How to use the average calculator
- On the Basic tab, type or paste your list into Numbers, separated by commas, spaces or new lines. Results update as you type.
- Read the Mean, Median, Mode, Range, Sum, Count, Min and Max.
- When some numbers count more than others, open Weighted and enter a Value and a Weight on each row.
- To keep a tally as numbers arrive, open Running and use Next number and Add.
How each average is calculated
Mean = sum ÷ count
The median is the middle value of the sorted list, or the mean of the two middle values when the count is even. The mode is the value that appears most often. The range is the largest value minus the smallest. A weighted average is Σ (value × weight) ÷ Σ weight, and a running average is the sum so far divided by how many numbers you have added. NIST's handbook covers mean, median and mode, and Wikipedia explains the weighted mean.
Worked example
The Basic tab opens with 12, 15, 18, 22, 22, 29. The sum is 118 and the count is 6, so the mean is 118 ÷ 6 = 19.666667. The sorted list puts 18 and 22 in the middle, so the median is 20. The value 22 appears twice, so the mode is 22, and the range is 29 - 12 = 17. On Weighted, the starting rows 85 (weight 3), 90 (2) and 70 (5) give 785 ÷ 10 = 78.5, lower than the simple average of 81.666667 because the 70 carries the most weight. On Running, 80, 90 and 85 give 80, 85 and 85.
Limits and edge cases
- Commas always separate numbers, so 1,200 is read as 1 and 200. The page warns you when it sees that pattern.
- Entries that are not numbers are skipped and listed under the box. The calculator reads up to 100,000 numbers.
- One extreme value moves the mean a lot and the median very little, so use the median for skewed data such as incomes.
- To see how spread out your numbers are, use the standard deviation calculator. For a course grade, use the grade calculator, and for percent change or percent of a number, use the percentage calculator.
Average calculator FAQ
How do you calculate the average of a set of numbers?
Add the numbers and divide by how many there are. For 12, 15, 18, 22, 22 and 29, the sum is 118 and the count is 6, so the average is 118 ÷ 6 = 19.666667.
What is the difference between mean, median and mode?
The mean is the sum divided by the count, the median is the middle value of the sorted list, and the mode is the value that appears most often. For 1, 2, 3, 4 and 100 the mean is 22 but the median is 3, which is closer to a typical value.
How do I calculate a weighted average?
Multiply each value by its weight, add the products, and divide by the total of the weights. Values 85, 90 and 70 with weights 3, 2 and 5 give 785 ÷ 10 = 78.5. The weights do not have to add up to 100.
Can a list have more than one mode, or no mode?
Yes to both. If two or more values tie for the most appearances, all of them are modes. If every value appears once, there is no mode, and the calculator shows No mode.
How do I find the average of percentages?
If every percentage is out of the same total, the plain mean works. If the groups differ in size, use the Weighted tab with each group's size as its weight. A 50% result from 10 students and an 80% result from 90 students average (50 × 10 + 80 × 90) ÷ 100 = 77%, not 65%.
Sources: NIST/SEMATECH e-Handbook of Statistical Methods, Measures of Location; Weighted arithmetic mean.