Statistical Mode Formula

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

Mathematical Equation

$$\text{Mode} = L + \left[ \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right] \times h$$

Variable Definitions

Mode

Most frequently occurring score or value

L

Lower boundary of modal class interval

f_1

Frequency of modal class

f_0

Frequency of class preceding modal class

f_2

Frequency of class following modal class

h

Width of modal class interval

Detailed Explanation

In-Depth Guide

The mode represents the specific value or continuous frequency peak that appears with the highest frequency in a statistical distribution.

How to Calculate: Step-by-Step

1. Count occurrence frequency of each unique number. 2. Identify value(s) with maximum occurrence count. 3. For grouped continuous frequency distribution tables, apply modal class interpolation formula.

Worked Calculation Example

Dataset [4, 7, 4, 8, 9, 4, 7]: - Frequency: 4 appears 3 times, 7 appears 2 times. - Mode = 4 (highest frequency count of 3).

Common Use Cases

  • E-commerce inventory sizing (most requested shoe size)
  • Election voting majority analysis
  • Retail product sales popularity

Frequently Asked Questions

The dataset is bimodal and has two modes. If 3 or more tie, it is multimodal.

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