The **3-sigma rule**, also known as the **68-95-99.7 rule** or the **empirical rule**, is a statistical guideline used in anomaly detection and quality control. 

It is based on the normal distribution and is used to identify outliers or anomalies in data. 
## Main aspects of this rule

1. **Normal Distribution Assumption**: The 3-sigma rule assumes that the data follows a normal distribution (Gaussian distribution). In a normal distribution, approximately `68%` of the data falls within **one standard deviation (sigma)** of the mean, approximately `95%` falls within **two standard deviations**, and about `99.7%` falls within **three standard deviations**;
2. **Identification of Outliers**: According to the 3-sigma rule, data points that **fall more than three standard deviations away from the mean are considered potential outliers**. These data points are significantly different from the majority of the data and are often flagged for further investigation.


## 3-sigma rule implementation

``` python
def three_sigma_rule(data):

    # Calculate mean and standard deviation of the data
    mean = np.mean(data)
    std_dev = np.std(data)

    # Identify outliers based on the 3-sigma rule
    outliers = data[np.abs(data - mean) > 3 * std_dev]

    return outliers
```

Assume that you have data from some unknown distribution. Which method should you use to detect outliers in this data?

Anomaly detection is integral to any data scientist's work: high-quality, cleaned, and well-prepared data is the key to success for almost any machine learning problem. 

Let's delve into the concept of data anomalies, their classification, and their impact on decision-making. Throughout this exploration, we will gain a comprehensive understanding of these topics, accompanied by real-life examples to illustrate their significance.

Statistical methods play a crucial role in various domains, including finance, cybersecurity, manufacturing, and healthcare, where detecting anomalies can prevent fraud, ensure data quality, and improve overall system reliability. These methods are particularly valuable when dealing with large datasets and complex systems, as they provide a systematic and quantitative approach to anomaly detection.

Now, let's explore how machine learning methods can effectively address anomalies. We will examine various techniques, including clustering, regularization, dropout, and more, that are employed for this purpose.

Data Anomaly Detection

3-Sigma Rule

Main aspects of this rule

3-sigma rule implementation