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What is the inter-quartile range for the data

To find the interquartile range (IQR) of the data, we need to calculate the first quartile (Q1) and the third quartile (Q3), and then subtract Q1 from Q3.

### Steps:

1. **Sort the Data:**
   First, arrange the numbers in ascending order.
   
   Sorted dataTo find the interquartile range (IQR) of the data, we need to calculate the first quartile (Q1) and the third quartile (Q3), and then subtract Q1 from Q3.

### Steps:

1. **Sort the Data:**
   First, arrange the numbers in ascending order.
   
   Sorted  4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33

2. **Find Q1 (First Quartile):**
   Q1 is the median of the first half of the data. 
   
   For the sorted list: 4, 9, 15, 16, 18  
   Q1 is the median of this subset, which is 15.

3. **Find Q3 (Third Quartile):**
   Q3 is the median of the second half of the data.
   
   For the sorted list: 25, 27, 30, 31, 33  
   Q3 is the median of this subset, which is 30.

4. **Calculate the IQR:**
   \[
   IQR = Q3 - Q1 = 30 - 15 = 15
   \]

### Answer:
The interquartile range (IQR) is **15**.

Would you like more details or have any questions?

Here are some related questions:
1. How do you calculate the median of a data set?
2. What is the difference between IQR and range?
3. How can outliers affect the IQR?
4. Why is the IQR a useful measure of spread?
5. How do you determine if a data point is an outlier using IQR?

**Tip:** The IQR is a great measure to identify the spread of the middle 50% of data points, reducing the effect of outliers!

Learn how to calculate the interquartile range (IQR) of a dataset step-by-step. Understand the importance of IQR in statistics and data analysis. Suitable for students and professionals interested in statistical measures.

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