How to use the average calculator
- Choose Average (mean) for a plain average, or Weighted average when values count for different amounts.
- For a plain average, type or paste your numbers, separated by commas, spaces or new lines. Anything that isn't a number is skipped and listed under the result.
- For a weighted average, enter the values and then the weights in the same order: one weight per value.
- Read the average and the working. The plain average also shows the median, the range and how far each number is from the mean.
How the average is calculated
The mean adds every value x and divides by how many there are, n. A weighted average multiplies each value by its weight w before adding, then divides by the total weight instead of the count. When all the weights are equal, it gives exactly the same answer as the plain mean.
Weights don't have to add up to 100 or to 1. Course credits (3, 4, 3), percentages (50%, 30%, 20%) or numbers of items bought all work, because the formula divides by whatever total they reach.
Worked example
The calculator starts with five test scores: 85, 92, 78, 90 and 88.
- Add them: 85 + 92 + 78 + 90 + 88 = 433.
- Count them: 5 scores.
- Divide: 433 ÷ 5 = 86.6.
Sorted, the scores are 78, 85, 88, 90, 92, so the median (the middle one) is 88 and the range is 92 − 78 = 14. The distances from the mean are −1.6, +5.4, −8.6, +3.4 and +1.4, which add up to 0. That is always true, and it is why the mean is called the balance point of the data.
For the weighted average, the defaults are an exam worth 50% with a score of 90, homework worth 30% at 80, and quizzes worth 20% at 70:
- 90 × 50 = 4,500, 80 × 30 = 2,400 and 70 × 20 = 1,400
- 4,500 + 2,400 + 1,400 = 8,300, and the weights total 100
- 8,300 ÷ 100 = 83
The plain average of 90, 80 and 70 would be 80. The weighted result is higher because the best score carries the most weight.
Mean, median or mode?
| Measure | What it is | Best when |
|---|---|---|
| Mean | Sum ÷ count | Data is fairly symmetric, like test scores |
| Median | Middle value when sorted | A few extreme values would distort the mean, like incomes or house prices |
| Mode | Most common value | Categories or repeated values, like shoe sizes |
One very large or small number pulls the mean toward it, but barely moves the median. Five salaries of $40,000 and one of $1,000,000 have a mean of $200,000 but a median of $40,000. To see all of these measures at once, use the mean, median, mode and range calculator.
Frequently asked questions
How do I calculate a weighted grade?
Multiply each category's score by its weight, add those products, and divide by the total weight. With homework 80 at 30%, an exam 90 at 50% and quizzes 70 at 20%, the grade is (80 × 30 + 90 × 50 + 70 × 20) ÷ 100 = 83. For a GPA from letter grades and credits, the GPA calculator does the same thing with grade points.
Do the weights have to add up to 100?
No. The formula divides by the sum of the weights, whatever it is. Weights of 3, 4 and 3 credits give the same answer as 30%, 40% and 30%, because both describe the same proportions.
Can I average negative numbers and decimals?
Yes. Negative values lower the sum, and decimals are added like any other number. The average of -4, 2.5 and 7 is 5.5 ÷ 3 = 1.8333.
What is the difference between the average and the mean?
In everyday use they are the same thing: the arithmetic mean, the sum divided by the count. In statistics, "average" can loosely refer to the median or mode as well, so the calculator labels its main answer as the mean to be clear.
Related calculators
- Mean, Median, Mode & Range Calculator — The mean, median, mode and range of a list of numbers, with the sorted list and each step explained.
- Standard Deviation Calculator — Sample and population standard deviation, variance and mean of a list of numbers, with every step shown.
- GPA Calculator — Semester and cumulative GPA on the 4.0 scale with plus and minus grades, for up to 10 courses.
- Percentage Calculator — Percent of a number, what percent one number is of another, percentage change and difference.
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