https://file.aiquickdraw.com/mathbot/file/172904639195804fq8wqg.jpg

To calculate the boundaries for detecting outliers, we use the Interquartile Range (IQR). The IQR is calculated as:

\[
IQR = Q3 - Q1
\]

From the five-number summary in the image:
- \( Q1 = 29 \)
- \( Q3 = 41 \)

So, the IQR is:

\[
IQR = 41 - 29 = 12
\]

The boundaries for outliers are determined as follows:

- **Lower Bound (for low outliers):**  
\[
Q1 - 1.5 \times IQR = 29 - 1.5 \times 12 = 29 - 18 = 11
\]

- **Upper Bound (for high outliers):**  
\[
Q3 + 1.5 \times IQR = 41 + 1.5 \times 12 = 41 + 18 = 59
\]

### Conclusion:
- **Low Outliers** are any values less than **11**.
- **High Outliers** are any values greater than **59**.

Since the minimum value is 14 and the maximum is 53, no data points fall below 11 or above 59. Therefore, **no outliers exist** in this dataset.

---

Do you need more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you calculate the IQR if given different data?
2. What other methods can be used to detect outliers in a dataset?
3. Why is the factor 1.5 used to determine outliers?
4. What does the distribution of birth rates suggest about the population growth in these nations?
5. How would the outlier analysis change if the dataset had extreme values?

**Tip:** IQR is a robust measure of spread and is less sensitive to outliers than other measures like standard deviation.

Are there any outliers in the distribution of birthrates? Calculate the upper and lower boundaries.

Determine the upper and lower boundaries for outliers in a dataset of birthrates using the Interquartile Range (IQR). Learn how to apply statistical formulas to detect outliers. This problem covers important statistical concepts suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation