https://file.aiquickdraw.com/mathbot/file/1729323430037x6o7jnvu.jpg

The image shows a statistics problem involving the **five-number summary** of a dataset. Let’s walk through the steps needed to determine the outlier bounds.

### Five-number summary:
- **Minimum (Q0)**: 46  
- **First Quartile (Q1)**: 56  
- **Median (Q2)**: 61  
- **Third Quartile (Q3)**: 67  
- **Maximum (Q4)**: 70  

### Step 1: Interquartile Range (IQR)  
The IQR measures the spread of the middle 50% of the dataThe image shows a statistics problem involving the **five-number summary** of a dataset. Let’s walk through the steps needed to determine the outlier bounds.

### Five-number summary:
- **Minimum (Q0)**: 46  
- **First Quartile (Q1)**: 56  
- **Median (Q2)**: 61  
- **Third Quartile (Q3)**: 67  
- **Maximum (Q4)**: 70  

### Step 1: Interquartile Range (IQR)  
The IQR measures the spread of the middle 50% of the   
\[
\text{IQR} = Q3 - Q1 = 67 - 56 = 11
\]

### Step 2: Outlier Boundaries  
- **Lower Bound**:  
\[
\text{Lower Bound} = Q1 - 1.5 \times \text{IQR} = 56 - 1.5 \times 11 = 56 - 16.5 = 39.5
\]
Any value below 39.5 will be considered a **lower outlier**.

- **Upper Bound**:  
\[
\text{Upper Bound} = Q3 + 1.5 \times \text{IQR} = 67 + 1.5 \times 11 = 67 + 16.5 = 83.5
\]
Any value above 83.5 will be considered an **upper outlier**.

### Answers:
- An observation is considered an outlier if it is **below**: **39.5**  
- An observation is considered an outlier if it is **above**: **83.5**

Would you like further clarification or more examples?

---

**5 Related Questions:**
1. What is the purpose of the IQR in detecting outliers?
2. How is the five-number summary used to describe the spread of data?
3. What happens if a dataset contains no outliers?
4. How do we adjust if extreme outliers are detected beyond 3 IQRs?
5. Can box plots visually represent outliers?

**Tip:** For large datasets, plotting the data using a **box plot** can provide a quick visualization of outliers and the five-number summary.

The five-number summary of a dataset was found to be: 46, 56, 61, 67, 70. An observation is considered an outlier if it is below or above certain values.

Learn how to detect outliers using the five-number summary of a dataset. This example includes key statistics concepts such as Interquartile Range (IQR) and how to apply the IQR rule to identify data points that fall outside the lower and upper bounds.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation