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.

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**Problem: Analyzing Highway Mileage of Car Models**

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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

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### 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:
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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