The highway mìleage (mpg) for a sample of 8 different models of a car company can be found below. 18, 20, 23, 26, 35, 29, 33, 35 Find the 5-number summary, check for any outliers using fences, and create a boxplot.
The highway mìleage (mpg) for a sample of 8 different models of a car company can be found below. 18, 20, 23, 26, 35, 29, 33, 35 Find the 5-number summary, check for any outliers using fences, and create a boxplot.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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![**Problem: Analyzing Highway Mileage of Car Models**
---
The highway mileage (mpg) for a sample of 8 different models of a car company can be found below.
18, 20, 23, 26, 35, 29, 33, 35
**Tasks:**
1. **Find the 5-number summary.**
2. **Check for any outliers using fences.**
3. **Create a boxplot.**
---
### 5-Number Summary
1. **Minimum (Min):** The smallest value in the dataset.
2. **First Quartile (Q1):** The median of the lower half of the dataset.
3. **Median (Q2):** The middle value of the dataset.
4. **Third Quartile (Q3):** The median of the upper half of the dataset.
5. **Maximum (Max):** The largest value in the dataset.
**Given Data**: 18, 20, 23, 26, 29, 33, 35, 35
---
### Steps for Finding the 5-Number Summary:
1. **Order the Data:**
18, 20, 23, 26, 29, 33, 35, 35
2. **Minimum (Min):** 18
3. **Median (Q2):**
- Number of data points, \( n = 8 \) (even number).
- Median is the average of the 4th and 5th data points.
- Median (Q2) = \( \frac{26+29}{2} = 27.5 \)
4. **First Quartile (Q1):**
- The median of the lower half (first 4 numbers): 18, 20, 23, 26
- Q1 = Median of the lower half = \( \frac{20+23}{2} = 21.5 \)
5. **Third Quartile (Q3):**
- The median of the upper half (last 4 numbers): 29, 33, 35, 35
- Q3 = Median of the upper half = \( \frac{33+35}{2} = 34 \)
6. **Maximum (Max):** 35
**5-Number Summary:**
- Minimum:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F151810f2-60bf-4788-a032-c5382383fa7c%2Fe44172a1-bc12-4de7-83b1-aa378c4b110e%2Fnzu453_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Analyzing Highway Mileage of Car Models**
---
The highway mileage (mpg) for a sample of 8 different models of a car company can be found below.
18, 20, 23, 26, 35, 29, 33, 35
**Tasks:**
1. **Find the 5-number summary.**
2. **Check for any outliers using fences.**
3. **Create a boxplot.**
---
### 5-Number Summary
1. **Minimum (Min):** The smallest value in the dataset.
2. **First Quartile (Q1):** The median of the lower half of the dataset.
3. **Median (Q2):** The middle value of the dataset.
4. **Third Quartile (Q3):** The median of the upper half of the dataset.
5. **Maximum (Max):** The largest value in the dataset.
**Given Data**: 18, 20, 23, 26, 29, 33, 35, 35
---
### Steps for Finding the 5-Number Summary:
1. **Order the Data:**
18, 20, 23, 26, 29, 33, 35, 35
2. **Minimum (Min):** 18
3. **Median (Q2):**
- Number of data points, \( n = 8 \) (even number).
- Median is the average of the 4th and 5th data points.
- Median (Q2) = \( \frac{26+29}{2} = 27.5 \)
4. **First Quartile (Q1):**
- The median of the lower half (first 4 numbers): 18, 20, 23, 26
- Q1 = Median of the lower half = \( \frac{20+23}{2} = 21.5 \)
5. **Third Quartile (Q3):**
- The median of the upper half (last 4 numbers): 29, 33, 35, 35
- Q3 = Median of the upper half = \( \frac{33+35}{2} = 34 \)
6. **Maximum (Max):** 35
**5-Number Summary:**
- Minimum:
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