📊 Average Calculator
Calculate mean, median, mode, range, and geometric mean for any set of numbers. Perfect for students, teachers, and data analysis professionals.
Input Options
Quick Stats
Arithmetic Mean
📊Sum ÷ Count
Median
📏Middle value
Mode
🔢Most frequent
Geometric Mean
📐For positive numbers
Sorted Numbers
Frequency Distribution
Statistical Measures
Data Distribution Visualization
Frequently Asked Questions
How do I calculate the mean?
Add all numbers together, then divide by how many numbers there are. For example, numbers 10,20,30,40,50: sum = 150, count = 5, mean = 150 ÷ 5 = 30.
What's the difference between mean and median?
Mean is affected by extreme values (outliers), while median is not. For salaries: if one person earns $1M and nine earn $50K, mean = $145K, median = $50K (more representative).
How do I find the mode when there are multiple modes?
If two or more numbers appear with the same highest frequency, the dataset is multimodal. Our calculator shows all modes. Example: 10,10,20,20,30 has modes 10 and 20.
When should I use geometric mean?
Use geometric mean for percentages, growth rates, and ratios. For example, if investments grow by 10%, 20%, and -5% over three years, geometric mean gives the average growth rate.
📚 Understanding Averages: Complete Guide
Arithmetic Mean
The sum of all values divided by the number of values. Best for normally distributed data without extreme outliers.
Formula: (x₁ + x₂ + ... + xₙ) ÷ n
Median
The middle value when data is sorted. Not affected by outliers, good for skewed distributions like income data.
Mode
The most frequently occurring value. Useful for categorical data and identifying popular items or common values.
Range
The difference between maximum and minimum values. Shows the spread of your data.
When to Use Which Average?
- • Mean: Test scores, average income (normal distribution)
- • Median: House prices, salaries (skewed data with outliers)
- • Mode: Favorite color, most common shoe size (categorical data)
- • Geometric Mean: Investment returns, population growth (percentages/rates)
⚠️ Note: Geometric mean is only calculated for positive numbers. If any number is zero or negative, geometric mean is not displayed as it would be undefined or complex.