Mean Absolute Deviation Calculator
Enter your numbers to find the mean absolute deviation, the average distance of each value from the mean, with the working shown.
- MAD with steps
- Absolute deviations table
- Compare with SD
- Paste from Excel
Your data
8 values.
Results
Mean absolute deviation (MAD)
3.75
Mean (x̄)
9
Sample standard deviation (s)
4.5981
Count (n)
8
Center
- Count (n)
- 8
- Sum (Σx)
- 72
- Mean
- 9
- Median
- 7.5
- Mode
- 6 (×2)
Spread
- Sample standard deviation (s)
- 4.5981
- Population standard deviation (σ)
- 4.3012
- Sample variance (s²)
- 21.1429
- Population variance (σ²)
- 18.5
- Sum of squares (SS)
- 148
- Mean absolute deviation
- 3.75
- Standard error of the mean
- 1.6257
- Coefficient of variation (σ ÷ mean)
- 47.79%
- Minimum
- 3
- Maximum
- 16
- Range
- 13
Quartiles and outliers
- Q1
- 6
- Q3
- 13
- Interquartile range (IQR)
- 7
- Five number summary
- 3, 6, 7.5, 13, 16
- Outlier fences
- −4.5 and 23.5
- Outliers (1.5 × IQR)
- None
Empirical rule (using σ)
- Within 1 SD (68% if normal)
- 5 of 8 (62.5%)
- Within 2 SD (95% if normal)
- 8 of 8 (100%)
- Within 3 SD (99.7% if normal)
- 8 of 8 (100%)
Step-by-step working
Count the values
n = 8
Find the mean
x̄ = Σx ÷ n
Σx = 3 + 6 + 6 + 7 + 8 + 11 + 15 + 16 = 72
x̄ = 72 ÷ 8 = 9
Find the distance of each value from the mean (ignore minus signs)
|x − x̄|
|3 − 9| = 6
|6 − 9| = 3
|6 − 9| = 3
…and the same for every value. The table lists them all.
Add up the absolute deviations
Σ|x − x̄|
Σ|x − x̄| = 6 + 3 + 3 + 2 + 1 + 2 + 6 + 7 = 30
Divide by the number of values
MAD = Σ|x − x̄| ÷ n
MAD = 30 ÷ 8 = 3.75
| # | x | x − μ | |x − x̄| | z |
|---|---|---|---|---|
| 1 | 3 | −6 | 6 | −1.395 |
| 2 | 6 | −3 | 3 | −0.6975 |
| 3 | 6 | −3 | 3 | −0.6975 |
| 4 | 7 | −2 | 2 | −0.465 |
| 5 | 8 | −1 | 1 | −0.2325 |
| 6 | 11 | 2 | 2 | 0.465 |
| 7 | 15 | 6 | 6 | 1.395 |
| 8 | 16 | 7 | 7 | 1.6275 |
| Σ | 72 | 0 | 30 |
Rows with |z| above 3 are highlighted. The Σ row of x shows Σx.
What is the mean absolute deviation?
The mean absolute deviation (MAD) is the average distance between each value and the mean. Find the mean, work out how far each value is from it while ignoring minus signs, add those distances and divide by how many values there are. A MAD of 3 means values are, on average, 3 units from the mean. It is a simpler measure of spread than the standard deviation, which is why it is taught first in middle school (Common Core grade 6 and 7), and it is less affected by a single extreme value because distances are not squared. The calculator also shows the standard deviation so you can compare the two; for most data the standard deviation is a little larger than the MAD.
How to find the mean absolute deviation
- Type or paste your numbers, separated by commas, spaces or new lines.
- Read the MAD at the top of the results, with the mean and count beside it.
- Follow the steps: the mean, each value’s absolute deviation |x − x̄|, their sum and the division by n.
- Copy the result or the table for homework or a worksheet.
Mean absolute deviation formulas
- Mean absolute deviation
MAD = Σ|x − x̄| ÷ n
Average distance from the mean.
- From a frequency table
MAD = Σf|x − x̄| ÷ Σf
Weight each distance by its frequency.
- Mean
x̄ = Σx ÷ n
The centre the distances are measured from.
- Compared with standard deviation
σ = √( Σ(x − μ)² ÷ N )
Squares the distances instead of taking absolute values.
Why use this mean absolute deviation calculator
- Working shown with your numbersEvery answer comes with the formula and each line of arithmetic filled in with your data, plus a table of deviations, so you can check homework or copy the method into an exam answer.
- Absolute deviations tableEvery value’s distance from the mean is listed, the same table teachers ask you to fill in.
- MAD and SD side by sideSee the mean absolute deviation next to the standard deviation, variance and range to understand how they differ.
- Frequency tables and grouped dataType each value once with how often it appears, or enter class intervals such as 10-19 and the calculator uses their midpoints. No need to repeat a value 30 times.
- Paste straight from a spreadsheetCopy a column from Excel, Google Sheets or Numbers and paste it. Commas, spaces, tabs and new lines all work, headers like “Score” are skipped, and multi-column pastes let you pick one column.
- Private, free and instantCalculations run in your browser as you type. Nothing is sent to a server, there is no sign-up, no limit on how many numbers you enter and no “show steps” paywall.
Common uses for the mean absolute deviation
- Middle school math. Check grade 6 and 7 statistics homework and worksheets.
- Grades and test scores. See how spread out a class’s scores are and how far one score sits from the average.
- Sports and fitness. Compare how consistent lap times, scores or training numbers are from week to week.
- Forecast accuracy. Average how far forecasts or estimates were off.
- Quality control. Track how much part sizes, fill weights or process times vary, and spot values outside the usual range.
- Statistics homework. Check answers for AP Statistics, intro stats and lab reports, and copy the step-by-step working.
The same statistics in Excel, Google Sheets and a TI-84
To check an answer or redo it in a spreadsheet, use these functions (they work the same in Google Sheets). On a TI-83 or TI-84, enter the data in L1, press STAT, CALC, 1-Var Stats; for a frequency table put the counts in L2 and set FreqList to L2.
| Statistic | Excel and Google Sheets | TI-84 (1-Var Stats) |
|---|---|---|
| Sample standard deviation (s) | =STDEV.S(A2:A20) | Sx |
| Population standard deviation (σ) | =STDEV.P(A2:A20) | σx |
| Sample variance (s²) | =VAR.S(A2:A20) | Sx² |
| Population variance (σ²) | =VAR.P(A2:A20) | σx² |
| Mean | =AVERAGE(A2:A20) | x̄ |
| Median | =MEDIAN(A2:A20) | Med |
| Mode | =MODE.MULT(A2:A20) | Not shown |
| Q1 and Q3 | =QUARTILE.INC(A2:A20, 1) and 3, or QUARTILE.EXC | Q1, Q3 (textbook method) |
| Sum of squares (SS) | =DEVSQ(A2:A20) | Not shown (Σx² is) |
| Mean absolute deviation | =AVEDEV(A2:A20) | Not shown |
| Standard error of the mean | =STDEV.S(A2:A20)/SQRT(COUNT(A2:A20)) | Sx ÷ √n |
| Z-score of a value | =STANDARDIZE(x, mean, sd) | (x − x̄) ÷ Sx |
| Percentile from a z-score | =NORM.S.DIST(z, TRUE) | normalcdf(−1E99, z) |
What this calculator does that most others leave out
We compared the top standard deviation, variance, z-score and quartile calculators in October 2026. Most return one number for one mode, show the formula without your numbers, or cap the number of values. This one was built to cover the gaps.
- Both versions at once. Most calculators make you pick sample or population first. Here s, σ, s² and σ² are always on screen.
- Working with your own numbers. Not just the formula: the mean, every squared deviation, the sum of squares and the final square root are written out with your data.
- Frequency and grouped data. Enter value and count pairs or class intervals instead of typing repeated numbers.
- Quartiles that match your class. Choose the textbook / TI-84 method or Excel’s QUARTILE.INC or QUARTILE.EXC.
- Z-scores and outliers. Every value gets a z-score, and values beyond 1.5 × IQR or 3 standard deviations are flagged.
- No limits, fully private. Paste thousands of values or open a CSV file. Everything is processed on your device and never sent anywhere.
More math and statistics tools
Only need the mean, median and mode, or a weighted average for grades? Use the average calculator. For percentages and percent change, try the percentage calculator, and to type formulas like σ = √(Σ(x − μ)² ÷ N) for a report, use the online math editor. Browse all student tools and calculators.
Worked example: mean absolute deviation of 8 numbers
Data: 3, 6, 6, 7, 8, 11, 15, 16. 1. Mean: 72 ÷ 8 = 9. 2. Absolute deviations: |3 − 9| = 6, |6 − 9| = 3, 3, 2, 1, 2, 6, 7. 3. Sum of absolute deviations: 30. 4. MAD = 30 ÷ 8 = 3.75. On average, the values are 3.75 away from the mean. For comparison, the sample standard deviation of the same data is 4.5981.
What to expect from the result
This calculator gives the mean absolute deviation around the mean, the version used in school math. The median absolute deviation (also sometimes shortened to MAD) is a different, more robust statistic that uses medians instead. MAD always divides by n, whether the data is a sample or a population.
Mean Absolute Deviation Calculator questions
What is the formula for mean absolute deviation?
MAD = Σ|x − x̄| ÷ n. Subtract the mean from each value, drop any minus signs, add the results and divide by the number of values.
What is the difference between MAD and standard deviation?
Both measure spread around the mean. MAD averages the plain distances; standard deviation squares them first, averages, then takes the square root. Squaring gives large deviations more weight, so the standard deviation is usually larger and more sensitive to outliers.
What does the mean absolute deviation tell you?
How far values typically are from the average. A small MAD means the data is clustered tightly around the mean; a large MAD means it is spread out. It is in the same units as the data.
Is mean absolute deviation the same as median absolute deviation?
No. Mean absolute deviation averages the distances from the mean. Median absolute deviation takes the median of the distances from the median and is used in robust statistics. School courses mean the first one.
Is my data sent to a server?
No. The calculator runs entirely in your browser. Numbers you type, paste or open from a file never leave your device, which makes it safe for unpublished research, grades and business data.