Average Calculator
Calculate statistical measures including mean, median, mode, range, and standard deviation from comma or newline separated numbers.
Enter numbers separated by commas or on new lines
Mean (Average)
30.00
Median
30.00
Mode
No mode
Range
40.00
Minimum
10.00
Maximum
50.00
Count
5
Sum
150.00
Geometric Mean
26.32
Standard Deviation
15.81
Sorted Data
10, 20, 30, 40, 50
Data Visualization
How to Use the Average Calculator
Enter your numbers in the text area, separated by commas or on new lines. The calculator instantly computes all statistical measures including mean, median, mode, range, minimum, maximum, count, sum, geometric mean, and standard deviation.
- Enter your numbers separated by commas or newlines
- Results update automatically showing all statistical measures
- View sorted data and visual dot plot below
- Use preset buttons for quick examples
Statistical Formulas
Mean (Average):
Mean = Sum of all numbers / Count of numbers
Median:
Median = Middle value when numbers are sorted (or average of two middle values)
Mode:
Mode = Most frequently occurring number(s)
Range:
Range = Maximum - Minimum
Standard Deviation (Sample):
σ = sqrt(Σ(x - mean)² / (n - 1))
Geometric Mean:
GM = nth root of (x₁ × x₂ × ... × xₙ)
Understanding the Results
- Mean: The arithmetic average, calculated by summing all numbers and dividing by the count
- Median: The middle value when data is sorted, less affected by outliers than mean
- Mode: The most frequent value(s) in the dataset
- Range: The difference between maximum and minimum values
- Standard Deviation: Measures how spread out numbers are from the mean
- Geometric Mean: Useful for calculating average rates of growth or ratios
Frequently Asked Questions
The mean is the sum of all values divided by the count, while the median is the middle value when data is sorted. Median is less affected by outliers and extreme values, making it more robust for skewed distributions.
Mode is the most frequently occurring value in a dataset. A dataset can have no mode (all values unique), one mode (unimodal), or multiple modes (multimodal). Mode is useful for categorical data and finding the most common occurrence.
Standard deviation measures spread from the mean. It's calculated by finding the square root of the average of squared differences from the mean. This calculator uses sample standard deviation (n-1 denominator) which is appropriate for samples from a larger population.
Geometric mean is ideal for calculating average rates of return, growth rates, or ratios. It's the nth root of the product of n numbers. Use it when dealing with percentages, ratios, or exponential growth rather than simple averages.
Yes, mean, median, mode, range, and standard deviation work with negative numbers. However, geometric mean requires all positive numbers (or an even count of negative numbers) as it involves taking roots of products.
The dot plot is a simple visual representation of your data distribution. Each dot represents one value in your dataset, positioned according to its magnitude. This helps you quickly see patterns, clusters, and outliers in your data.