Mean Absolute Deviation Calculator / MAD Calculation Formula

This mean absolute deviation (MAD) calculator is a statistical tool used to measure the average distance between each data point in a dataset and the mean of that dataset using Step by step calculation.

This calculator automates the process of computing the MAD, saving time and reducing the likelihood of errors in manual calculations. It’s particularly useful for analyzing data dispersion and identifying outliers in large datasets.

The MAD calculator typically requires users to input a set of numbers, after which it performs the following steps:

1. Calculates the mean of the dataset
2. Computes the absolute difference between each data point and the mean
3. Calculates the average of these absolute differences

Mean Absolute Deviation Calculator

Dataset	Mean	Mean Absolute Deviation
1, 2, 3, 4, 5	3	1.2
10, 20, 30, 40, 50	30	12
5, 5, 5, 5, 5	5	0
1, 1, 1, 1, 100	20.8	31.36
2, 4, 6, 8, 10	6	2.4

What is the mean absolute deviation of 4 5 4 8 6 10 2 5 3 1?

Let’s calculate:

1. Mean = (4 + 5 + 4 + 8 + 6 + 10 + 2 + 5 + 3 + 1) / 10 = 48 / 10 = 4.8
2. Absolute deviations: |4-4.8|, |5-4.8|, |4-4.8|, |8-4.8|, |6-4.8|, |10-4.8|, |2-4.8|, |5-4.8|, |3-4.8|, |1-4.8|
3. Sum of absolute deviations = 0.8 + 0.2 + 0.8 + 3.2 + 1.2 + 5.2 + 2.8 + 0.2 + 1.8 + 3.8 = 20
4. MAD = 20 / 10 = 2

The mean absolute deviation is 2.

What is the mean absolute deviation of 4 6 12 8 10 10 6 8?

Let’s calculate:

1. Mean = (4 + 6 + 12 + 8 + 10 + 10 + 6 + 8) / 8 = 64 / 8 = 8
2. Absolute deviations: |4-8|, |6-8|, |12-8|, |8-8|, |10-8|, |10-8|, |6-8|, |8-8|
3. Sum of absolute deviations = 4 + 2 + 4 + 0 + 2 + 2 + 2 + 0 = 16
4. MAD = 16 / 8 = 2

The mean absolute deviation is 2.

What is the mean absolute deviation of 10 8 10 6 6 2 10 4?

Let’s calculate:

1. Mean = (10 + 8 + 10 + 6 + 6 + 2 + 10 + 4) / 8 = 56 / 8 = 7
2. Absolute deviations: |10-7|, |8-7|, |10-7|, |6-7|, |6-7|, |2-7|, |10-7|, |4-7|
3. Sum of absolute deviations = 3 + 1 + 3 + 1 + 1 + 5 + 3 + 3 = 20
4. MAD = 20 / 8 = 2.5

The mean absolute deviation is 2.5.

Mean Absolute Deviation Calculation Formula

The formula for calculating the Mean Absolute Deviation is:

MAD = Σ|x – μ| / n

Where:

• MAD is the Mean Absolute Deviation
• Σ represents the sum of
• |x – μ| is the absolute difference between each data point (x) and the mean (μ)
• n is the number of data points in the dataset

To use this formula:

1. Calculate the mean (μ) of the dataset
2. Subtract the mean from each data point and take the absolute value of the difference
3. Sum up all these absolute differences
4. Divide the sum by the number of data points (n)

What is the mean absolute deviation of 2 8, 6 8, 6 8 10 12?

Let’s assume this is a list of numbers: 2, 8, 6, 8, 6, 8, 10, 12

Calculating:

1. Mean = (2 + 8 + 6 + 8 + 6 + 8 + 10 + 12) / 8 = 60 / 8 = 7.5
2. Absolute deviations: |2-7.5|, |8-7.5|, |6-7.5|, |8-7.5|, |6-7.5|, |8-7.5|, |10-7.5|, |12-7.5|
3. Sum of absolute deviations = 5.5 + 0.5 + 1.5 + 0.5 + 1.5 + 0.5 + 2.5 + 4.5 = 17
4. MAD = 17 / 8 = 2.125

The mean absolute deviation is 2.125.

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What is Mean Absolute Deviation?

Mean Absolute Deviation (MAD) is a measure of variability in a dataset that calculates the average distance between each data point and the mean.

It provides insight into how spread out the data is from the central tendency (mean) of the dataset.

Key features of MAD include:

• It uses absolute values, making it less sensitive to extreme outliers compared to standard deviation
• It’s expressed in the same units as the original data, making it easier to interpret
• It provides a more robust measure of dispersion for datasets with non-normal distributions

MAD is particularly useful in situations where:

• The dataset contains outliers that might skew other measures of dispersion
• You need a measure that’s more intuitive to understand than variance or standard deviation
• You’re working with financial data or other datasets where large deviations are significant

What is the mean absolute deviation of 10 4 12 4 2 10 10 6?

Let’s calculate the MAD for the dataset: 10, 4, 12, 4, 2, 10, 10, 6

1. Calculate the mean: μ = (10 + 4 + 12 + 4 + 2 + 10 + 10 + 6) / 8 = 58 / 8 = 7.25
2. Calculate absolute differences from the mean: |10 – 7.25| = 2.75 |4 – 7.25| = 3.25 |12 – 7.25| = 4.75 |4 – 7.25| = 3.25 |2 – 7.25| = 5.25 |10 – 7.25| = 2.75 |10 – 7.25| = 2.75 |6 – 7.25| = 1.25
3. Sum the absolute differences: 2.75 + 3.25 + 4.75 + 3.25 + 5.25 + 2.75 + 2.75 + 1.25 = 26
4. Divide by the number of data points: MAD = 26 / 8 = 3.25

Therefore, the mean absolute deviation of the dataset is 3.25.

What is the mean absolute deviation of 6 2 8 4 8 6 8 8?

Let’s calculate the MAD for the dataset: 6, 2, 8, 4, 8, 6, 8, 8

1. Calculate the mean: μ = (6 + 2 + 8 + 4 + 8 + 6 + 8 + 8) / 8 = 50 / 8 = 6.25
2. Calculate absolute differences from the mean: |6 – 6.25| = 0.25 |2 – 6.25| = 4.25 |8 – 6.25| = 1.75 |4 – 6.25| = 2.25 |8 – 6.25| = 1.75 |6 – 6.25| = 0.25 |8 – 6.25| = 1.75 |8 – 6.25| = 1.75
3. Sum the absolute differences: 0.25 + 4.25 + 1.75 + 2.25 + 1.75 + 0.25 + 1.75 + 1.75 = 14
4. Divide by the number of data points: MAD = 14 / 8 = 1.75

Therefore, the mean absolute deviation of the dataset is 1.75.

What is the mean absolute deviation of 2 3 8 5 7?

Let’s calculate the MAD for the dataset: 2, 3, 8, 5, 7

1. Calculate the mean: μ = (2 + 3 + 8 + 5 + 7) / 5 = 25 / 5 = 5
2. Calculate absolute differences from the mean: |2 – 5| = 3 |3 – 5| = 2 |8 – 5| = 3 |5 – 5| = 0 |7 – 5| = 2
3. Sum the absolute differences: 3 + 2 + 3 + 0 + 2 = 10
4. Divide by the number of data points: MAD = 10 / 5 = 2

Therefore, the mean absolute deviation of the dataset is 2.