https://file.aiquickdraw.com/mathbot/file/1729890815560fie6g070.jpg

To address the problem, let's proceed step by step:

### Step 1: Organize Data for Stem-and-Leaf Display
The first task is to create a stem-and-leaf display using the given octane ratings. I will first organize the data numerically.

### Step 2: Calculate the Median and Quartiles
I will also calculate the median (Q2), the first quartile (Q1), and the third quartile (Q3) for these data.

Let's start by listing out the numerical data for a proper analysis.

The data provided are:
```
88.5, 98.8, 89.6, 92.2, 92.7, 91.8, 91.0, 91.0, 
94.7, 88.3, 90.4, 83.4, 87.9, 88.4, 87.5, 90.9, 
84.3, 90.4, 91.6, 91.0, 93.0, 92.6, 87.8, 89.9, 
90.1, 91.2, 90.7, 88.2, 94.4, 93.7, 88.3, 91.8, 
89.0, 90.6, 88.6, 88.5, 90.4, 96.5, 89.2, 89.7, 
89.8, 92.2, 88.3, 93.3, 91.2, 84.3, 92.3, 92.2, 
91.6, 87.7, 94.2, 87.4, 91.2, 93.2, 88.9, 88.9, 
90.3, 91.1, 85.3, 91.1, 86.7, 88.6, 88.9, 89.8, 
90.0, 86.7, 90.1, 90.5, 94.2, 88.7, 92.7, 92.7, 
91.5, 93.4, 89.3, 100.3, 90.8, 92.7, 93.3, 91.3, 
89.9, 96.1, 91.1, 87.6, 90.1, 89.3, 86.7, 86.7
```

### Stem-and-Leaf Display:
Let's create the display by separating the tens and ones digits.

```
Stem | Leaf
----------------
83   | 4
84   | 3, 3
85   | 3
86   | 7, 7, 7, 7
87   | 4, 5, 6, 7, 8, 8, 9, 9
88   | 2, 3, 3, 3, 3, 4, 5, 5, 6, 6, 9, 9, 9
89   | 0, 2, 3, 3, 6, 7, 8, 8, 9, 9
90   | 0, 1, 1, 1, 1, 3, 4, 4, 4, 5, 6, 8, 9
91   | 0, 0, 1, 1, 1, 2, 2, 2, 3, 5, 6, 6, 8
92   | 2, 2, 2, 3, 6, 7, 7, 7
93   | 0, 2, 3, 3, 4, 7
94   | 2, 2, 4, 4, 7
96   | 1, 5
98   | 8
100  | 3
```

### Step 3: Calculate the Median and Quartiles
1. **Sort the data**: (already done above).
2. **Median (Q2)**:
   Since there are 80 values, the median is the average of the 40th and 41st values.
3. **First Quartile (Q1)**:
   Q1 is the median of the first half (values 1 to 40).
4. **Third Quartile (Q3)**:
   Q3 is the median of the second half (values 41 to 80).

I'll proceed to calculate these:

Sorted Values:
```
83.4, 84.3, 84.3, 85.3, 86.7, 86.7, 86.7, 86.7, 87.4, 87.5, 
87.6, 87.7, 87.8, 87.8, 87.9, 88.2, 88.3, 88.3, 88.3, 88.3, 
88.4, 88.5, 88.5, 88.6, 88.6, 88.7, 88.9, 88.9, 88.9, 89.0, 
89.2, 89.3, 89.3, 89.6, 89.7, 89.8, 89.8, 89.9, 89.9, 89.9, 
90.0, 90.1, 90.1, 90.1, 90.1, 90.3, 90.4, 90.4, 90.4, 90.5, 
90.6, 90.7, 90.8, 90.9, 91.0, 91.0, 91.1, 91.1, 91.1, 91.2, 
91.2, 91.2, 91.3, 91.5, 91.6, 91.6, 91.8, 91.8, 92.2, 92.2, 
92.2, 92.3, 92.6, 92.7, 92.7, 92.7, 93.0, 93.2, 93.3, 93.3, 
93.4, 93.7, 94.2, 94.2, 94.4, 94.4, 94.7, 96.1, 96.5, 98.8, 100.3
```

- **Median (Q2)** = (89.9 + 90.0) / 2 = 89.95
- **First Quartile (Q1)** = (88.3 + 88.3) / 2 = 88.3
- **Third Quartile (Q3)** = (92.6 + 92.7) / 2 = 92.65

### Summary:
- **Stem-and-Leaf Display**: Constructed above.
- **Median (Q2)**: 89.95
- **First Quartile (Q1)**: 88.3
- **Third Quartile (Q3)**: 92.65

Would you like more details or have any questions on this analysis?

### 5 Related Questions:
1. What is the range of these data?
2. How would a histogram compare to a stem-and-leaf plot for this dataset?
3. Can we use this data to calculate interquartile range (IQR)?
4. How do we identify outliers in this dataset using quartiles?
5. What can the skewness of this data tell us about the gasoline blends?

### Tip:
Stem-and-leaf displays are useful for preserving the original data values while visualizing the distribution, especially for small datasets.

Construct a stem-and-leaf display for the provided data on the motor fuel octane ratings of several blends of gasoline. Calculate the median and quartiles of these data.

Learn how to construct a stem-and-leaf display using octane ratings data. This solution includes step-by-step instructions for calculating the median, first quartile (Q1), and third quartile (Q3). Suitable for high school students in Grades 9-12.

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