Sixth grade $$ \quad 31.7 $$ Calculate quartiles and interquartile range MNV In the data set below, what is the interquartile range? $$ \begin{array}{lllllll}3 & 1 & 8 & 9 & 6 & 1\end{array} $$ Submit

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To find the **interquartile range (IQR)** of the given data set, follow these steps:

### **Step 1: Organize the Data in Ascending Order**
Start by arranging the numbers from smallest to largest.

Original data: 3, 1, 8, 9, 6, 1

Sorted data: **1, 1, 3, 6, 8, 9**

### **Step 2: Determine the Quartiles**

- **Number of Data Points (n):** 6

Since the number of data points is even, we'll split the data into two halves:
- **Lower Half:** 1, 1, 3
- **Upper Half:** 6, 8, 9

**First Quartile (Q₁):** This is the median of the lower half.
- For the lower half (1, 1, 3), the median is **1**.

**Third Quartile (Q₃):** This is the median of the upper half.
- For the upper half (6, 8, 9), the median is **8**.

### **Step 3: Calculate the Interquartile Range (IQR)**
$$ \text{IQR} = Q₃ - Q₁ $$
$$ \text{IQR} = 8 - 1 = 7 $$

### **Conclusion**
The **interquartile range** of the data set is **7**.
The interquartile range is 7.

Sixth grade \( \quad 31.7 \) Calculate quartiles and interquartile range MNV In the data set below, what is the interquartile range? \( \begin{array}{lllllll}3 & 1 & 8 & 9 & 6 & 1\end{array} \) Submit

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