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Last updated on August 26, 2025
In statistics, mean absolute deviation (MAD) is a measure of variability that quantifies the average distance between each data point and the mean of the dataset. In this topic, we will learn the formula for calculating the mean absolute deviation.
The mean absolute deviation is a way to measure the spread of data points in a dataset.
Let’s learn the formula to calculate the mean absolute deviation.
The mean absolute deviation is calculated by taking the average of the absolute deviations from the mean of the dataset. It is calculated using the formula:
MAD = (|x₁ - mean| + |x₂ - mean| + ... + |xₙ - mean|) / n, where x₁, x₂, ..., xₙ are the data values and n is the number of data values.
The mean absolute deviation formula is important for understanding the variability in a dataset. It is used to:
- Compare the spread of different datasets.
- Analyze the consistency of data points around the mean.
- Provide insights into data dispersion, which is crucial for probability, data analysis, and inferential statistics.
Students often find formulas tricky, but with some tips and tricks, you can master the mean absolute deviation formula:
- Remember that MAD deals with absolute values, which means focusing on the distance from the mean without considering direction.
- Connect the use of MAD with real-life data, such as analyzing variability in daily temperatures or test scores.
- Use flashcards to memorize the formula and rewrite it for quick recall; create a formula chart for quick reference.
The mean absolute deviation plays a significant role in real-life data analysis. Here are some applications:
- In finance, to assess the risk or volatility of investment returns over time.
- In quality control, to measure the consistency of product manufacturing.
- In meteorology, to evaluate the variability in weather patterns.
Students make errors when calculating mean absolute deviation. Here are some mistakes and ways to avoid them to master the concept.
Find the mean absolute deviation for the dataset: 2, 4, 6, 8, 10
The mean absolute deviation is 2.4
First, find the mean: (2 + 4 + 6 + 8 + 10) / 5 = 6
Calculate the absolute deviations: |2 - 6| = 4, |4 - 6| = 2, |6 - 6| = 0, |8 - 6| = 2, |10 - 6| = 4
MAD = (4 + 2 + 0 + 2 + 4) / 5 = 12 / 5 = 2.4
Determine the mean absolute deviation of the scores: 9, 7, 5, 7, 11
The mean absolute deviation is 1.6
First, find the mean: (9 + 7 + 5 + 7 + 11) / 5 = 7.8
Calculate the absolute deviations: |9 - 7.8| = 1.2, |7 - 7.8| = 0.8, |5 - 7.8| = 2.8, |7 - 7.8| = 0.8, |11 - 7.8| = 3.2
MAD = (1.2 + 0.8 + 2.8 + 0.8 + 3.2) / 5 = 8 / 5 = 1.6
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