Arithmetic Mean (Average) Formula

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

Mathematical Equation

$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$

Variable Definitions

\bar{x}

Arithmetic Mean (Average)

\sum x_i

Sum of all individual dataset values

n

Total count of observations in sample

Detailed Explanation

In-Depth Guide

The arithmetic mean formula calculates the central average value of a sample dataset by summing all observation values and dividing by the total sample count.

How to Calculate: Step-by-Step

1. Add all numerical data values together to find total sum (∑x). 2. Count total number of items n. 3. Divide total sum by count n.

Worked Calculation Example

Dataset [10, 15, 20, 25, 30]: - Sum = 10 + 15 + 20 + 25 + 30 = 100. - Count n = 5. - Mean x̄ = 100 / 5 = 20.

Common Use Cases

  • Academic grade point average calculation
  • Monthly sales revenue averages
  • Scientific measurement aggregation

Frequently Asked Questions

Extreme high or low outliers skew the mean heavily, which is why median is often preferred for skewed distributions like income data.

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