Z-Score Outlier Detection Practice Problem

This data science coding problem helps you practice Outlier Detection & Treatment, z-score outlier detection, and implementation skills. Read the problem statement, write your solution, and strengthen your understanding of Outlier Detection & Treatment.

• Problem ID: 164
• Problem key: 164-z-score-outlier-detection
• URL: https://datacrack.app/solve/164-z-score-outlier-detection
• Difficulty: medium
• Topic: Outlier Detection & Treatment
• Module: Data Cleaning

Problem Statement

# Z-Score Outlier Detection

### 🎯 Goal
Detect outliers in a numeric column using Z-score analysis — a statistical method based on standard deviations from the mean.

### 💻 Task
Implement `detect_outliers_zscore(data, column, threshold=2)` that:
1. Converts the input dictionary to a DataFrame
2. Computes the mean and standard deviation (using sample std, `ddof=1`)
3. Calculates Z-scores as `(x - mean) / std`
4. Flags values where `|z-score| > threshold` as outliers
5. Returns a dictionary with statistics and detected outliers

---

### 📥 Input
- `data`: A dictionary where keys are column names and values are lists of numbers
- `column`: The name of the column to check for outliers
- `threshold`: Z-score threshold (default: 2) — values with |z| > threshold are outliers

### 📤 Output
- A dictionary with:
  - `"mean"` (float, rounded to 2 decimals)
  - `"std"` (float, rounded to 2 decimals)
  - `"outlier_indices"` (list of integer indices)
  - `"outliers"` (list of outlier values)

---

### 🧩 Starter Code

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

def detect_outliers_zscore(data, column, threshold=2):
    """
    Detect outliers using Z-score analysis.

    Args:
        data (dict): Input data as dictionary (from JSON)
        column (str): Column name to check for outliers
        threshold (float): Z-score threshold (default 2)

    Returns:
        dict: Dictionary with mean, std, outlier_indices, outliers
    """
    # TODO: Convert input dictionary to a DataFrame
    # TODO: Compute mean and standard deviation (ddof=1)
    # TODO: Calculate z-scores for each value
    # TODO: Find outlier indices and values where |z| > threshold
    # TODO: Return result dictionary
    pass
```

---

### 💡 Examples

**Example 1:** Single extreme value
```python
data = {"values": [1, 2, 3, 4, 5, 6, 7, 8, 9, 100]}
detect_outliers_zscore(data, "values", threshold=2)
```
```
{
    "mean": 14.5,
    "std": 30.15,
    "outlier_indices": [9],
    "outliers": [100]
}
```

**Example 2:** Negative outlier
```python
data = {"values": [-50, 1, 2, 3, 4, 5, 6, 7, 8, 9]}
detect_outliers_zscore(data, "values", threshold=2)
```
```
{
    "mean": -0.5,
    "std": 17.58,
    "outlier_indices": [0],
    "outliers": [-50]
}
```

Starter Code

import pandas as pd
import numpy as np

def detect_outliers_zscore(data, column, threshold=2):
    """
    Detect outliers using Z-score analysis.

    Args:
        data (dict): Input data as dictionary (from JSON)
        column (str): Column name to check for outliers
        threshold (float): Z-score threshold (default 2)

    Returns:
        dict: Dictionary with mean, std, outlier_indices, outliers
    """
    # TODO: Convert input dictionary to a DataFrame
    # TODO: Compute mean and standard deviation (ddof=1)
    # TODO: Calculate z-scores for each value
    # TODO: Find outlier indices and values where |z| > threshold
    # TODO: Return result dictionary
    pass