That's the whole point of discrimination laws. I don't know if you ever checked but people aren't kidding when they say non-christians, non-whites, ... are more criminal and less smart and ... with the exception of one or two asian ethnicities. In theory saying this by itself is not discriminatory, only acting upon it is, but I doubt most people will agree. But you're going to find actual statistics supporting that. Yet any conclusions obviously are discriminatory.
What's worse is this. Suppose you have 2 groups with each a normal distributed variable (like weight, height, money, likelihood of criminal intent, ...) and let's say a 1% difference in the peak (which is what everyone will always report, standard deviations are also always different, but nobody ever reports them, but when people say Asians are less tall than Caucasians in 1% of cases (real figure is about 6%), this is what they mean). To make things simple, lets say
group A ~ N(100, 10)
group B ~ N(101, 10)
(N(100, 10) is like the "standard" normal distribution for things without reasonable units)
What do you see in practice ? Suppose you meet someone (randomly) from group A and someone (again, uniform random) from group B. What are the chances the member from group A is heavier/taller/richer/more criminal/... than the member of group B ?
E(X > Y, X ~= N(101, 10), Y ~= N(100, 10)) ~ 59%
So in our example, if you meet an Caucasian and an Asian, and there's 1% height difference between the groups, the chance is about 60% that the Caucasian is taller than the Asian. If taken the real figure, 6% difference, then the chance becomes 91%.
This is the problem that causes racism. Tiny differences in a normally distributed variable make a large difference in actual encounters.
What's worse is this. Suppose you have 2 groups with each a normal distributed variable (like weight, height, money, likelihood of criminal intent, ...) and let's say a 1% difference in the peak (which is what everyone will always report, standard deviations are also always different, but nobody ever reports them, but when people say Asians are less tall than Caucasians in 1% of cases (real figure is about 6%), this is what they mean). To make things simple, lets say
group A ~ N(100, 10)
group B ~ N(101, 10)
(N(100, 10) is like the "standard" normal distribution for things without reasonable units)
What do you see in practice ? Suppose you meet someone (randomly) from group A and someone (again, uniform random) from group B. What are the chances the member from group A is heavier/taller/richer/more criminal/... than the member of group B ?
E(X > Y, X ~= N(101, 10), Y ~= N(100, 10)) ~ 59%
So in our example, if you meet an Caucasian and an Asian, and there's 1% height difference between the groups, the chance is about 60% that the Caucasian is taller than the Asian. If taken the real figure, 6% difference, then the chance becomes 91%.
This is the problem that causes racism. Tiny differences in a normally distributed variable make a large difference in actual encounters.