Overview
This lecture explains the concept of mean absolute deviation (MAD), demonstrates how to calculate it using examples, and interprets its meaning.
Mean Absolute Deviation: Concept and Formula
- Mean absolute deviation (MAD) measures the average distance of data values from the mean.
- The formula is: MAD = (sum of absolute differences between each data point and the mean) ÷ n, where n is the count of data points.
Example 1: Calculating MAD with a Table
- Data set: 7, 11, 14, 19, 22, 29.
- Calculate the mean: (7 + 11 + 14 + 19 + 22 + 29) ÷ 6 = 102 ÷ 6 = 17.
- Find the difference of each value from the mean: 7-17, 11-17, etc.
- Take absolute values of differences: |−10|, |−6|, |−3|, |2|, |5|, |12| = 10, 6, 3, 2, 5, 12.
- Sum absolute values: 10 + 6 + 3 + 2 + 5 + 12 = 38.
- Divide by n: 38 ÷ 6 = 6.333… (MAD ≈ 6.33).
Example 2: Calculating MAD Without a Table
- Data set: 5, 9, 12, 16, 18.
- Calculate mean: (5 + 9 + 12 + 16 + 18) ÷ 5 = 60 ÷ 5 = 12.
- Find absolute differences: |5–12|=7, |9–12|=3, |12–12|=0, |16–12|=4, |18–12|=6.
- Sum absolute differences: 7 + 3 + 0 + 4 + 6 = 20.
- Divide by n: 20 ÷ 5 = 4 (MAD = 4).
Interpreting MAD Visually
- MAD tells you, on average, how far each value is from the mean.
- For the second example, each data point is about 4 units from the mean (12) on average.
Key Terms & Definitions
- Mean — The average of all data points.
- Absolute Deviation — The absolute value of the difference between a data point and the mean.
- Mean Absolute Deviation (MAD) — The average of all absolute deviations.
Action Items / Next Steps
- Practice calculating MAD for different data sets.
- Review how to find means and absolute values.