"I don't believe in averages"
Dude 1: The average Californian gets 11.6* inches of rain per year
Dude 2: That's bullshit.
Dude 1:
Dude 2:
Dude 1: The national weather service measures these things and publishes their findings. Unless you want to take issue with the national weather service you have to believe me.
Dude 2: Sacramento gets less rain
Dude 1: Sure
Dude 2: Santa Rosa gets more rain. Using an average for the state is meaningless. Averages mask variation within sub-populations. There's more to how much rain you get than being Californian. Rainfall in California has a large standard deviation. There's lots of variation. Since the standard deviation is large, you can't use the average.
Dude 1: The standard deviation and the average are two different statistics with two different applications. I didn't say that all Californians get the same amount of rain. I said that the average Californian gets a certain amount. If all we know about a person is that he or she is in California, then our best guess of the rain that person gets is the average rainfall for all Californians. It won't be right for everyone, but the average error for all our guesses should be zero if we guess the average. Just because the average isn't predictive in all cases, or off by a lot in some cases, doesn't change the fact that the average Californian will see a certain amount of rain. The predictive accuracy of a mean as measured by its standard deviation doesn't change its validity as the most probable value for any population member. Just like the best guess on a coin flip is 50% heads, 50% tails. It's the most accurate guess.
Dude 2: If things are different you can't average them together.
Dude 1: What, like Joules and kilograms?
Dude 2: No, like if your grades are better than mine, the class average is meaningless.
Dude 1: It tells the teacher how the class, as a group, is doing.
Dude 2: Averages mean every student has the same grades, which is false, so they are meaningless. You can't use averages.
Dude 1: This is pointless.
Dude 2: I have the last word. So I'm right.
*Fictitious number for allegorical purposes
Dude 2: That's bullshit.
Dude 1:
Dude 2:
Dude 1: The national weather service measures these things and publishes their findings. Unless you want to take issue with the national weather service you have to believe me.
Dude 2: Sacramento gets less rain
Dude 1: Sure
Dude 2: Santa Rosa gets more rain. Using an average for the state is meaningless. Averages mask variation within sub-populations. There's more to how much rain you get than being Californian. Rainfall in California has a large standard deviation. There's lots of variation. Since the standard deviation is large, you can't use the average.
Dude 1: The standard deviation and the average are two different statistics with two different applications. I didn't say that all Californians get the same amount of rain. I said that the average Californian gets a certain amount. If all we know about a person is that he or she is in California, then our best guess of the rain that person gets is the average rainfall for all Californians. It won't be right for everyone, but the average error for all our guesses should be zero if we guess the average. Just because the average isn't predictive in all cases, or off by a lot in some cases, doesn't change the fact that the average Californian will see a certain amount of rain. The predictive accuracy of a mean as measured by its standard deviation doesn't change its validity as the most probable value for any population member. Just like the best guess on a coin flip is 50% heads, 50% tails. It's the most accurate guess.
Dude 2: If things are different you can't average them together.
Dude 1: What, like Joules and kilograms?
Dude 2: No, like if your grades are better than mine, the class average is meaningless.
Dude 1: It tells the teacher how the class, as a group, is doing.
Dude 2: Averages mean every student has the same grades, which is false, so they are meaningless. You can't use averages.
Dude 1: This is pointless.
Dude 2: I have the last word. So I'm right.
*Fictitious number for allegorical purposes
posted by Kenneth at 11:06 AM
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