]

### Step 1: Sort the data
Here is the sorted version of your 
\[ 0.0, 0.0, 0.0, 0.0, 2.0, 5.0, 5.0, 5.0, 5.0, 10.0, 10.5, 47.0, 48.5, 48.6, 50.4, 54.0, 57.4, 90.6, 99.6 \]

### Step 2: Find the First Quartile (Q1)
- The lower half of the dataTo calculate the **interquartile range (IQR)**, we need to follow these steps:

1. **Sort the data** in ascending order.
2. **Find the first quartile (Q1)**, which is the median of the lower half of the data.
3. **Find the third quartile (Q3)**, which is the median of the upper half of the data.
4. **Calculate the IQR** using the formula:
   \[
   IQR = Q3 - Q1
   \]

### Step 1: Sort the data
Here is the sorted version of your 
\[ 0.0, 0.0, 0.0, 0.0, 2.0, 5.0, 5.0, 5.0, 5.0, 10.0, 10.5, 47.0, 48.5, 48.6, 50.4, 54.0, 57.4, 90.6, 99.6 \]

### Step 2: Find the First Quartile (Q1)
- The lower half of the  
  \[ 0.0, 0.0, 0.0, 0.0, 2.0, 5.0, 5.0, 5.0, 5.0 \]
- Q1 is the median of this set. Since there are 9 data points, Q1 is the 5th value:
  \[
  Q1 = 2.0
  \]

### Step 3: Find the Third Quartile (Q3)
- The upper half of the dataTo calculate the **interquartile range (IQR)**, we need to follow these steps:

1. **Sort the data** in ascending order.
2. **Find the first quartile (Q1)**, which is the median of the lower half of the data.
3. **Find the third quartile (Q3)**, which is the median of the upper half of the data.
4. **Calculate the IQR** using the formula:
   \[
   IQR = Q3 - Q1
   \]

### Step 1: Sort the data
Here is the sorted version of your 
\[ 0.0, 0.0, 0.0, 0.0, 2.0, 5.0, 5.0, 5.0, 5.0, 10.0, 10.5, 47.0, 48.5, 48.6, 50.4, 54.0, 57.4, 90.6, 99.6 \]

### Step 2: Find the First Quartile (Q1)
- The lower half of the  
  \[ 0.0, 0.0, 0.0, 0.0, 2.0, 5.0, 5.0, 5.0, 5.0 \]
- Q1 is the median of this set. Since there are 9 data points, Q1 is the 5th value:
  \[
  Q1 = 2.0
  \]

### Step 3: Find the Third Quartile (Q3)
- The upper half of the  
  \[ 10.0, 10.5, 47.0, 48.5, 48.6, 50.4, 54.0, 57.4, 90.6, 99.6 \]
- Q3 is the median of this set. The middle value is the 5th number:
  \[
  Q3 = 48.6
  \]

### Step 4: Calculate the Interquartile Range (IQR)
\[
IQR = Q3 - Q1 = 48.6 - 2.0 = 46.6
\]

So, the **Interquartile Range (IQR)** is **46.6**.

Would you like more details or have any questions?

---

### Follow-up Questions:
1. How is the interquartile range useful in statistical analysis?
2. What is the difference between IQR and standard deviation?
3. Can outliers affect the interquartile range calculation?
4. How can you visually represent IQR in a dataset?
5. What is the purpose of quartiles in data distribution?

**Tip:** The interquartile range is often used to identify outliers in data, as values falling 1.5 times above or below the IQR are considered outliers.

10.0 90.6 48.5 50.4 57.4 99.6 0.0 5.0 0.0 0.0 5.0 2.0 10.5 5.0 47.0 0.0 5.0 54.0 0.0 48.6 fine interquartile range

Learn how to calculate the interquartile range (IQR) for a dataset that includes values such as 10.0, 90.6, 48.5, and more. This problem teaches key statistical concepts like quartiles and IQR, using the formula IQR = Q3 - Q1. Suitable for students in Grades 8-10.

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