Table of Contents
What Are Min and Max?
The minimum (min) is the smallest value in a dataset, and the maximum (max) is the largest value. Together, they define the range of the data. These are the most basic descriptive statistics and are often the first things computed when exploring a dataset.
The range (max - min) gives a simple measure of spread, though it is sensitive to outliers. Min and max are used in data validation, normalization (min-max scaling), and as bounds for other calculations.
How to Find Them
Common Uses
| Application | Description |
|---|---|
| Data Validation | Check for impossible values |
| Normalization | Min-max scaling to [0,1] |
| Quality Control | Range charts for process monitoring |
| Outlier Detection | Identify extreme values |
Frequently Asked Questions
What is min-max normalization?
Min-max normalization scales data to a range of [0, 1] using the formula: x_normalized = (x - min) / (max - min). This is commonly used in machine learning to ensure all features are on the same scale.
Is the range a good measure of spread?
The range is simple but unreliable because it depends only on two extreme values. The IQR (interquartile range) or standard deviation are more robust measures of spread that consider all data points.
Can there be multiple minimum or maximum values?
Yes, if two or more values tie for the smallest or largest, there are multiple minima or maxima. The numerical value of min or max remains the same regardless of duplicates.