What Is Mean Absolute Value?
The mean absolute value is the average of the numbers after you drop their signs. It tells you the typical size of the values, whether they are positive or negative, so positives and negatives no longer cancel.
Enter your numbers, including negatives. The calculator returns the mean absolute value, the mean absolute deviation about the mean, the ordinary mean, the median of the absolute values and the root mean square, with a table of each value's absolute value.
People often confuse the mean absolute value with the mean absolute deviation. The first measures size, the second measures spread around the mean, so check which one your problem asks for.
How to Use the Mean Absolute Value Calculator
- Enter your numbers, including negatives.
- Read the mean absolute value.
- Compare it with the mean absolute deviation if your problem is about spread.
Mean Absolute Value Formula
Mean absolute value
Mean absolute deviation
Mean Absolute Value Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| x | Each number in the list | |
| |x| | Absolute value, the size without the sign | |
| n | How many numbers | |
| x̄ | Ordinary mean |
Mean Absolute Value Worked Example
With the example values loaded in the calculator above, the steps are:
- Take the absolute value of each number: 3, 1, 8, 5, 6.
- Add them: 23.
- Divide by n = 5: mean absolute value = 4.6.
- For comparison, the mean absolute deviation measures distance from the mean, 2.2: it is 4.16.
Result: Mean absolute value = 4.6; Mean absolute deviation (about the mean) = 4.16.
Worked example: 3, −1, 8, −5, 6
The absolute values are 3, 1, 8, 5 and 6, which add to 23. The mean absolute value is 23 ÷ 5 = 4.6.
The ordinary mean is 11 ÷ 5 = 2.2, because the negative values cancel part of the positive ones.
Mean absolute value versus mean absolute deviation
People often mix up the two. The mean absolute value measures the typical size of the numbers. The mean absolute deviation measures the typical distance from the mean, so it describes spread. For the numbers above, the first is 4.6 and the second, measured from the mean of 2.2, is 4.16.
Where Mean Absolute Value Is Used
Typical size of errors
Average the sizes of positive and negative errors without cancellation.
Signed data
Describe the typical magnitude of gains and losses.
Telling MAD and MAV apart
See both quantities for the same list.
Common Mean Absolute Value Mistakes to Avoid
- If every number is positive, the mean absolute value equals the ordinary mean.
- The mean absolute value is never smaller than the absolute value of the ordinary mean.
Mean Absolute Value Terms and Definitions
- Absolute value
- The size of a number without its sign: |−4| = 4.
Mean Absolute Value FAQs
What is the mean absolute value?
The average of the absolute values of a list of numbers.
How do you calculate it?
Take the absolute value of each number, add them and divide by how many there are.
Is it the same as the mean absolute deviation?
No. The deviation version subtracts the mean first, so it measures spread rather than size.
Why is it different from the ordinary mean?
Positive and negative numbers cancel in the ordinary mean but not in the mean absolute value.
When is the mean absolute value used?
To describe the typical size of signed quantities such as errors, returns or deviations.
Can it be negative?
No. It is an average of non-negative numbers.