How to Calculate Mean Absolute Deviation

Mean absolute deviation (MAD) is a measure of variability that indicates the average distance between data points and the mean of their distribution. It is less sensitive to outliers than the standard deviation and is therefore preferred when dealing with skewed data.

Steps to Calculate MAD

1. Calculate the mean of the data set:
   $\overline{x} = \frac{1}{n} \sum_{i=1}^{n} x_i$
2. Calculate the absolute deviation of each data point from the mean:
   $d_i = |x_i – \overline{x}|$
3. Find the average of the absolute deviations:
   $MAD = \frac{1}{n} \sum_{i=1}^{n} d_i$

Example

Consider the following data set:
{5, 7, 10, 12, 15}

1. Mean:
$\overline{x} = \frac{1}{5}(5 + 7 + 10 + 12 + 15) = 9.8$

2. Absolute deviations:
$d_1 = |5 – 9.8| = 4.8$
$d_2 = |7 – 9.8| = 2.8$
$d_3 = |10 – 9.8| = 0.2$
$d_4 = |12 – 9.8| = 2.2$
$d_5 = |15 – 9.8| = 5.2$

3. MAD:
$MAD = \frac{1}{5}(4.8 + 2.8 + 0.2 + 2.2 + 5.2) = 3$

Advantages of MAD

• Less sensitive to outliers
• Easy to calculate
• Provides a more robust estimate of dispersion than the standard deviation

Disadvantages of MAD

• Not as commonly used as the standard deviation
• Less efficient than the standard deviation for normally distributed data

Conclusion

Mean absolute deviation is a useful measure of variability that can be applied to various types of data. Its simplicity and robustness make it a valuable tool in data analysis and interpretation.

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