https://file.aiquickdraw.com/mathbot/file/1727758699366dbjm7r1u.jpg

To find the outliers from this dataset, we will apply the **Interquartile Range (IQR)** method. Outliers are typically defined as data points that are below \( Q1 - 1.5 \times IQR \) or above \( Q3 + 1.5 \times IQR \), where:

- \( Q1 \) is the first quartile (25th percentile),
- \( Q3 \) is the third quartile (75th percentile),
- \( IQR = Q3 - Q1 \).

### Steps for Outlier Detection:
1. **Compute IQR** for each country.
2. **Calculate lower and upper bounds** for detecting outliers:
   - Lower bound: \( Q1 - 1.5 \times IQR \)
   - Upper bound: \( Q3 + 1.5 \times IQR \)
3. **Check for any values outside these bounds** (either lower than the lower bound or higher than the upper bound).

### For Canada:
- \( Q1 = 32.4 \), \( Q3 = 33.2 \)
- \( IQR = 33.2 - 32.4 = 0.8 \)
- Lower bound: \( 32.4 - 1.5 \times 0.8 = 31.2 \)
- Upper bound: \( 33.2 + 1.5 \times 0.8 = 34.4 \)

Any values below 31.2 or above 34.4 would be considered outliers. The **minimum value** for Canada is 30.9, which is below the lower bound of 31.2, indicating an **outlier**.

### For the United States:
- \( Q1 = 36.4 \), \( Q3 = 36.9 \)
- \( IQR = 36.9 - 36.4 = 0.5 \)
- Lower bound: \( 36.4 - 1.5 \times 0.5 = 35.65 \)
- Upper bound: \( 36.9 + 1.5 \times 0.5 = 37.65 \)

Since the **minimum value** for the United States is 35.7, and it is slightly higher than the lower bound of 35.65, there are **no outliers** in the United States dataset.

### Summary of Outliers:
- **Canada**: 30.9 (outlier)
- **United States**: No outliers

Would you like further details or have any questions?

### Further Questions:
1. How is the IQR method different from other outlier detection methods?
2. Why is 1.5 used as a multiplier in the IQR method?
3. Can boxplots visually help in identifying outliers from a dataset?
4. How would results change if the dataset's standard deviation were higher?
5. What are some other contexts where outliers might be relevant?

**Tip:** When detecting outliers, always visualize the data with boxplots or histograms to get a clearer view of its distribution.

Learn how to detect outliers in the dataset from Canada and the United States using the Interquartile Range (IQR) method. This solution includes step-by-step calculations, explaining the concepts of quartiles and how the IQR method is applied to find outliers, specifically identifying one outlier in Canada. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation