> MAD, however is nicer for reporting data since it is more intuitive.
I have a hard time fathoming how anyone could think such a thing. This is math: we should be using things because they map to reality in some way, not because they are aesthetically pleasing.
The standard deviation maps to processes where the "importance" of changes is proportional to their square. For example, electrical power is proportional to the square of voltage, so AC power systems are conventionally rated by standard deviation. My 120 V power outlet has a standard deviation of its potential of 120 volts.
Standard deviation is also commonly used in situations where we cannot put a number on the importance of the deviation but we know it is big.
The mean average deviation is useful for numbers that are directly proportional to their importance. For example, if we have a hundred lamps and we measure their optical power outputs, the MAD would be a useful measure of their variation. Optical power is already in units of oomph.
> The standard deviation maps to processes where the "importance" of changes is proportional to their square.
Sure, but the point of the article is that STD is used very commonly, in places where that does not make sense. For example, it is common to see things like "the weight of the test subjects was 170cm (STD 5cm)".
Because of the central limit theorem, many distributions encountered in science are approximately Gaussian, which is parameterized by its mean and standard deviation. According to Wikipedia: "Height is sexually dimorphic and statistically it is more or less normally distributed, but with heavy tails."
On top of that, we have well-understood and easy to compute estimators for standard deviation. Using the sample variance is not a bad estimator at all, the only real disagreement is whether you divide by N or N-1.
I have a hard time fathoming how anyone could think such a thing. This is math: we should be using things because they map to reality in some way, not because they are aesthetically pleasing.
The standard deviation maps to processes where the "importance" of changes is proportional to their square. For example, electrical power is proportional to the square of voltage, so AC power systems are conventionally rated by standard deviation. My 120 V power outlet has a standard deviation of its potential of 120 volts.
Standard deviation is also commonly used in situations where we cannot put a number on the importance of the deviation but we know it is big.
The mean average deviation is useful for numbers that are directly proportional to their importance. For example, if we have a hundred lamps and we measure their optical power outputs, the MAD would be a useful measure of their variation. Optical power is already in units of oomph.