https://file.aiquickdraw.com/mathbot/file/1726724696584tm4hgatv.jpg

The image provides the three quartiles for systolic blood pressure in a sample of 3164 men:

- \( Q_1 = 115 \)
- \( Q_2 = 129 \)
- \( Q_3 = 142 \)

It asks for the upper and lower outlier boundaries. To find these boundaries, we use the following formulas:

1. **Lower Outlier Boundary:**
   \[
   \text{Lower Boundary} = Q_1 - 1.5 \times IQR
   \]

2. **Upper Outlier Boundary:**
   \[
   \text{Upper Boundary} = Q_3 + 1.5 \times IQR
   \]

Where \( IQR \) (Interquartile Range) is calculated as:

\[
IQR = Q_3 - Q_1
\]

Let's calculate the values.

1. Calculate the \( IQR \):
\[
IQR = 142 - 115 = 27
\]

2. Calculate the lower and upper outlier boundaries:

\[
\text{Lower Boundary} = 115 - 1.5 \times 27 = 115 - 40.5 = 74.5
\]

\[
\text{Upper Boundary} = 142 + 1.5 \times 27 = 142 + 40.5 = 182.5
\]

The given values match the calculated ones:

- Lower Outlier Boundary = 74.5
- Upper Outlier Boundary = 182.5

These are the correct outlier boundaries for the given quartiles. 

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do you identify an outlier in a data set?
2. What is the significance of using 1.5 in the outlier formula?
3. How do quartiles help in understanding the spread of data?
4. What are the implications of outliers in medical statistics?
5. Can the interquartile range (IQR) be used in other types of data analysis?

**Tip:** Outliers can significantly affect statistical analyses and may indicate special cases, data errors, or variability in measurements.

The three quartiles for systolic blood pressure in a sample of 3164 men were Q1 = 115, Q2 = 129, and Q3 = 142. Find the upper and lower outlier boundaries.

Learn how to find the upper and lower outlier boundaries for systolic blood pressure data in a sample of 3164 men, using quartiles and interquartile range (IQR). This step-by-step guide covers key statistical concepts, suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation