Mean Absolute Deviation Calculator

A Mean Absolute Deviation Calculator is a free online statistics tool that helps you measure how far numerical observations are, on average, from a selected center value.

The most common version is mean absolute deviation from the mean, where the absolute distance between each value and the arithmetic mean is averaged.

Calculator Pool’s free Mean Absolute Deviation Calculator online also lets you calculate the average absolute distance from the median. This makes it useful for understanding different ways of measuring data dispersion.

The calculator provides:

• Mean Absolute Deviation
• Selected center
• Mean
• Median
• Total Absolute Deviation
• Count
• Minimum
• Maximum

For example, consider:

10, 20, 30, 40, 50

The mean is:

30

The absolute deviations from the mean are:

20, 10, 0, 10, 20

Their sum is:

60

Therefore:

MAD = 60 ÷ 5 = 12

So the Mean Absolute Deviation = 12.

Important: Mean absolute deviation depends on the center used. MAD from the mean and MAD from the median can produce different results. Also, “mean absolute deviation from the median” should not be confused with the separate robust statistic called “median absolute deviation,” which takes the median of the absolute deviations.

What Is Mean Absolute Deviation?

Mean Absolute Deviation, commonly abbreviated as MAD, is a measure of statistical dispersion.

It tells you the average absolute distance between observations and a chosen center.

For mean absolute deviation from the mean:

MAD = Σ|x − x̄| ÷ n

where:

• x = each observation
• x̄ = arithmetic mean
• n = number of observations
• |x − x̄| = absolute deviation from the mean

In simple terms, it answers:

“On average, how far are the observations from the center?”

Because absolute values are used, negative and positive deviations do not cancel each other out.

What Is a Mean Absolute Deviation Calculator?

A Mean Absolute Deviation Calculator is an online statistics calculator that automatically calculates the average absolute distance of observations from a selected center.

Calculator Pool lets you choose:

Mean

or:

Median

as the center.

The calculator then returns:

Mean Absolute Deviation

along with:

Mean

Median

Total Absolute Deviation

Count

Minimum

and:

Maximum

This makes the tool useful for students, teachers, researchers and anyone working with numerical data.

How to Use the Mean Absolute Deviation Calculator

Using Calculator Pool’s online mean absolute deviation calculator is simple.

Step 1: Enter Your Numbers

Enter a dataset such as:

10, 20, 30, 40, 50

You can also enter values using spaces or line breaks.

Step 2: Choose the Center

Select:

Mean

or:

Median

from the Deviation From option.

Step 3: Calculate

Click:

Calculate MAD

The calculator immediately displays the result and supporting statistics.

Mean Absolute Deviation Formula

The standard mean absolute deviation formula about the mean is:

MAD = Σ|x − x̄| ÷ n

For mean absolute deviation about the median, replace the center with the median:

MAD from Median = Σ|x − Median| ÷ n

The main idea remains the same:

Find each absolute deviation → Add them → Divide by the number of observations

What Does Absolute Deviation Mean?

An absolute deviation is the distance between an observation and the selected center without considering its sign.

For example, if:

Mean = 30

and an observation is:

10

then:

Deviation = 10 − 30 = −20

The absolute deviation is:

|−20| = 20

For an observation of:

50

the deviation is:

50 − 30 = 20

and the absolute deviation is:

20

Both values are therefore 20 units away from the mean.

Why Are Absolute Values Used?

Suppose the dataset is:

10, 20, 30, 40, 50

Mean:

30

Ordinary deviations are:

−20, −10, 0, +10, +20

Adding them gives:

0

That would not measure dispersion.

Using absolute deviations:

20, 10, 0, 10, 20

gives:

60

and the average is:

12

This is why the absolute value is used in mean absolute deviation calculation.

Mean Absolute Deviation Example

Consider:

10, 20, 30, 40, 50

Step 1: Find the Mean

Mean = 30

Step 2: Find Absolute Deviations

Step 3: Add the Absolute Deviations

20 + 10 + 0 + 10 + 20 = 60

Step 4: Divide by the Count

60 ÷ 5 = 12

Therefore:

Mean Absolute Deviation = 12

Mean Absolute Deviation From Median

Calculator Pool also allows you to calculate absolute deviation from the median.

Using:

10, 20, 30, 40, 50

Median:

30

Absolute deviations from the median are:

20, 10, 0, 10, 20

So:

MAD from Median = 12

For this symmetric dataset, MAD from the mean and MAD from the median are the same.

That will not always happen.

Mean Absolute Deviation From Mean vs Median

The selected center affects the result.

MAD From Mean

Uses:

|x − Mean|

MAD From Median

Uses:

|x − Median|

The two values can be different when the dataset is skewed.

For example:

1, 2, 3, 4, 20

Mean:

6

Median:

3

MAD from mean:

6.4

MAD from median:

6.0

This demonstrates why the choice of center matters.

Mean Absolute Deviation Calculation Table

For:

1, 2, 3, 4, 20

The difference occurs because mean and median are different centers for this skewed dataset.

What Is the Total Absolute Deviation?

The total absolute deviation is the sum of all absolute distances from the selected center.

The formula is:

Total Absolute Deviation = Σ|x − center|

Mean absolute deviation is then:

MAD = Total Absolute Deviation ÷ n

For:

10, 20, 30, 40, 50

the total absolute deviation from the mean is:

60

and:

MAD = 60 ÷ 5 = 12

Calculator Pool displays the total absolute deviation so you can better understand the calculation.

MAD and Mean

The mean is one of the most common centers used for absolute deviation.

For each observation:

Absolute deviation = |x − Mean|

The average of these deviations gives:

Mean Absolute Deviation

The arithmetic mean itself is calculated as:

Mean = Σx ÷ n

Calculator Pool also provides a dedicated Average Calculator.

MAD and Median

The median is another center that can be used for absolute-deviation calculations.

For median-based MAD:

MAD = Σ|x − Median| ÷ n

Because the median is often less influenced by extreme observations than the mean, the two approaches can behave differently for skewed datasets.

Is Mean Absolute Deviation the Same as Median Absolute Deviation?

No.

This is a very important distinction.

Mean Absolute Deviation

Calculates the average of the absolute deviations from a chosen center.

For example:

MAD = mean(|x − center|)

Median Absolute Deviation

A separate robust statistic that typically calculates the median of the absolute deviations from the median:

Median Absolute Deviation = median(|x − median(x)|)

Both are sometimes abbreviated as:

MAD

Because of this abbreviation overlap, the full term should be used when clarity matters.

Calculator Pool’s current tool calculates Mean Absolute Deviation, using either the mean or median as the center.

Mean Absolute Deviation vs Median Absolute Deviation

These are different statistics.

This distinction is important when searching for an MAD calculator, because different websites may use the same abbreviation for different statistics.

Mean Absolute Deviation vs Standard Deviation

Both are measures of dispersion.

Mean Absolute Deviation

Uses absolute deviations:

Σ|x − center| ÷ n

Standard Deviation

Uses squared deviations and then takes the square root:

√[Σ(x − mean)² ÷ denominator]

Standard deviation gives greater weight to large deviations because they are squared.

MAD treats deviations linearly using their absolute values.

MAD vs Variance

Variance uses squared deviations:

Variance = Σ(x − mean)² ÷ denominator

Mean absolute deviation uses:

MAD = Σ|x − center| ÷ n

Because variance squares deviations, it is more sensitive to large deviations and outliers.

Calculator Pool also has a dedicated Variance Calculator.

MAD vs Range

The range is:

Maximum − Minimum

Mean absolute deviation considers every observation.

For:

10, 20, 30, 40, 50

Range:

50 − 10 = 40

MAD:

12

Range depends only on the two extremes, while MAD incorporates the entire dataset.

MAD vs IQR

The interquartile range, or IQR, is:

Q3 − Q1

IQR measures the spread between the first and third quartiles.

Mean absolute deviation measures the average absolute distance from a selected center.

Both are measures of dispersion, but they summarize different aspects of a dataset.

Calculator Pool also provides a Quartile Calculator.

MAD vs Percentile

A percentile identifies a value at a specific position in an ordered distribution.

Mean absolute deviation measures average distance from a center.

For example:

75th percentile

and:

MAD

are fundamentally different statistics.

Calculator Pool’s Percentile Calculator handles percentile calculations separately.

MAD vs Mean Absolute Error

These terms sound similar but can refer to different concepts.

Mean Absolute Deviation

Measures average absolute distance of observations from a statistical center.

Mean Absolute Error

Measures average absolute prediction error:

MAE = Σ|Actual − Predicted| ÷ n

MAD is generally descriptive.

MAE is generally used to evaluate predictions or forecasts.

MAD vs Mean Squared Error

Mean Absolute Deviation uses absolute differences.

Mean Squared Error (MSE) uses squared differences.

MAD:

Σ|Error| ÷ n

MSE:

ΣError² ÷ n

MSE gives greater emphasis to larger errors because the errors are squared.

MAD and Outliers

Mean absolute deviation can be affected by outliers, particularly when the mean is used as the center.

For example:

10, 20, 30, 40, 500

The value:

500

creates a very large absolute deviation from the mean.

As a result, MAD increases.

Using the median as the center can sometimes reduce the effect of extreme values compared with using the mean, although mean absolute deviation from the median is still not the same as median absolute deviation.

MAD and Skewed Data

For skewed datasets, the mean and median can be substantially different.

Because MAD depends on the selected center, the result can also differ.

This is one reason Calculator Pool provides both:

Deviation From Mean

and:

Deviation From Median

MAD and Data Spread

A larger MAD generally indicates that observations are farther from the selected center on average.

A smaller MAD generally indicates that observations are closer to the selected center.

For example:

Dataset A

49, 50, 51

has very little spread.

Dataset B

10, 50, 90

has much greater spread.

Their means may both be:

50

but their mean absolute deviations are very different.

Example: Same Mean, Different MAD

Consider:

Dataset A

45, 50, 55

Mean:

50

Absolute deviations:

5, 0, 5

MAD:

10 ÷ 3 ≈ 3.3333

Dataset B

10, 50, 90

Mean:

50

Absolute deviations:

40, 0, 40

MAD:

80 ÷ 3 ≈ 26.6667

Both have the same mean:

50

but Dataset B has much greater dispersion.

Mean Absolute Deviation and Standard Deviation Example

For:

10, 20, 30, 40, 50

Mean:

30

MAD:

12

Population standard deviation:

14.1421

The two statistics measure spread differently.

MAD is based on average absolute distance.

Standard deviation is based on squared deviations.

Mean Absolute Deviation in Statistics

MAD is a useful descriptive statistic in statistics because it provides a direct measure of average absolute distance from a center.

It is easy to explain:

“The observations are, on average, this many units away from the center.”

This makes it particularly useful for introductory statistics.

Mean Absolute Deviation for Students

A mean absolute deviation calculator for students can help with:

• Statistics homework
• Data dispersion problems
• Absolute deviation exercises
• Mean and median
• Descriptive statistics
• Comparing datasets
• Checking manual calculations

It can also help students understand why positive and negative deviations cannot simply be added.

Mean Absolute Deviation Calculator for Data Analysis

A MAD calculator for data analysis can provide a quick measure of dispersion.

A basic workflow is:

Find the center

→ Calculate absolute deviations

→ Sum deviations

→ Divide by count

This is especially useful when you need a simple descriptive measure of average distance from the center.

Mean Absolute Deviation Calculator for Research

A mean absolute deviation calculator for research may be useful for exploratory descriptive analysis.

Researchers can compare MAD with:

• Standard deviation
• Variance
• IQR
• Median
• Percentiles
• Range

The choice of measure should depend on the research question and distribution of the data.

Mean Absolute Deviation for Experimental Data

Suppose repeated measurements are:

98, 99, 101, 100, 102

The MAD can describe the average absolute distance from the mean.

For experimental measurements, this may provide an intuitive description of spread.

Researchers should still select the dispersion statistic that best fits the measurement process and reporting standard.

Mean Absolute Deviation for Exam Scores

Consider exam scores:

70, 72, 75, 78, 80

A mean absolute deviation calculation can show how far the scores are from the average score on average.

This can help compare the consistency of different groups of scores.

Mean Absolute Deviation for Salary Data

Salary data can contain extreme values.

For example:

30,000

32,000

35,000

38,000

200,000

The mean can be pulled upward by the extreme salary.

In such cases, analysts may compare MAD with median-based measures and quartiles to better understand the distribution.

Mean Absolute Deviation and Median-Based Analysis

For skewed data, the median is often useful because it is less sensitive to extreme observations than the mean.

Calculator Pool therefore lets you calculate the average absolute distance from the median.

However, remember:

Mean absolute deviation from median ≠ Median absolute deviation

The former averages absolute distances.

The latter takes the median of absolute distances.

Mean Absolute Deviation and Quartiles

Quartiles divide ordered data into sections.

For example:

Q1 = 25th percentile

Q2 = Median

Q3 = 75th percentile

MAD measures average distance from a center, while IQR measures the middle spread.

Using both can provide more information than relying on one statistic alone.

Calculator Pool’s Quartile Calculator calculates Q1, Q2, Q3 and IQR.

MAD and Interquartile Range

Suppose:

Q1 = 20

and:

Q3 = 40

Then:

IQR = 20

If MAD is:

12

the two statistics describe spread differently.

IQR focuses on the central quartile interval.

MAD uses average absolute distance from the selected center.

MAD and Coefficient of Variation

The coefficient of variation (CV) expresses standard deviation relative to the mean.

A common formula is:

CV = SD ÷ |Mean| × 100

MAD does not divide by the mean.

Therefore:

MAD = Absolute dispersion

while:

CV = Relative dispersion

Calculator Pool also provides a Coefficient of Variation Calculator.

MAD and Z-Score

A z-score describes how far an individual observation is from the mean in standard-deviation units.

MAD describes the average absolute distance of all observations from a center.

Therefore:

Z-score → Individual standardized position

MAD → Overall average absolute dispersion

Calculator Pool also provides a Z-Score Calculator.

MAD and Standard Error

Standard error measures sampling variability of an estimator, commonly the sample mean.

Mean absolute deviation measures dispersion among observations.

So:

MAD ≠ Standard Error

They are used for different statistical purposes.

Calculator Pool also provides a Standard Error Calculator.

MAD and Confidence Intervals

A confidence interval estimates uncertainty around a parameter.

Mean absolute deviation describes data dispersion.

These are different concepts.

A research report may include descriptive dispersion measures such as MAD, while inferential analysis may report a confidence interval.

Calculator Pool also provides a Confidence Interval Calculator.

MAD and Correlation

Correlation measures the relationship between two variables.

MAD measures dispersion within one dataset relative to a center.

Therefore:

MAD → Single-dataset dispersion

Correlation → Two-variable linear association

Calculator Pool also provides a Correlation Calculator.

MAD and Covariance

Covariance measures how two variables vary together.

MAD measures average absolute distance from a center.

They answer different statistical questions.

Calculator Pool’s Covariance Calculator is designed for paired X and Y datasets.

MAD and Linear Regression

Linear regression models the relationship between X and Y.

Mean absolute deviation describes dispersion in a single dataset.

Regression residuals can also be analyzed with absolute errors, but that is a different use of MAD-related terminology.

Calculator Pool provides a separate Linear Regression Calculator.

How to Calculate MAD Step by Step

Consider:

4, 6, 8, 10, 12

Step 1: Find the Mean

Mean = 8

Step 2: Calculate Deviations

−4, −2, 0, +2, +4

Step 3: Take Absolute Values

4, 2, 0, 2, 4

Step 4: Add Them

4 + 2 + 0 + 2 + 4 = 12

Step 5: Divide by Number of Values

12 ÷ 5 = 2.4

Therefore:

Mean Absolute Deviation = 2.4

MAD Example With an Even Number of Values

Consider:

10, 20, 30, 40

Mean:

25

Absolute deviations:

15, 5, 5, 15

Total:

40

MAD:

40 ÷ 4 = 10

Therefore:

MAD = 10

MAD Example With Decimal Values

Consider:

1.5, 2.5, 3.5, 4.5

Mean:

3

Absolute deviations:

1.5, 0.5, 0.5, 1.5

Total:

4

MAD:

4 ÷ 4 = 1

Therefore:

MAD = 1

MAD Example With Negative Values

Consider:

−10, −5, 0, 5, 10

Mean:

0

Absolute deviations:

10, 5, 0, 5, 10

Total:

30

MAD:

30 ÷ 5 = 6

Negative observations are handled normally because absolute values are used.

MAD Example With Repeated Values

Consider:

10, 10, 20, 20, 30

Mean:

18

Absolute deviations:

8, 8, 2, 2, 12

Total:

32

MAD:

32 ÷ 5 = 6.4

Repeated values are included normally.

MAD When All Values Are Equal

Consider:

20, 20, 20, 20, 20

Mean:

20

Every absolute deviation is:

0

Therefore:

MAD = 0

A zero MAD means there is no absolute dispersion around the selected center.

Can Mean Absolute Deviation Be Negative?

No.

Absolute deviations are always:

≥ 0

Therefore, their average is also:

≥ 0

A MAD of zero indicates no deviation from the selected center.

Can Mean Absolute Deviation Be a Decimal?

Yes.

For example:

MAD = 2.4

is perfectly valid.

MAD can be a whole number or decimal depending on the dataset.

Does MAD Have Units?

Yes.

Mean absolute deviation has the same units as the original variable.

For example:

If observations are measured in:

kilograms

MAD is measured in:

kilograms

If observations are measured in:

dollars

MAD is measured in:

dollars

This differs from variance, which is measured in squared units.

MAD vs Variance Units

Suppose the original data is measured in meters.

Then:

MAD → meters

Standard Deviation → meters

Variance → meters²

This makes MAD relatively easy to interpret because it remains in the original unit.

Is MAD Sensitive to Outliers?

Yes, but its sensitivity depends on the selected center.

Using the mean as the center can make MAD more affected by extreme observations because the mean itself can shift.

Using the median as the center can reduce the effect of extreme values on the center.

However, MAD from the median should not be confused with the more robust median absolute deviation statistic.

Which Center Should I Use?

There is no universally correct choice for every dataset.

Mean as Center

Useful when the mean is an appropriate summary of the data.

Median as Center

Useful when you want to measure absolute distance from the median, particularly when the distribution is skewed.

The choice should match the purpose of your analysis.

Mean Absolute Deviation and Symmetric Data

When data is symmetric around its center, mean and median may be the same or very close.

In such cases:

MAD from Mean

and:

MAD from Median

may also be the same or very similar.

For asymmetric data, the difference can become more noticeable.

Mean Absolute Deviation and Skewness

Skewness can make the mean and median diverge.

For example:

1, 2, 3, 4, 20

has:

Mean = 6

Median = 3

Therefore, deviation from mean and deviation from median produce different results.

This is why the calculator lets you choose the center.

Why Use a Mean Absolute Deviation Calculator?

Manually calculating MAD requires:

Mean or Median

→ Absolute Deviations

→ Total Absolute Deviation

→ Divide by Count

For small datasets this is easy.

For larger datasets, an online MAD calculator saves time and reduces arithmetic errors.

Calculator Pool makes the calculation automatic.

Benefits of Calculator Pool’s MAD Calculator

Calculator Pool’s free Mean Absolute Deviation Calculator online provides:

Mean Absolute Deviation

Selected Center

Mean

Median

Total Absolute Deviation

Count

Minimum

Maximum

You can also switch between:

Mean

and:

Median

as the center.

This makes the tool useful for both learning and quick descriptive statistics.

Common Mean Absolute Deviation Mistakes

Forgetting Absolute Values

Do not average signed deviations directly.

Use:

|x − center|

Using the Wrong Center

Mean-based and median-based MAD can differ.

Dividing by the Wrong Number

Mean absolute deviation is the average of the absolute deviations, so divide by the number of observations.

Confusing MAD With Median Absolute Deviation

These are different statistics despite sharing the abbreviation MAD.

Confusing MAD With Mean Absolute Error

Mean absolute error is typically based on actual versus predicted values.

Confusing MAD With Variance

Variance uses squared deviations.

Confusing MAD With Standard Deviation

Standard deviation is based on squared deviations and a square root.

Frequently Asked Questions

What is a Mean Absolute Deviation Calculator?

A Mean Absolute Deviation Calculator calculates the average absolute distance of observations from a selected center such as the mean or median.

What is mean absolute deviation?

It is the average of the absolute deviations from a selected center.

What is the mean absolute deviation formula?

For a center c:

MAD = Σ|x − c| ÷ n

When c is the mean:

MAD = Σ|x − x̄| ÷ n

What does MAD measure?

MAD measures the average absolute distance of observations from a chosen center.

What is absolute deviation?

Absolute deviation is the absolute distance between an observation and the selected center.

Why do we use absolute values?

Absolute values prevent positive and negative deviations from cancelling each other out.

What is MAD from the mean?

It is the average absolute distance of observations from the arithmetic mean.

What is MAD from the median?

It is the average absolute distance of observations from the median.

Is MAD from the mean the same as MAD from the median?

No. They can produce different results because the centers are different.

What is the difference between mean absolute deviation and median absolute deviation?

Mean absolute deviation calculates the average absolute distance from a chosen center. Median absolute deviation typically calculates the median of absolute distances from the median.

Are MAD and median absolute deviation the same?

No. They are different statistics that happen to share the abbreviation MAD.

Which MAD does Calculator Pool calculate?

The current calculator calculates Mean Absolute Deviation, using either the mean or median as the selected center.

Can MAD be zero?

Yes. MAD is zero when all observations are equal to the selected center.

Can MAD be negative?

No. Absolute deviations cannot be negative.

Can MAD be a decimal?

Yes.

Does MAD have the same units as the data?

Yes.

Is MAD a measure of dispersion?

Yes. It describes average absolute dispersion around a chosen center.

Is MAD the same as variance?

No.

Is MAD the same as standard deviation?

No.

Is MAD the same as range?

No.

Is MAD the same as IQR?

No.

Is MAD the same as standard error?

No.

Is MAD the same as mean absolute error?

No. Mean absolute error usually measures prediction errors, while mean absolute deviation measures deviations from a statistical center.

Is MAD sensitive to outliers?

It can be, especially when the mean is used as the center. Using the median as center can reduce the effect of extreme observations on the center.

Is MAD useful for skewed data?

Yes, but the choice of center matters. Median-based analysis may provide a useful complementary perspective for skewed datasets.

Which is better, MAD or standard deviation?

Neither is universally better. They measure dispersion differently and may be useful for different analytical purposes.

Is MAD robust?

Mean absolute deviation from the mean is not especially robust to outliers. Measures based on the median are generally more resistant to extreme observations.

What is the relationship between MAD and standard deviation?

Both measure dispersion, but MAD uses absolute deviations while standard deviation uses squared deviations.

What is the relationship between MAD and variance?

Variance is based on squared deviations, while mean absolute deviation uses absolute deviations.

What is the relationship between MAD and IQR?

Both describe dispersion, but IQR focuses on Q1 and Q3, while MAD measures average absolute distance from a chosen center.

What is the relationship between MAD and median?

The median can be selected as the center for calculating mean absolute deviation.

Can MAD be calculated from negative numbers?

Yes.

Can MAD be calculated from decimal numbers?

Yes.

Can MAD be calculated with repeated numbers?

Yes.

Can MAD be calculated from an even number of observations?

Yes.

Can MAD be calculated from an odd number of observations?

Yes.

Can MAD be calculated for a large dataset?

Yes. An online MAD calculator can automate the arithmetic.

What does a low MAD mean?

It indicates that observations are, on average, relatively close to the selected center.

What does a high MAD mean?

It indicates greater average absolute distance from the selected center.

How do I calculate MAD manually?

Find the selected center, calculate each absolute deviation, add them, and divide by the number of observations.

What is total absolute deviation?

It is the sum of all absolute deviations from the selected center.

What happens if the mean and median are the same?

MAD from the mean and MAD from the median will be the same because the center is the same.

Why might MAD from mean and MAD from median differ?

Because the mean and median can be different, especially in skewed datasets.

Can MAD help compare two datasets?

Yes, provided the datasets are comparable and the same definition and center are used.

Is MAD useful for exam scores?

Yes. It can describe how far exam scores lie from the average or median score.

Is MAD useful for salary data?

Yes, although salary distributions can be skewed, so MAD should often be considered alongside median and quartile measures.

Is MAD useful in research?

Yes, as a descriptive measure of dispersion when appropriate.

Is MAD useful in experimental data?

Yes. It can describe average absolute variation in repeated measurements.

Is MAD useful in data analysis?

Yes. It provides an intuitive measure of absolute dispersion.

Does MAD use the mean?

Only when the mean is selected as the center. The Calculator Pool tool also supports median as the center.

Does MAD use the median?

Yes, when median is selected as the center.

What is the formula for MAD from the median?

MAD = Σ|x − Median| ÷ n

when calculating mean absolute deviation around the median.

What is the difference between mean deviation and mean absolute deviation?

Mean deviation can sometimes refer to average deviations from a center, while mean absolute deviation specifically uses absolute deviations. The full definition should be checked in the context.

Is mean absolute deviation the same as average absolute deviation?

Yes, those terms are commonly used for the same concept when referring to the average of absolute deviations from a chosen center.

Is Mean Absolute Deviation useful for students?

Yes.

Is the Mean Absolute Deviation Calculator free?

Yes. Calculator Pool’s Mean Absolute Deviation Calculator is free to use online.

Related Calculators

You may also find these Calculator Pool tools useful:

Average Calculator

Calculate the arithmetic mean, sum, count, minimum and maximum.

Median Calculator

Find the middle value of an ordered dataset.

Variance Calculator

Calculate population or sample variance with mean and standard deviation.

Standard Deviation Calculator

Calculate population or sample standard deviation.

Quartile Calculator

Calculate Q1, Q2, Q3 and interquartile range.

Percentile Calculator

Calculate any percentile from 0 to 100.

Coefficient of Variation Calculator

Calculate population or sample coefficient of variation.

Standard Error Calculator

Calculate the standard error using standard deviation and sample size.

Z-Score Calculator

Calculate standardized distance from the mean.

Correlation Calculator

Calculate Pearson correlation between two numerical datasets.

Covariance Calculator

Calculate population or sample covariance between paired datasets.

Linear Regression Calculator

Calculate slope, intercept, regression equation, Pearson r, R² and predicted Y.

Probability Calculator

Calculate basic probability from numerical inputs.

Mean Absolute Deviation Calculator – Quick Summary

A Mean Absolute Deviation Calculator measures the average absolute distance of observations from a selected center.

The general formula is:

MAD = Σ|x − center| ÷ n

When the center is the mean:

MAD = Σ|x − x̄| ÷ n

When the center is the median:

MAD = Σ|x − Median| ÷ n

For example, consider:

10, 20, 30, 40, 50

Mean:

30

Absolute deviations:

20, 10, 0, 10, 20

Total absolute deviation:

60

Therefore:

MAD = 60 ÷ 5 = 12

Mean absolute deviation is useful because it gives an intuitive description of average absolute dispersion in the same units as the original data.

For example, a MAD of:

5 kg

means observations are, on average, 5 kilograms away from the selected center.

MAD differs from other measures of dispersion.

Range uses only minimum and maximum.

IQR uses Q1 and Q3.

Variance uses squared deviations.

Standard deviation is the square root of variance.

Coefficient of variation expresses standard deviation relative to the mean.

It is also important to distinguish mean absolute deviation from median absolute deviation. Mean absolute deviation averages absolute distances from a selected center, whereas median absolute deviation typically takes the median of the absolute deviations from the median.

Calculator Pool’s free Mean Absolute Deviation Calculator online lets you choose:

Mean

or:

Median

as the center and displays:

MAD

Mean

Median

Total Absolute Deviation

Count

Minimum

and:

Maximum

Use Calculator Pool’s online MAD calculator to quickly calculate average absolute deviation and better understand the spread of your numerical dataset.