Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 41 50 35 43 41 37 41 46 43 39 36 54 42 35 15 53 37 49 29 29 a. Find the quartiles. The first quartile, Q₁, is. The second quartile, Q₂, is. The third quartile, Q3, is (Type integers or decimals.) b. Find the interquartile range. The interquartile range (IQR) is. (Type an integer or a decimal.) c. Identify any outliers. Choose the correct choice below. OA. There exists at least one outlier in the data set at (Use a comma to separate answers as needed.) OB. There are no outliers the data set.
Use the accompanying data set to complete the following actions. a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 41 50 35 43 41 37 41 46 43 39 36 54 42 35 15 53 37 49 29 29 a. Find the quartiles. The first quartile, Q₁, is. The second quartile, Q₂, is. The third quartile, Q3, is (Type integers or decimals.) b. Find the interquartile range. The interquartile range (IQR) is. (Type an integer or a decimal.) c. Identify any outliers. Choose the correct choice below. OA. There exists at least one outlier in the data set at (Use a comma to separate answers as needed.) OB. There are no outliers the data set.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 26PFA
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![### Quartiles, Interquartile Range, and Outliers
#### Instructions:
Use the accompanying data set to complete the following actions:
a. Find the quartiles.
b. Find the interquartile range.
c. Identify any outliers.
#### Data Set:
41, 50, 35, 43, 41, 37, 41, 46, 43, 39, 36, 54, 42, 35, 15, 53, 37, 49, 29, 29
---
### Solutions:
#### a. Find the quartiles.
The first quartile, \( Q_1 \), is __.
The second quartile, \( Q_2 \), is __.
The third quartile, \( Q_3 \), is __.
*(Type integers or decimals.)*
#### b. Find the interquartile range.
The interquartile range (IQR) is __.
*(Type an integer or a decimal.)*
#### c. Identify any outliers. Choose the correct choice below.
- [ ] A. There exists at least one outlier in the data set at __. \
*(Use a comma to separate answers as needed.)*
- [ ] B. There are no outliers in the data set.
---
### Detailed Explanation:
1. Quartiles divide the data set into four equal parts.
- **First Quartile \( (Q_1) \)**: The median of the lower half of the data.
- **Second Quartile \( (Q_2) \)**: The median of the data set.
- **Third Quartile \( (Q_3) \)**: The median of the upper half of the data.
2. The **Interquartile Range (IQR)** is calculated as:
\[
IQR = Q_3 - Q_1
\]
3. **Outliers** are typically identified using the IQR method:
- Lower Bound: \( Q_1 - 1.5 \times IQR \)
- Upper Bound: \( Q_3 + 1.5 \times IQR \)
- Any data point below the Lower Bound or above the Upper Bound is considered an outlier.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febc6c9e4-20c2-4aa0-9f79-b773de998cf1%2Fe670f53c-bf2f-4b31-9ad2-98befcb7554c%2F3f64u6c_processed.png&w=3840&q=75)
Transcribed Image Text:### Quartiles, Interquartile Range, and Outliers
#### Instructions:
Use the accompanying data set to complete the following actions:
a. Find the quartiles.
b. Find the interquartile range.
c. Identify any outliers.
#### Data Set:
41, 50, 35, 43, 41, 37, 41, 46, 43, 39, 36, 54, 42, 35, 15, 53, 37, 49, 29, 29
---
### Solutions:
#### a. Find the quartiles.
The first quartile, \( Q_1 \), is __.
The second quartile, \( Q_2 \), is __.
The third quartile, \( Q_3 \), is __.
*(Type integers or decimals.)*
#### b. Find the interquartile range.
The interquartile range (IQR) is __.
*(Type an integer or a decimal.)*
#### c. Identify any outliers. Choose the correct choice below.
- [ ] A. There exists at least one outlier in the data set at __. \
*(Use a comma to separate answers as needed.)*
- [ ] B. There are no outliers in the data set.
---
### Detailed Explanation:
1. Quartiles divide the data set into four equal parts.
- **First Quartile \( (Q_1) \)**: The median of the lower half of the data.
- **Second Quartile \( (Q_2) \)**: The median of the data set.
- **Third Quartile \( (Q_3) \)**: The median of the upper half of the data.
2. The **Interquartile Range (IQR)** is calculated as:
\[
IQR = Q_3 - Q_1
\]
3. **Outliers** are typically identified using the IQR method:
- Lower Bound: \( Q_1 - 1.5 \times IQR \)
- Upper Bound: \( Q_3 + 1.5 \times IQR \)
- Any data point below the Lower Bound or above the Upper Bound is considered an outlier.
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