# Technical Document Extraction: MER Average Line Chart
## Chart Overview
The image is a **line chart** titled **"MER Average"**, depicting the performance of different algorithms across varying sample sizes (`N`). The y-axis represents the **MER Average** (Mean Endpoint Risk), ranging from **0.18 to 0.30**, while the x-axis represents **N** (sample size), ranging from **100 to 700** in increments of 100.
---
## Legend and Data Series
The legend is located in the **upper-right corner** of the chart. Each line corresponds to a specific algorithm configuration, with colors and markers as follows:
| Legend Label | Color | Marker |
|-----------------------|--------|---------|
| CUSUM | Blue | Circle |
| `m^(1),L=1` | Orange | Triangle|
| `m^(2),L=1` | Green | Diamond |
| `m^(1),L=5` | Red | Square |
| `m^(1),L=10` | Purple | Cross |
---
## Key Trends and Data Points
### 1. **CUSUM (Blue Line)**
- **Trend**: Starts at **0.28** (N=100), decreases sharply to **0.25** (N=200), stabilizes between **0.245–0.255** for N=300–500, then slightly declines to **0.25** (N=600–700).
- **Data Points**:
- N=100: 0.28
- N=200: 0.25
- N=300: 0.245
- N=400: 0.245
- N=500: 0.255
- N=600: 0.25
- N=700: 0.25
### 2. **`m^(1),L=1` (Orange Line)**
- **Trend**: Starts at **0.30** (N=100), drops sharply to **0.22** (N=200), fluctuates between **0.20–0.21** for N=300–700.
- **Data Points**:
- N=100: 0.30
- N=200: 0.22
- N=300: 0.205
- N=400: 0.21
- N=500: 0.215
- N=600: 0.21
- N=700: 0.205
### 3. **`m^(2),L=1` (Green Line)**
- **Trend**: Starts at **0.28** (N=100), drops sharply to **0.195** (N=200), rises to **0.21** (N=500), then stabilizes at **0.205** (N=600–700).
- **Data Points**:
- N=100: 0.28
- N=200: 0.195
- N=300: 0.20
- N=400: 0.205
- N=500: 0.21
- N=600: 0.205
- N=700: 0.205
### 4. **`m^(1),L=5` (Red Line)**
- **Trend**: Starts at **0.235** (N=100), drops sharply to **0.185** (N=200), rises to **0.21** (N=500), then stabilizes at **0.205** (N=600–700).
- **Data Points**:
- N=100: 0.235
- N=200: 0.185
- N=300: 0.20
- N=400: 0.205
- N=500: 0.21
- N=600: 0.205
- N=700: 0.205
### 5. **`m^(1),L=10` (Purple Line)**
- **Trend**: Starts at **0.235** (N=100), drops sharply to **0.185** (N=200), rises to **0.21** (N=500), then stabilizes at **0.205** (N=600–700).
- **Data Points**:
- N=100: 0.235
- N=200: 0.185
- N=300: 0.20
- N=400: 0.205
- N=500: 0.21
- N=600: 0.205
- N=700: 0.205
---
## Spatial Grounding and Validation
- **Legend Placement**: Upper-right corner (confirmed via visual inspection).
- **Color Consistency**: All line colors match the legend labels (e.g., blue = CUSUM, orange = `m^(1),L=1`).
- **Axis Labels**:
- X-axis: **N** (sample size, 100–700).
- Y-axis: **MER Average** (0.18–0.30).
---
## Observations
1. **CUSUM** consistently outperforms other configurations for larger N (>300), maintaining the lowest MER Average.
2. **`m^(1),L=1`** exhibits the highest initial MER Average but converges toward CUSUM's performance for N > 500.
3. **`m^(2),L=1`**, **`m^(1),L=5`**, and **`m^(1),L=10`** show similar trends, with slight variations in early-stage performance.
---
## Conclusion
The chart illustrates the trade-offs between algorithm configurations and sample size in terms of MER Average. CUSUM emerges as the most stable and efficient choice for larger datasets, while other configurations require larger N to achieve comparable performance.
