Average deviation, also known as mean absolute deviation (MAD), measures the average distance between each data point and the mean or median of the data set. It’s a useful tool in statistics to understand variability and data spread.
Steps to Calculate Average Deviation
- Calculate the Mean or Median
- Mean: Add all data points and divide by the number of values.
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Median: Order the data points. If the count is odd, pick the middle value. If even, average the two middle values.
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Find Deviations from the Mean
- Subtract the mean from each data point.
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Convert all results to absolute values (ignore negatives).
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Sum All Deviations
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Add the absolute deviations from all data points.
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Calculate the Average Deviation
- Divide the total of absolute deviations by the number of data points.
Example
Data Set:
Scores: 23, 30, 31, 15, 46
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Calculate Mean:
( {Mean} = \frac{23 + 30 + 31 + 15 + 46}{5} = 29 )
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Find Deviations:
- ( |23 - 29| = 6 )
- ( |30 - 29| = 1 )
- ( |31 - 29| = 2 )
- ( |15 - 29| = 14 )
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( |46 - 29| = 17 )
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Sum of Deviations:
( 6 + 1 + 2 + 14 + 17 = 40 )
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Average Deviation:
( {Average Deviation} = \frac{40}{5} = 8 )
Result: The average deviation is 8.
Key Comparisons
1. Absolute Deviation vs. Average Deviation
- Absolute Deviation: The deviation of individual points from the mean.
- Average Deviation: The average of all absolute deviations.
2. Mean Average vs. Average Deviation
- Mean Average: The arithmetic average of all data points.
- Average Deviation: Measures how far, on average, each point is from the mean.
3. Standard Deviation vs. Average Deviation
- Standard Deviation squares deviations before averaging, making it sensitive to extreme values.
- Average Deviation uses absolute values, providing a simpler measure of variability.
Applications
- Data Analysis: Understanding variability in data sets.
- Finance: Evaluating volatility and risk in investments.
- Quality Control: Assessing consistency in processes.
By understanding and calculating average deviation, you can gain insights into the spread and reliability of data sets, helping in decision-making across various fields!