Statistical Metrics

With a Claude’s Help
This image shows a diagram explaining three key statistical metrics used in data analysis:

1. Z-score:

• Definition: How far from a mean with standard variation unit
• Formula: Z = (X – μ) / σ
  • X: The value
  • μ: The mean of the distribution
  • σ: The standard deviation of the distribution
• Main use: Quickly detect outliers in individual values
• Application: Monitoring cooling temperature and humidity levels

2. IQR (Interquartile Range):

• Definition: The range that covers the middle 50% of the data
• Formula: IQR = Q3 – Q1
  • Q1: The value below which 25% of the data falls
  • Q3: The value below which 75% of the data falls
• Main use: Detect outliers in highly variable data
• Application: Power consumption and power usage effectiveness

3. Mahalanobis Distance:

• Definition: In multivariate data, it is a distance measure that indicates how far a point is from the center of the data distribution
• Formula: D(x) = √((x – μ)’ Σ^(-1) (x – μ))
  • x: The data point
  • μ: The mean vector of the data
  • Σ: The covariance matrix of the data
• Main use: Outlier detection that takes into account multivariate correlations
• Application: Analyzing relationships between cooling temperature vs power consumption and humidity vs power consumption

These three metrics each provide different approaches to analyzing data characteristics and detecting outliers, particularly useful in practical applications such as facility management and energy efficiency monitoring. Each metric serves a specific purpose in statistical analysis, from simple individual value comparisons (Z-score) to complex multivariate analysis (Mahalanobis Distance).