Average Calculator
Press Calculate to see the results.
Paste or type numbers separated by commas, spaces or line breaks, and this average calculator returns their arithmetic mean along with the sum and count.
An average condenses a list of numbers into one representative value. This tool uses the arithmetic mean, the everyday meaning of average: add the numbers and divide by how many there are. It also reports the median, mode and geometric mean so you can see whether the mean tells the whole story.
What is an average?
In everyday speech an average is a typical or central value of a group. Mathematicians call such a value a measure of central tendency, and there are several. The arithmetic mean is by far the most common: the total of all values shared out equally. If seven friends have 10, 2, 38, 23, 38, 23 and 21 marbles, together they have 155, and if they pooled and split them evenly each would get 155 ÷ 7 ≈ 22.14.
The median is the middle value once the list is sorted, and the mode is the value that occurs most often. In the marble example the sorted list is 2, 10, 21, 23, 23, 38, 38, so the median is 23, and both 23 and 38 appear twice, making two modes. When a list contains an extreme value, such as one person with 1,000 marbles, the mean is pulled strongly toward it while the median barely moves. That is why house prices and incomes are usually reported as medians.
The geometric mean multiplies the values and takes the nth root. It is the right average for growth rates and ratios: an investment that gains 50% one year and loses 50% the next has an arithmetic average return of 0% but actually ends 25% down, which the geometric mean of the growth factors 1.5 and 0.5, √0.75 ≈ 0.866, correctly reflects.
Average = (x₁ + x₂ + … + xₙ) ÷ n
- xᵢ
- each number in the list
- n
- how many numbers there are
Sometimes the values should not count equally. A course grade where homework is worth 20%, the midterm 30% and the final 50% is a weighted average: multiply each score by its weight, add the products, and divide by the total weight. Scores of 90, 75 and 82 give (0.2 × 90 + 0.3 × 75 + 0.5 × 82) ÷ 1 = 81.5.
A grade point average works the same way, with credit hours as weights, and so does the average price of shares bought at different prices. If you enter a value several times in the list above, it is effectively given extra weight, which is a quick way to compute a weighted average with whole-number weights.
Frequently asked questions
How do I calculate an average?
Add all the numbers together and divide by how many numbers there are. The average of 4, 8 and 9 is 21 ÷ 3 = 7.
What is the difference between mean, median and mode?
The mean is the sum divided by the count, the median is the middle value when sorted, and the mode is the most frequent value.
Can an average be a number that is not in the list?
Yes. The mean of 1 and 2 is 1.5, which is in neither position of the list. The median of an even-length list can also fall between two values.
When should I use the median instead of the mean?
Use the median when the data is skewed or has outliers, such as incomes or home prices, because a few extreme values can distort the mean.
How do I calculate a weighted average?
Multiply each value by its weight, add the products, and divide by the sum of the weights. Exam scores of 80, 90 and 70 weighted 25%, 25% and 50% give (0.25 × 80 + 0.25 × 90 + 0.5 × 70) ÷ 1 = 77.5, lower than the simple average of 80 because the weakest score carries the most weight.
How do I work out my average share price after buying more?
Divide the total amount paid by the total number of shares. Buying 100 shares at $50 and then 50 more at $38 costs $5,000 + $1,900 = $6,900 for 150 shares, an average of $46 a share. That is a weighted average with share counts as weights, which is why averaging down moves the price less than the simple average of the two prices, $44.
Updated by Calculator.hair. How we build and check our calculators