Robust Scaling Practice Problem

This data science coding problem helps you practice Feature Scaling & Transformation, robust scaling, and implementation skills. Read the problem statement, write your solution, and strengthen your understanding of Feature Scaling & Transformation.

• Problem ID: 36
• Problem key: 36-robust-scaling
• URL: https://datacrack.app/solve/36-robust-scaling
• Difficulty: medium
• Topic: Feature Scaling & Transformation
• Module: Data Cleaning

Problem Statement

# Robust Scaling

### 🎯 Goal
Scale numeric columns using median and interquartile range (IQR), making the transformation robust to outliers.

### 💻 Task
Implement `robust_scale(data)` that:
1. Converts the input dictionary to a DataFrame
2. Applies the Robust Scaling formula to each numeric column: `(x - median) / IQR`
3. Computes IQR as Q3 (75th percentile) minus Q1 (25th percentile)
4. Returns the scaled DataFrame rounded to 2 decimal places

---

### 📥 Input
- `data`: A dictionary where keys are column names and values are lists of numeric data

### 📤 Output
- A pandas DataFrame with all numeric columns scaled using median/IQR, rounded to 2 decimals

---

### 🧩 Starter Code

```python
import pandas as pd
import numpy as np

def robust_scale(data):
    """
    Scale numeric columns using median and IQR (robust to outliers).

    Args:
        data (dict): Input data as dictionary (from JSON)

    Returns:
        pd.DataFrame: DataFrame with robust-scaled values rounded to 2 decimals
    """
    # TODO: Convert the input dictionary to a DataFrame
    # TODO: Compute Q1 (25th percentile), Q3 (75th percentile), and median
    # TODO: Calculate IQR = Q3 - Q1
    # TODO: Apply (x - median) / IQR to each column
    # TODO: Round and return
    pass
```

---

### 💡 Examples

**Example 1:** Symmetric data
```python
data = {"A": [1.0, 2.0, 3.0, 4.0, 5.0]}
robust_scale(data)
```
```
     A
0 -1.0
1 -0.5
2  0.0
3  0.5
4  1.0
```

**Example 2:** Scaled symmetric data
```python
data = {"X": [10.0, 20.0, 30.0, 40.0, 50.0]}
robust_scale(data)
```
```
     X
0 -1.0
1 -0.5
2  0.0
3  0.5
4  1.0
```

**Example 3:** Data with an outlier
```python
data = {"A": [2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 14.0, 100.0]}
robust_scale(data)
```
```
       A
0  -0.88
1  -0.62
2  -0.38
3  -0.12
4   0.12
5   0.38
6   0.62
7  11.38
```

Starter Code

import pandas as pd
import numpy as np

def robust_scale(data):
    """
    Scale numeric columns using median and IQR (robust to outliers).

    Args:
        data (dict): Input data as dictionary (from JSON)

    Returns:
        pd.DataFrame: DataFrame with robust-scaled values rounded to 2 decimals
    """
    # TODO: Convert the input dictionary to a DataFrame
    # TODO: Compute Q1 (25th percentile), Q3 (75th percentile), and median
    # TODO: Calculate IQR = Q3 - Q1
    # TODO: Apply (x - median) / IQR to each column
    # TODO: Round and return
    pass

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