Mean Calculator
Find the arithmetic average of any data set. Enter numbers separated by commas or spaces to calculate the mean instantly.
Result
- Number of Values
- 0
- Mean (Average)
- 0
Formula & Guide
Formula
μ
Arithmetic Mean
Mean = (x₁ + x₂ + ... + xₙ) / n
Sum of all values divided by count
=
Alternative Notation
Mean = Σx / n
Sum (Σ) of all values divided by n
Formula Variables
x₁, x₂, ..., xₙ
Values
Individual numbers in the dataset
n
Count
The total number of values in the dataset
Σ
Sum
The sum of all values (addition of all numbers)
Mean
Mean (Average)
The arithmetic average of all values
Step-by-Step Scenario
Example Scenario
Values
10, 20, 30, 40, 50
1
Add All Values
- Sum = 10 + 20 + 30 + 40 + 50
Add all numbers together
2
Count the Values
- There are 5 values in the dataset
3
Divide Sum by Count
- Mean = 150 ÷ 5
Additional Examples
Test Scores
Scores: 85, 90, 78, 92, 88
Sum
85 + 90 + 78 + 92 + 88 = 433
Mean
433 ÷ 5 = 86.6
Temperature Data
Temperatures: 72, 75, 68, 80, 73
Sum
72 + 75 + 68 + 80 + 73 = 368
Mean
368 ÷ 5 = 73.6°F
Characteristics of Mean
Most Common Average
The mean is the most widely used measure of central tendency. It's simple to calculate and understand, making it popular in everyday use.
Sensitive to Outliers
The mean is affected by extreme values (outliers). A single very large or very small number can significantly change the mean.
Statistical Foundation
The mean is fundamental to statistics, used in many formulas including standard deviation, variance, and regression analysis.
Balanced Center
The mean represents the balancing point of the data. If you imagine the values on a number line, the mean is where they balance.
Important Notes
- The mean is sensitive to outliers. If your data has extreme values, consider using the median instead.
- All values are weighted equally in the mean calculation. Each number contributes the same amount to the final result.
- The mean can be a decimal even if all input values are whole numbers. For example, the mean of 1, 2, 3 is 2, but the mean of 1, 2, 3, 4 is 2.5.
- Negative numbers are handled correctly. The mean of -5, 0, 5 is 0, which makes sense as the center point.
- For large datasets, the mean provides a single representative value that summarizes the entire dataset.
Frequently Asked Questions
Find answers to common questions about mean calculations.