Sure! Let's go through the stem-and-leaf plot step by step to understand it and extract the data.
### Step 1: Understand the Stem-and-Leaf Plot
The stem-and-leaf plot is a way to organize and display data. Each "stem" represents a group of which the "leaves" represent individual data points within that group. The key given (`Key: 1 | 0 = 10`) indicates that each leaf value is to be multiplied by 10 and then added to the corresponding stem value to get the actual data points.
### Step 2: Breakdown Each Row into Data Points
Using the key provided and the arrangement of stems and leaves, we can now extract the data points:
#### Stem 1
- Leaves: 2, 7
- Data points: [tex]\( 1 \times 10 + 2 = 12 \)[/tex], [tex]\( 1 \times 10 + 7 = 17 \)[/tex]
- Data for Stem 1: [12, 17]
#### Stem 2
- Leaves: 3, 3, 4, 8
- Data points: [tex]\( 2 \times 10 + 3 = 23 \)[/tex], [tex]\( 2 \times 10 + 3 = 23 \)[/tex], [tex]\( 2 \times 10 + 4 = 24 \)[/tex], [tex]\( 2 \times 10 + 8 = 28 \)[/tex]
- Data for Stem 2: [23, 23, 24, 28]
#### Stem 3
- Leaves: 0, 2, 2
- Data points: [tex]\( 3 \times 10 + 0 = 30 \)[/tex], [tex]\( 3 \times 10 + 2 = 32 \)[/tex], [tex]\( 3 \times 10 + 2 = 32 \)[/tex]
- Data for Stem 3: [30, 32, 32]
#### Stem 4
- Leaves: 1
- Data points: [tex]\( 4 \times 10 + 1 = 41 \)[/tex]
- Data for Stem 4: [41]
### Step 3: Concatenate All Extracted Data
Let's gather all the data points extracted from each stem:
- Data for Stem 1: [12, 17]
- Data for Stem 2: [23, 23, 24, 28]
- Data for Stem 3: [30, 32, 32]
- Data for Stem 4: [41]
Combine all the data:
- Combined Data: [12, 17, 23, 23, 24, 28, 30, 32, 32, 41]
So, here are the detailed extracted data:
- From stem 1: [tex]\([12, 17]\)[/tex]
- From stem 2: [tex]\([23, 23, 24, 28]\)[/tex]
- From stem 3: [tex]\([30, 32, 32]\)[/tex]
- From stem 4: [tex]\([41]\)[/tex]
- Combined data: [tex]\([12, 17, 23, 23, 24, 28, 30, 32, 32, 41]\)[/tex]
These are the correct data points converted from the given stem-and-leaf plot.
