Mean Absolute Deviation Calculator

Mean absolute deviation, often abbreviated MAD, describes how far values in a data set typically lie from their arithmetic mean. It is a measure of dispersion: a small result indicates that observations cluster tightly around the mean, while a large result indicates that they are spread farther apart. Because it uses the same units as the original values, the answer is usually easy to interpret. If a class has a mean score of 80 and a mean absolute deviation of 4, for example, each score is four points away from 80 on average. The calculation begins by adding all observations and dividing by their count to find the arithmetic mean. Next, subtract the mean from every value. Some differences are negative and others are positive, so each difference is converted to its absolute value. Finally, add those absolute distances and divide by the number of observations. The formula is MAD = Σ|xi − mean| / n. This calculator performs every step using the full data set as the population, so the divisor is n rather than n − 1. Mean absolute deviation is useful for comparing consistency across groups measured on the same scale. Teachers can compare variation in test scores, manufacturers can monitor deviations in part dimensions, and analysts can summarize fluctuations in sales or demand. It is often more intuitive than variance because variance squares every difference and therefore reports squared units. Standard deviation restores the original units by taking a square root, but its emphasis on large deviations can still make it less transparent for an introductory analysis. MAD around the mean should not be confused with median absolute deviation, which first finds the median and then takes the median of the absolute distances from it. Median absolute deviation is highly resistant to outliers, while mean absolute deviation incorporates every distance equally in an average. The two measures can produce different answers even for the same observations. Choose the mean-based measure when the arithmetic mean is the center you want to describe, and choose the median-based measure when robustness to extreme values is more important. You may enter integers, decimals, negative values, or a mixture of these formats. Commas and spaces are accepted as separators. Review the displayed mean, sum, and count alongside the MAD to verify that the input was interpreted correctly. For comparisons between data sets with very different means or measurement scales, consider supplementing MAD with a relative measure, since an absolute spread of five may be small in one context and large in another.