"Average" usually means the arithmetic mean: add the numbers and divide by how many there are. Statistics recognises other measures of the centre, though. The median is the middle value once the list is sorted, and the mode is the value that appears most often. Each answers a slightly different question. This average calculator computes all three from a list you type or paste, along with the range, the sum and the standard deviation, so you can see how spread out the numbers are.
Teachers averaging test scores may also want the test grade calculator. Students combining weighted assignment categories should use the grade calculator, because a simple mean ignores the weights.
How to use the average calculator
- Type or paste your numbers, separated by commas, spaces or line breaks. Copying a spreadsheet column works.
- Read the mean, then compare it with the median. A big gap suggests outliers or a skewed list.
- The mode line lists every value tied for most frequent, or says there is no mode.
- Use the sample standard deviation when your numbers are a sample from a larger group, and the population value when they are the whole group.
Formula
Worked example
Eight quiz scores: 78, 85, 92, 85, 64, 99, 85, 71.
- Sum: 78 + 85 + 92 + 85 + 64 + 99 + 85 + 71 = 659. Mean: 659 ÷ 8 = 82.375.
- Sorted: 64, 71, 78, 85, 85, 85, 92, 99. With eight values, the median is the average of the 4th and 5th: (85 + 85) ÷ 2 = 85.
- Mode: 85 appears three times, so the mode is 85.
- Range: 99 − 64 = 35.
Mean, median or mode: which average should you use?
The mean uses every value, which makes it sensitive to outliers. One very low score pulls a class mean down noticeably. The median isn't affected by how extreme the highest and lowest values are, which is why house prices and incomes are usually reported as medians. The mode is the only average that works for categories (the most common shoe size or answer choice) and is useful when you care about the typical case.
OpenStax Introductory Statistics (section 2.6) explains that in skewed data the mean is pulled toward the long tail, away from the median. In the example above the mean (82.4) is below the median (85) because of the low score of 64.
Weighted averages
If some values count more than others, a plain mean is wrong. Multiply each value by its weight, add the products, and divide by the total weight. Course grades with categories (homework 20%, tests 50%, final 30%) and GPAs weighted by credit hours both work this way; see the grade calculator and the college gpa calculator.
Caveats and assumptions
- Entries that aren’t numbers are ignored and counted in the working line.
- Thousands separators are not supported: enter 1500, not 1,500 (a comma separates values).
- A list in which no value repeats has no mode; if several values tie, all are listed.
- Results are rounded to four decimal places for display.
Frequently asked questions
How do I calculate the average of a list of numbers?
Add all the numbers and divide by how many there are. For 4, 8 and 9: (4 + 8 + 9) ÷ 3 = 7.
How do I find the median with an even number of values?
Sort the values and average the two in the middle. For 3, 5, 8, 10 the median is (5 + 8) ÷ 2 = 6.5.
Can there be more than one mode?
Yes. If two or more values tie for the highest frequency, each is a mode, and the data are called bimodal or multimodal.
What is the difference between sample and population standard deviation?
The sample version divides by n − 1 instead of n to correct for estimating spread from a sample. Use it when your list is a sample of a larger group.
Why is my mean different from my median?
Extreme values pull the mean towards them, while the median stays at the middle of the sorted list. A large gap usually means the data are skewed or contain outliers.
Sources
- OpenStax Introductory Statistics 2e — 2.5 Measures of the Center of the Data — mean, median, mode and skew
- OpenStax Prealgebra 2e — 5.5 Averages and Probability — mean, median and mode definitions
- OpenStax Introductory Statistics 2e — 2.6 Skewness and the Mean, Median, and Mode — how skew separates mean and median
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