Mean Absolute Deviation Worksheet

Introduction to Mean Absolute Deviation

The mean absolute deviation (MAD) is a measure of the average distance between each data point in a set and the mean. It is a way to describe the spread or dispersion of a set of data. The MAD is calculated by taking the absolute value of the difference between each data point and the mean, then finding the average of these absolute differences.

Calculating Mean Absolute Deviation

To calculate the MAD, follow these steps:

• Find the mean of the dataset.
• Subtract the mean from each data point to find the deviation of each point.
• Take the absolute value of each deviation.
• Find the average of these absolute deviations.

The formula for MAD is: MAD = (Σ|xi - μ|) / N, where xi represents each data point, μ is the mean, and N is the number of data points.

Example Calculation

Consider a dataset with the following values: 2, 4, 6, 8, 10.

1. Calculate the mean: (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
2. Subtract the mean from each data point and take the absolute value:
   • |2 - 6| = 4
   • |4 - 6| = 2
   • |6 - 6| = 0
   • |8 - 6| = 2
   • |10 - 6| = 4
3. Calculate the MAD: (4 + 2 + 0 + 2 + 4) / 5 = 12 / 5 = 2.4.

Importance of Mean Absolute Deviation

The MAD is important because it gives a clear picture of how spread out the data is from the average value. A lower MAD indicates that the data points are closer to the mean, suggesting less variability. Conversely, a higher MAD shows that the data points are more spread out, indicating more variability.

Applications of Mean Absolute Deviation

The MAD has various applications in:

• Finance: To measure the volatility of investment returns.
• Quality Control: To monitor the consistency of manufacturing processes.
• Weather Forecasting: To predict temperature variations.

Dataset	Mean	MAD
1, 2, 3, 4, 5	3	1.2
10, 12, 15, 18, 20	15	3.6

📝 Note: The MAD is sensitive to the scale of the data. Therefore, it's essential to consider the context and units of measurement when interpreting MAD values.

As we summarize the key points, it’s clear that the mean absolute deviation is a valuable statistical measure that helps in understanding the variability within a dataset. By calculating the MAD, individuals can gain insights into how data points deviate from the mean value, which is crucial for making informed decisions in various fields such as finance, quality control, and weather forecasting. The calculation process, although straightforward, requires attention to detail to ensure accuracy. With its application across different sectors, the mean absolute deviation stands out as a fundamental concept in statistics, offering a simple yet effective method to assess data dispersion.