Mean, Median, Mode & Range Formula

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

Mathematical Equation

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}, \quad \text{Median} = x_{\left(\frac{n+1}{2}\right)}$$

Variable Definitions

\bar{x}

Arithmetic Mean (Average) of dataset

x_i

Individual numerical sample data values

n

Total count of numbers in dataset

Median

Middle value of sorted dataset

Mode

Most frequently occurring number in dataset

Range

Spread between maximum and minimum value (Max - Min)

Detailed Explanation

In-Depth Guide

Central tendency formulas calculate the arithmetic average (Mean), middle ranking value (Median), most repeated entry (Mode), and total statistical spread (Range) for a numerical dataset.

How to Calculate: Step-by-Step

1. Mean: Sum all numbers together and divide by total count n. 2. Median: Sort numbers ascending. Pick middle number if n is odd, or average the two middle numbers if n is even. 3. Mode: Identify the number(s) appearing with highest frequency. 4. Range: Subtract smallest value from largest value.

Worked Calculation Example

Dataset [3, 7, 5, 7, 10]: - Sorted: [3, 5, 7, 7, 10] (Count n = 5). - Mean = (3 + 5 + 7 + 7 + 10) / 5 = 32 / 5 = 6.4. - Median = 3rd element = 7. - Mode = 7 (appears twice). - Range = 10 - 3 = 7.

Common Use Cases

  • Descriptive statistical analysis
  • Exam score distribution & grading
  • Financial market asset return profiling

Frequently Asked Questions

Yes, a dataset can be bimodal (2 modes), multimodal (multiple modes), or have no mode if all numbers appear with equal frequency.

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