What is the interquartile range for this data set? 

5, 7, 5, 1, 1, 9, 4, 5, 3, 4, 6 
 

To determine the interquartile range (IQR) for the data set:

### 1. **Organize the data in ascending order:**

1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9

### 2. **Determine the quartiles:**
   - The **first quartile (Q1)** is the median of the lower half of the data (not including the median itself if the number of data points is odd).
   - The **third quartile (Q3)** is the median of the upper half of the data.

- **Median (Q2)** of the entire data set:  
  Since there are 11 data points, the median is the 6th value, which is **5**.

- Lower half: 1, 1, 3, 4, 4  
  Q1 = 3 (the median of the lower half)

- Upper half: 5, 5, 6, 7, 9  
  Q3 = 6 (the median of the upper half)

### 3. **Calculate the IQR:**

IQR = Q3 - Q1  
IQR = 6 - 3 = 3

**The IQR of the data set is 3.**

Do you want more details or have any questions?

Here are 5 related questions you might find useful:
1. How does the IQR help in detecting outliers?
2. What is the significance of the median in calculating the IQR?
3. How would you find quartiles for a data set with an even number of points?
4. Can the IQR ever be negative? Why or why not?
5. How does skewness in the data affect the IQR?

**Tip:** The IQR represents the range within which the middle 50% of the data points lie, making it a valuable measure of central spread.

Learn how to calculate the interquartile range (IQR) for a given data set step-by-step. Understand the significance of quartiles and how they are used to measure the spread of data. Suitable for students and individuals interested in statistics and data analysis.

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