ganak.appAverage Calculator
Calculate the average (arithmetic mean), weighted average, median, mode, range, sum, and standard deviation of any set of numbers. Supports both simple and weighted averages with step-by-step formula breakdowns. Essential for grades, statistics, data analysis, and everyday math.
Calculate the arithmetic mean of a set of numbers
Supports commas, spaces, tabs, or new lines. Paste from spreadsheets works too.
Statistical Summary
Complete breakdown of your dataset
Step-by-Step Calculation
How the arithmetic mean is computed
Formula
Mean = Sum of values / Number of values
Step 1: Add all values together
10 + 20 + 30 + 40 + 50 = 150
Step 2: Divide by the count (5)
150 / 5 = 30
Value Distribution
Frequency distribution of your dataset
What Is an Average?
Understanding mean, median, mode, and more
An average is a single number that represents the central or typical value of a dataset. The most common type is the arithmetic mean, calculated by adding all values and dividing by the count. Averages are used everywhere — from school grades and sports statistics to financial analysis and scientific research.
Arithmetic Mean Formula
Mean = (x₁ + x₂ + ... + xₙ) / n
Types of Averages
Different measures of central tendency explained
Arithmetic Mean (Simple Average)
The sum of all values divided by the count. Most commonly used average. Sensitive to outliers — a single extreme value can shift the mean significantly.
Weighted Average
Each value is multiplied by a weight reflecting its importance before summing and dividing by the total weight. Used in GPA calculations, stock portfolio returns, and grade averages where different assignments have different point values.
Median
The middle value when data is sorted in order. If the count is even, it is the average of the two middle values. Less sensitive to outliers than the mean, making it better for skewed distributions like income data.
Mode
The value that appears most frequently. A dataset can have no mode (all values unique), one mode (unimodal), or multiple modes (bimodal, multimodal). Useful for categorical data where mean and median are not applicable.
How Weighted Average Works
When simple averages are not enough
A weighted average assigns different levels of importance (weights) to each value. This is essential when some data points matter more than others.
Weighted Average Formula
Weighted Avg = (w₁x₁ + w₂x₂ + ... + wₙxₙ) / (w₁ + w₂ + ... + wₙ)
Example: A student scores 90 on a final exam (weight 50%), 80 on a midterm (weight 30%), and 85 on homework (weight 20%). The weighted average is (90 x 0.5 + 80 x 0.3 + 85 x 0.2) / (0.5 + 0.3 + 0.2) = 86.
Real-World Example
Worked example: Test scores 85, 90, 78, 92, 88
A teacher wants to analyze test scores: 85, 90, 78, 92, 88. Here is the full statistical breakdown:
Calculation
- Sum: 85 + 90 + 78 + 92 + 88 = 433
- Count: 5
- Mean: 433 / 5 = 86.6
- Sorted: 78, 85, 88, 90, 92
- Median: 88 (middle value)
Results
- Mean: 86.6
- Median: 88
- Mode: None (all unique)
- Range: 92 - 78 = 14
- Std Dev: 4.67
Common Mistakes When Calculating Averages
Pitfalls to avoid for accurate results
Using the mean for skewed data. Median is more appropriate when outliers are present (e.g., salary data where a few very high earners skew the mean).
Averaging percentages directly without accounting for different sample sizes. A 90% on a 10-question quiz and a 70% on a 100-question exam should not be weighted equally.
Forgetting that the average of averages is not the same as the overall average unless all groups have the same size.
Confusing population standard deviation with sample standard deviation. This calculator uses population standard deviation (dividing by N, not N-1).
Assuming the mean always represents a typical value. In bimodal distributions, the mean may fall between two clusters where no data points actually exist.
Frequently Asked Questions
Common questions about averages, weighted averages, and statistics