Finding the average
The average, or arithmetic mean, is the single number that best stands for a whole list: add everything up and divide by how many values there are. It turns a set of test marks into one score, a month of daily sales into a typical day, or a week of commutes into a usual journey time.
This average calculator does that for any list you type or paste, and shows the median and mode beside it, since they can tell a different story. The weighted mode is for lists where some values count more than others, such as course marks with different weights or prices bought in different amounts.
How to use it
- For a plain average, type or paste the numbers into the box, separated by commas, spaces or new lines.
- For a weighted average, choose Weighted average and fill in each value with its weight.
- Read the average at the top, with the sum, count, median and mode underneath.
- Open the working to see the sum and the division.
The formulas
average = (x1 + x2 + … + xn) ÷ n
weighted average = (x1 × w1 + x2 × w2 + …) ÷ (w1 + w2 + …)A plain average is a weighted average where every weight is 1. When weights are percentages that add up to 100, the bottom of the weighted formula is simply 100.
Worked example: five test scores
- Scores: 72, 85, 90, 68 and 95
- Sum: 72 + 85 + 90 + 68 + 95 = 410
- Average: 410 ÷ 5 = 82
The average score is 82. The median is 85, the middle score once they are sorted, and there is no mode because no score repeats.
| Part | Score | Weight | Score × weight |
|---|---|---|---|
| Homework | 90 | 20 | 1,800 |
| Midterm | 80 | 30 | 2,400 |
| Final | 70 | 50 | 3,500 |
| Total | 100 | 7,700 |
The weighted average is 7,700 ÷ 100 = 77. A plain average of the three scores would say 80, which overstates the result because the lowest score carries half of the weight.
Mean, median or mode?
- Mean: uses every value, so one very large or very small number pulls it hard.
- Median: the middle value, which stays put when there are a few extreme values. House prices and pay are usually reported this way.
- Mode: the most common value, best for categories or repeated values such as shoe sizes.
Here is a quick test. Five people earn 30, 32, 35, 38 and 40 thousand a year: the mean is 35 and so is the median. Add a sixth person on 400 thousand, and the mean jumps to 95.8 while the median only moves to 36.5. The median still describes a typical person; the mean no longer does.
If the mean and median are far apart, the list is lopsided. For the spread as well as the middle, use the statistics calculator.
Frequently asked questions
How do I calculate the average?
Add all the numbers together, then divide by how many numbers there are. For 4, 8 and 12, the sum is 24 and there are 3 numbers, so the average is 8. Paste your list into the calculator above and it does both steps, and shows the median and mode as well.
What is a weighted average?
It is an average where some values count more than others. Multiply each value by its weight, add those products, and divide by the total of the weights. Course grades often work this way: a final worth 50% has five times the pull of a quiz worth 10%.
Is the average the same as the mean?
In everyday use, yes. Average usually means the arithmetic mean: the sum divided by the count. Strictly speaking, the median and mode are also kinds of average, which is why reports sometimes say median income or median price. This calculator shows all three.
How do I average percentages?
If each percentage comes from the same sized group, a plain average works. If the groups differ in size, weight each percentage by its group size. Averaging 50% of 10 people and 90% of 90 people gives 86%, not the 70% a plain average would show.
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