Statistical Range Formula

Mathematics & Education Formula • Published on July 30, 2026 • Last updated July 30, 2026

Mathematical Equation

$$\text{Range} = x_{\max} - x_{\min}$$

Variable Definitions

Range

Total numerical spread of dataset

x_{\max}

Highest / maximum value in sample

x_{\min}

Lowest / minimum value in sample

Detailed Explanation

In-Depth Guide

The statistical range formula measures total dispersion by calculating the numerical distance between the highest and lowest values in a distribution.

How to Calculate: Step-by-Step

1. Identify maximum value in dataset (x_max). 2. Identify minimum value in dataset (x_min). 3. Subtract minimum from maximum: Range = x_max - x_min.

Worked Calculation Example

Dataset [12, 45, 8, 29, 63]: - Maximum x_max = 63. - Minimum x_min = 8. - Range = 63 - 8 = 55.

Common Use Cases

  • Stock price daily volatility trading range
  • Temperature fluctuation ranges
  • Manufacturing quality control tolerances

Frequently Asked Questions

Range measures total distance from min to max, whereas IQR measures middle 50% spread (Q3 - Q1).

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