Find the mean
Add the five values to get 30, then divide by five. The mean gives you the center to measure from.
(2 + 4 + 6 + 8 + 10) / 5 = 6
A LITTLE LESS GUESSWORK. A LOT MORE CLARITY.
MAD Calculator
This MAD calculator finds the mean absolute deviation of your data—the average distance from the mean. Enter your numbers to see each distance, or switch to median mode.
Your result
02 / OUTPUTA clearer picture of your data.
Enter your numbers, then select Calculate MAD. The calculator will show your result and the distance of each value from the selected center.
Every number. Every step.Results use JavaScript floating-point arithmetic. ≈ marks rounded values.
Data points
The breakdown
| # | Value | Absolute deviation |
|---|
✓ Step-by-step results✓ Mean & median modes✓ No sign-up needed
START WITH YOUR NUMBERS
How to use the MAD calculator
- Enter your data. Type or paste one group of numbers into the calculator. Use a decimal point for decimals; a comma separates values, so
1,000means two numbers, not one thousand. - Choose a method. Leave the calculator in mean mode for average distance from the mean. Select median mode only when your question asks for it.
- Calculate and review. The calculator shows the MAD, data count, center, and individual distances in the results table.
The MAD calculator keeps repeated values because each observation counts. After editing your data or changing modes, select Calculate MAD again. Load example fills a practice set; Clear removes your input and result.
UNDERSTAND THE FORMULA
01What is MAD?
Mean absolute deviation tells you how far the numbers are from their mean, on average. The mean is the sum of the numbers divided by how many there are. A deviation is a difference from that mean; its absolute value gives the distance.
The MAD formula in plain English
MAD = total distance from the mean ÷ number of values
MAD = Σ |xᵢ − x̄| / n
The symbols are a shorter way to write those same instructions. Read the formula from the inside out: subtract the mean, take each distance, add the distances, then divide by the count.
What does each symbol mean?
Match each symbol to the example data: 2, 4, 6, 8, 10.
| Symbol | Meaning | In this example |
|---|---|---|
| MAD | The average of all the distances: your final answer. | 2.4 |
| xᵢ | One number from your data. | 2, 4, 6, 8, or 10 |
| i | A small position label called a subscript, not multiplication. | x₁ = 2; x₂ = 4 |
| x̄ | “X-bar”: the mean of the data. | 6 |
| xᵢ − x̄ | One number minus the mean. | 2 − 6 = −4 |
| | | | Absolute value: distance without a negative sign. | |−4| = 4 |
| Σ | “Sigma”: add the distances together. | 4 + 2 + 0 + 2 + 4 = 12 |
| n | The number of values, not their sum. | 5 |
| / | Division, also written as a fraction bar. | 12 ÷ 5 = 2.4 |
TRY IT YOURSELF
02How to calculate MAD by hand
Use the MAD calculator to check your answer after working through these steps for 2, 4, 6, 8, 10.
Measure each distance
Subtract 6 from each value. The differences are −4, −2, 0, 2, and 4. Take their absolute values.
|2 − 6|, |4 − 6|, |6 − 6|, |8 − 6|, |10 − 6|
= 4, 2, 0, 2, 4
Average the distances
The distances total 12. Divide by 5 because you are averaging five distances, including the zero.
(4 + 2 + 0 + 2 + 4) / 5 = 2.4
Why take absolute values?
Without them, the negative and positive differences cancel: −4 − 2 + 0 + 2 + 4 = 0. That would hide the spread. Compare these distances with the breakdown in the calculator to check your work. A number four units below the mean is just as far away as one four units above it.
The mean absolute deviation is 2.4. In a sentence: “The numbers are 2.4 units away from the mean, on average.” This does not mean every number is exactly 2.4 units away.
PUT THE ANSWER IN CONTEXT
Understanding your MAD calculator results
A mean tells you the center; MAD adds information about the spread. Consider these two groups of daily reading times, measured in minutes:
- 4, 5, 6: mean = 5; mean MAD ≈ 0.666667 minutes.
- 1, 5, 9: mean = 5; mean MAD ≈ 2.666667 minutes.
Both groups average five minutes, but the second varies more. Try each group in the MAD calculator and compare the distance columns: the second group has more time values farther from five.
A lower MAD means less spread, not automatically a better outcome. The calculator’s result uses your original units, such as minutes or centimeters; it is not a percentage. Convert to matching units before comparing groups, and consider their typical sizes too.
The calculator uses ≈ to mark rounded results. Keep full precision while calculating and round your final answer to the places requested in your assignment.
CHOOSE THE RIGHT MEASURE
03Mean MAD, median MAD, or standard deviation?
| Measure | Calculation | Useful for |
|---|---|---|
| Mean absolute deviation | Average distance from the mean. | Describing average distance in the original units. |
| Median absolute deviation | Median distance from the median. | Describing spread with less influence from extreme values. |
| Standard deviation | Square root of summed squared differences divided by n (population) or n − 1 (sample). | Analyses that give large differences more weight. |
How median mode works
The median is the middle value after sorting. With an even count, average the middle two values. Find each distance from that center, then take the median of those distances: median(|xᵢ − median(x)|).
For 1, 2, 100, mean MAD is about 43.777778, but median MAD is 1. The extreme value changes the measures differently. This MAD calculator reports raw median MAD, without a scaling factor.
Further reading: NIST’s guide to measures of scale.
CHECK YOUR WORK
Common mistakes when calculating MAD
If your answer differs from the MAD calculator result, check these steps before starting over:
- Use the requested center. Mean and median are different, even though both measures may be called MAD.
- Keep every distance. Take absolute values and include zeros. The calculator lists repeated input values separately.
- Divide by n for mean MAD. The n − 1 rule belongs to sample variance and standard deviation, not this calculation.
- Round at the end. Rounding the mean first can change the distances.
- Check the input count. Compare the data count shown by the calculator with your original list. An extra comma in a large number may split it into two values.
YOUR NEXT QUESTIONS
MAD calculator FAQ
More help with inputs, different answers, and other ways to calculate.
Which mode should I choose in the MAD calculator?
MAD can mean mean absolute deviation or median absolute deviation. Match the mode to the full name in your assignment. This MAD calculator defaults to mean mode. Forecasting MAD instead measures errors between paired actual and predicted values; that two-column calculation is not supported here.
Can the calculator handle negative numbers and decimals?
Yes. Enter signs and decimal points as written; do not turn negative inputs positive first. For −2, 0, and 2, the mean is 0 and the distances are 2, 0, and 2. Mean MAD is approximately 1.333333.
Why does the calculator show zero for different values?
Check your selected mode. Mean MAD is zero only when all values are equal. Median MAD can be zero for unequal values: for 1, 1, and 9, the median is 1. The distances are 0, 0, and 8, whose median is 0.
Why does my answer differ from the calculator’s result?
Compare the input count and method, then check whether you rounded the mean before calculating distances. Some tools multiply median MAD by about 1.4826 to estimate a normal distribution’s standard deviation. Our MAD calculator reports the raw value, so the scaled result will differ.
Can I paste numbers from Excel into the calculator?
Yes. Copy a column of numeric cells without headers or units. Multiple rows or columns are treated as one data set, not calculated separately. Remove thousands separators before pasting.
To check mean MAD in Excel, use =AVEDEV(A1:A10). For median MAD, enter =ABS(A1-MEDIAN($A$1:$A$10)) in B1, fill down to B10, then use =MEDIAN(B1:B10). Adjust the ranges to your numeric cells and avoid blanks in this helper-column example.
Why did my result disappear after I changed the input?
The MAD calculator hides the previous result whenever you edit your numbers or change modes, so you do not mistake an old answer for a new one. Select Calculate MAD again when you are ready. Load example fills the input without calculating automatically.
Does the calculator save or upload my numbers?
No. Calculations run in your browser, and your entries are not uploaded or saved by the site. You do not need an account. Website delivery may involve hosting access logs; see our Privacy Policy for the distinction between calculation inputs and website visits.