The mean absolute deviation (MAD) is the average distance between each data value and the mean. Find the mean, find how far each value is from it, then average those distances. A small MAD means the data cluster close to the mean; a large MAD means they are spread out.
In Spanish
desviación media absoluta
Also called
MAD, average absolute deviation, mean deviation
Grade level
6-8
Grade 6Grade 7CCSS 6.SP.B.5.cSTAARSBACPARCC
Mean Absolute Deviation in a picture
The MAD measures every value’s distance to the mean and averages those distances. Distances on either side count the same.
Formal definition and notation
For data values x1, …, xn with mean x̄, the mean absolute deviation is MAD = Σ |xi − x̄|n: add the absolute values of the deviations xi − x̄ and divide by the number of values. Absolute values are needed because the signed deviations always add to 0. The MAD is in the same units as the data and is a measure of variability.
how far each value is from the mean (never negative)
n
the number of values
Three steps: find the mean, find each distance from the mean, then find the mean of the distances.
Mean Absolute Deviation examples, step by step
Example 1: MAD of four values
Warm-up
Find the mean absolute deviation of 3, 5, 7, 9.
Mean: 3 + 5 + 7 + 94 = 244 = 6.
Distances from 6: 3, 1, 1, 3.
Average the distances: 3 + 1 + 1 + 34 = 84 = 2.
Answer: The MAD is 2.
Example 2: Unordered data
Core
Five plants grew 12, 15, 10, 18 and 20 cm. Find the MAD.
Mean: 12 + 15 + 10 + 18 + 205 = 755 = 15.
Distances from 15: |12 − 15| = 3, 0, 5, 3, 5.
Sum of distances: 3 + 0 + 5 + 3 + 5 = 16.
MAD: 165 = 3.2.
Answer: The MAD is 3.2 cm.
Example 3: Which class is more consistent?
Test-style
Class A scored 6, 7, 8, 9, 10 on a quiz. Class B scored 2, 5, 8, 11, 14. Both means are 8. Use the MAD to decide which class has more consistent scores.
Class A distances from 8: 2, 1, 0, 1, 2. MAD = 65 = 1.2.
Class B distances from 8: 6, 3, 0, 3, 6. MAD = 185 = 3.6.
The smaller MAD means scores stay closer to the mean.
Answer: Class A is more consistent: its MAD is 1.2, compared with 3.6 for Class B.
Common mistakes
✗ MistakeKeeping the signs: deviations −4, −2, 0, 2, 4 give MAD = 05 = 0.
Standard deviation squares the deviations, averages them and takes a square root, so big deviations count more. For 2, 4, 6, 8, 10 the MAD is 2.4 and the population standard deviation is about 2.83.
The range uses only the two extreme values: 10 − 2 = 8. The MAD averages how far all the values are from the mean.
Quick check: 3 questions
Question 1 of 3
What is the MAD of 1, 3, 5, 7?
Show answer and explanation
Answer: B. The mean is 4, the distances are 3, 1, 1, 3, and 84 = 2. 4 is the mean, 0 comes from keeping the signs, and 8 is the sum of the distances before dividing.
Question 2 of 3
Data set P has MAD 1.5 and data set Q has MAD 6. Which statement is true?
Show answer and explanation
Answer: C. A larger MAD means values are farther from the mean on average, so Q is more spread out. The MAD says nothing about the size of the mean or the number of values.
Question 3 of 3
The data 10, 10, 10, 10 have what MAD?
Show answer and explanation
Answer: D. Every value equals the mean, 10, so every distance is 0 and the MAD is 0. 10 is the mean, 40 is the sum and 1 has no basis.
Mean Absolute Deviation: frequently asked questions
Why do you use absolute value in the mean absolute deviation?
Because values below the mean give negative deviations and values above give positive ones, and they always cancel to a total of 0. Taking the absolute value turns each deviation into a distance, which is never negative, so the average of the distances shows how far values typically sit from the mean.
What does a MAD of 0 mean?
It means every value in the data set is exactly the same, so each one equals the mean and has distance 0. For example, 7, 7, 7, 7 has a mean of 7 and a MAD of 0. Any data set with at least two different values has a MAD greater than 0.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 6.SP.B.5.c
Cite this entry
Effortless Math Team. “Mean Absolute Deviation.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/mean-absolute-deviation/
Flashcard
TermMean Absolute Deviationaverage distance from the mean
DefinitionAverage how far each value is from the mean. For 2, 4, 6, 8, 10 (mean 6) the distances are 4, 2, 0, 2, 4, so MAD = 2.4.
MeanThe mean is the sum of the values divided by the number of values. It is the arithmetic average: add every value and divide by how many there are. For 3, 7, 5 and 9, the mean is 24 ÷ 4 = 6. The mean is the balance point of the data, so one outlier can pull it far.Statistics · Grade 5, Grade 6, Grade 7DataData are facts or values collected to answer a question, such as survey answers, measurements or counts. Numerical data are numbers you measure or count, like heights; categorical data are labels or groups, like favorite colors. Data are organized in tables and shown in graphs so patterns are easy to see.Statistics · Grade 2, Grade 3, Grade 6Absolute ValueThe absolute value of a number is its distance from zero on the number line, so it is never negative. It is written with two vertical bars: |−6| = 6 and |6| = 6. A positive number and 0 keep their value; a negative number loses its minus sign.Number System · Grade 6, Grade 7, Grade 8NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2AverageAn average is one number that stands for the typical size of the values in a data set. In everyday math, average means the mean: add all the values, then divide by how many values there are. In statistics, the median and the mode are also kinds of average.Statistics · Grade 5, Grade 6, Grade 7MedianThe median is the middle value when data are listed in order. If there is an even number of values, the median is the average of the two middle values. Half the data lie at or below the median and half at or above it, and outliers barely move it.Statistics · Grade 5, Grade 6, Grade 7Interquartile RangeThe interquartile range (IQR) is the spread of the middle half of a data set: the third quartile minus the first quartile, IQR = Q3 − Q1. Because it ignores the lowest and highest quarters of the data, outliers barely change it. In a box plot it is the length of the box.Statistics · Grade 6, Grade 7, Algebra 1Standard DeviationStandard deviation is a number that measures how spread out data values are from their mean: roughly, the typical distance of a value from the mean. A small standard deviation means the values cluster near the mean; a large one means they are spread out. It is the square root of the variance.Statistics · Algebra 1, StatisticsSquareA square is a quadrilateral with four equal sides and four right angles. It is a special rectangle and a special rhombus at the same time. For a square with side s, the perimeter is 4s, the area is s2, and each diagonal is s√2.Geometry · Kindergarten, Grade 2, Grade 3Square RootA square root of a number is a value that, multiplied by itself, gives that number. The square root of 36 is 6 because 6 × 6 = 36. Every positive number has two square roots, such as 6 and −6, but the radical sign √ means the principal square root, which is the non-negative one.Number System · Grade 8, Algebra 1PopulationA population in statistics is the whole group of people, animals or objects you want to learn about, such as every student in a school or every bulb a factory makes. Measuring all of them is often too costly, so you study a sample, a part of the population, and use it to draw conclusions about the whole group.Statistics · Grade 7, Statistics, Algebra 1RangeThe range of a data set is the difference between the greatest and least values: maximum minus minimum. For 2, 5, 9, the range is 9 − 2 = 7. Range is a simple measure of spread: it tells how far apart the extreme values are, though one outlier can make it misleading about the rest of the data.Statistics · Grade 5, Grade 6, Grade 7Dot PlotA dot plot is a graph that shows each data value as a dot above its place on a number line. Dots for repeated values stack up in a column, so the tallest stack shows the mode, and you can see the center, spread, gaps and outliers of the data at a glance.Statistics · Grade 3, Grade 4, Grade 5VarianceVariance is a measure of spread: the average of the squared distances of the data values from their mean. Find each value’s distance from the mean, square it, add the squares, and divide by n for a population (or n − 1 for a sample). Larger variance means more spread. Its square root is the standard deviation.Statistics · Algebra 1, Statistics