How do you interpret the mean absolute deviation (MAD) in data analytics?

To understand Mean Absolute Deviation, let us split both words and try to figure out their meaning. ‘Mean’ refers to the average of the observations and deviation implies departure or variation from a preset standard. When put together, we can define mean deviation as the mean distance of each observation from the mean of the data. Mean Absolute Deviation Formula The ratio of the sum of all absolute values of deviation from the central measure to the total number of observations. M.A. D = (Σ Absolute Values of Deviation from Central Measure) / (Total Number of Observations)

Mean Absolute Deviation Formula The ratio of the sum of all absolute values of deviation from the central measure to the total number of observations. M.A. D = (Σ Absolute Values of Deviation from Central Measure) / (Total Number of Observations)

Below is how you can calculate MAD, Let's say you have a dataset representing the daily temperatures (in degrees Fahrenheit) for a week: Data: 78, 82, 79, 85, 87, 88, 76 Step 1: Calculate the Mean (Average) Mean = (78 + 82 + 79 + 85 + 87 + 88 + 76) / 7 = 595 / 7 ≈ 85 Step 2: Calculate the Absolute Deviations Absolute Deviation for 78 = |78 - 85| = 7 Absolute Deviation for 82 = |82 - 85| = 3 Absolute Deviation for 79 = |79 - 85| = 6 Absolute Deviation for 85 = |85 - 85| = 0 Absolute Deviation for 87 = |87 - 85| = 2 Absolute Deviation for 88 = |88 - 85| = 3 Absolute Deviation for 76 = |76 - 85| = 9 Step 3: Calculate the Mean Absolute Deviation MAD = (7 + 3 + 6 + 0 + 2 + 3 + 9) / 7 ≈ 4.14

Interpreting MAD can be useful in several ways For example: 1. Assessing the consistency of data: A low MAD indicates that the data points are generally close to the mean, suggesting that the dataset is relatively consistent. Conversely, a high MAD suggests that the data points are more spread out, indicating greater variability or inconsistency in the data. Project managers can use this information to determine whether the data is reliable enough to draw meaningful conclusions or whether further data collection is necessary.

If you want to know the degree of variation across statistical data points; Mean absolute deviation is an easy way to understand.

Yes, it is possible for two people to interpret the same mean absolute deviation (MAD) differently depending on their understanding of the context and their interpretation of the results. It is important to clearly define the context and the goals of the analysis when interpreting MAD to ensure that all stakeholders have a consistent understanding of the results.

To understand how data is spread across, in other words, the difference between two data points from the mean. It helps to understand if data is centralized or spread on different points as well as to understand the outliers of the data.

MAD is a great measure to determine quick variance/distribution in the dataset(say you want to quickly present your findings in a meeting but did not have the opportunity to study quickly) but it shouldn’t be used as a measure even for exploratory data analysis (EDA). It shows how much the data is skewed but it doesn’t talk about direction (left or right) due to absolute values. Other ways that could be used to study numeric data variance are histograms and box-plots. Histogram displays frequency of numeric data and hence we can visualize distribution. Box-plots are important to highlight outliers, mean as well as interquartile range (IQR). A picture is worth 1000 words and hence visualization are better to display data distribution.

Mean Absolute Deviation (MAD) is a statistical tool that calculates the average absolute difference between data points and their mean. It's useful when robustness to outliers is needed, and it's adaptable to non-normally distributed data. MAD's interpretability in original units makes it advantageous for explaining variability to diverse audiences. Applications include finance, quality control, and forecasting. Still, its appropriateness depends on data characteristics and analysis goals, with alternatives like the standard deviation being more suitable when normal distribution assumptions are met.

All to often I've seen people 'default' to metrics that don't always fit the use case, e.g. using R-squared without thinking through whether an error of 2 is four times as costly as as error of 1 or twice as costly.

Use the Mean Absolute Deviation (MAD) when you want to measure the average variability or dispersion of data points from their mean in datasets, providing insight into data's overall spread. MAD is particularly useful when dealing with data that may contain outliers or when you want a robust measure of dispersion that isn't heavily influenced by extreme values. It's commonly used in statistics, finance, and quality control.

I get all this, but why is this method any better than the more common standard deviation measure? Is it because it doesn't "over emphasize" the differences of the extreme values, because no squaring is involved? Just about every library and tool out there has facilities to easily calculate common standard deviation - for example, Excel has the =stdev() family of functions, numpy has the "std" function. How/why is MAD better? Can you elaborate?