Yes! Okay! Thank you for explaining how you were thinking about the data. I don’t know your background in statistics, but since you’re arguing that median is problematic, I’m guessing you have a misconception about how to think about central tendency.
When deciding which measure of central tendency is best to use to measure the “average”, you have to know what your sample data look like (because it is just a sample, albeit hopefully a good, random sample of some N sufficient enough to be considered a good representation of the population).
You can use mean to measure central tendency if your data are normally distributed:
In fact, when the data are distributed like this, the mean, median and mode are all the same, right?
But, income data are not normally distributed, and they are often skewed one way or the other. You might have a negative skew if you have many people working are paid higher on the scale for whatever reason (mode is red, mean is green, and median is blue):
Or, you might have a positive skew if you have many low paid people in your distribution:
In these cases, you cannot use mean, because they don’t represent the true average of the distribution. Instead, median is a much better representation of the average, or at least, the “central tendency” of the data.
In general, the “mean” is the one measure that is trotted out again and again as some sort of statistical “gold standard” when in reality it’s probably misused more often than not. You have to know your data, and then pick the measure of central tendency that is appropriate for your data.
In any case, I am guessing that the Dept. of Labor actually employ statisticians to do these kinds of things; people much smarter than you and I, at least when it comes to stats and the analysis thereof.
If you’re not willing to understand the difference between mean, median, and mode, then our conversation ends here, I guess. Horse to water and all that jazz. I would like to note, for the record, that I thought I did an excellent job ignoring your insults, and instead provided a glimpse into what civilized discourse my look like. You’ll get a lot farther if you can actually talk about the issues instead of “thick skulls”.
In any case, I do hope that you have learned something new about statistics, and that at least, you understand why median is a fine way to talk about the central tendency of skewed data.
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