Average Calculator
Calculate the arithmetic mean, sum, count, and weighted average for any custom dataset or list of numbers.
Values List
Enter individual numbers to compute the total sum and arithmetic mean.
Average (Arithmetic Mean)
How Averages Are Calculated
Pure mathematical formulas for arithmetic mean and weighted average calculations.
1. Arithmetic Mean Formula
The standard arithmetic mean is calculated by summing all individual numerical values and dividing that sum by the total count of values (n).
When to use: Use when all numbers in your dataset contribute equally to the final summary metric.
2. Weighted Average Formula
The weighted mean accounts for the varying relative importance of each value by multiplying each item by its weight, summing the weighted products, and dividing by the total weight sum.
When to use: Use for semester course grades with credit hours, portfolio asset allocation returns, or surveys with unequal sample sizes.
Practical Calculation Examples
Real-world scenarios illustrating step-by-step numbers, inputs, and verified outputs.
Example 1: Basic Integer Average
Calculate the simple arithmetic mean of 10, 20, and 30.
Example 2: Decimal Values Average
Calculate the mean of 5, 7.5, and 10.
Example 3: Negative & Zero Numbers
Arithmetic average of -10, 0, and 10.
Example 4: Weighted Exam & Assignment Grades
Score 80 with 40% weight and score 90 with 60% weight.
Frequently Asked Questions
Clear answers to common questions about calculating arithmetic mean, weighted averages, handling negative numbers, and dataset sizes.
How do I calculate an average using a calculator?
To calculate an average on a calculator, add all individual numbers together to find their total sum, then divide that sum by the total count of numbers. In this calculator, simply enter your numbers in the 'Simple Average' tab to get the mean, count, sum, and step-by-step formula breakdown.
How do I calculate the average of several numbers?
Add all the numbers in your dataset together, then divide by the total number of values: Average = (x₁ + x₂ + ... + xₙ) ÷ n. For example, for 10, 20, and 30: Sum = 60, Count = 3, Average = 60 ÷ 3 = 20.
What is the difference between a simple average and a weighted average?
In a simple average (arithmetic mean), every number contributes equally to the final result. In a weighted average, different values carry different degrees of importance or weight (such as a 4-credit course vs a 2-credit course, or a 60% exam vs a 40% assignment).
When should I use a weighted average?
Use a weighted average whenever data points have unequal significance, such as calculating semester GPA with varied credit hours, portfolio investment returns with unequal capital allocations, or academic course grades with weighted exams and homework.
Do weights in a weighted average have to add up to 100%?
No. While percentage weights often add up to 100%, this calculator supports any non-negative weights (such as course credits 4, 3, 2 or test point totals). The calculation automatically normalizes by dividing by the sum of all weights.
Can an average include negative numbers and zeros?
Yes. Negative numbers and zeros are fully valid in average calculations. For instance, the average of -10, 0, and 10 is exactly 0.
Can I enter decimal numbers?
Yes. You can enter fractional or decimal numbers for both values and weights (such as 7.5, 3.14, or 0.25) with full floating-point precision.
What is the difference between mean, median, and mode?
The mean is the mathematical average (sum divided by count). The median is the middle value when numbers are sorted in order. The mode is the value that appears most frequently in a dataset.
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