Mean (Average) – Complete Guide and Calculator
The mean, also called the arithmetic average, is the most widely used measure of central tendency in statistics.
📘 Page Index
Count: —
Example input: 4, 8, 15, 16, 23, 42
What Is the Mean?
The mean summarizes a dataset by distributing the total value equally across all observations. Every data point contributes equally to the final result.
In statistics, the population mean is written as μ, while the sample mean is written as x̄.
Mean Formula Explained
Mean = (x₁ + x₂ + … + xₙ) / n
Because every value affects the total sum, the mean is highly sensitive to extreme values.
Step-by-Step Examples
Sum = 100
Count = 4
Mean = 25
With outlier: 5, 6, 7, 100 → Mean = 29.5 (distorted by 100)
Types of Mean
Arithmetic Mean
Standard average used in most situations.
Weighted Mean
Used when values have different importance.
Geometric Mean
Used for growth rates and percentages.
Harmonic Mean
Used for rates such as speed.
When to Use the Mean
When Not to Use the Mean
Why Is the Mean Sensitive to Outliers?
Since the mean redistributes the total sum equally, an extreme value can shift the result significantly.
Mean vs Median vs Mode
| Measure | Definition | Outlier Sensitive? |
|---|---|---|
| Mean | Arithmetic average | Yes |
| Median | Middle value | No |
| Mode | Most frequent value | No |
Real-World Applications
Common Mistakes
Frequently Asked Questions
Is mean the same as average?
Yes, in most contexts.
Can the mean be negative?
Yes.
Is the mean always the best measure?
No, it depends on distribution and outliers.