 In this lab, you'll be working with this learning object, which is to help you understand how we put a number on segregation. How do we measure dissimilarity? This learning object is not intended to oversimplify a complex issue, but it is simply intended to help you understand how to use this formula. We have a large geographic area. Of course, in real life, a large geographic area will have more than 256 houses. This large geographical area is divided into census tracts, which is what really happens. There would likely be more than 16 homes in each census tract. Once we have a set of black homes in this census tract, a set of white homes in this census tract, we're calling them over here, the white home is representing the majority population, and the black home is representing the minority population. Again, this may seem to oversimplify something. It's entirely possible and expected that there are also multiple races living in a large geographical area, or multiple races living in any of these homes. But the purpose of this learning object is to learn how to apply this formula to a large geographical area to be able to understand the dissimilarity index. Here's how this formula works. This symbol means to take the sum. In mathematics, whenever you see this symbol, it's a Greek letter called sigma. It means sum. It means you should add up everything that comes next. So in this case, where I would be adding up 16 census tracts, census tract one, plus census tract two, plus census tract three, plus census tract four, etc., this is just a shorthand way of saying you're going to add up all those census tracts. That's what that sigma means. You already know what absolute value means. It's really defined as a distance on a number line from zero. In practice, what we're going to do in this case is just take the positive difference. So it doesn't really matter if there are more black people in a census tract or white people in a census tract. When we take the difference, we're just going to automatically say the positive difference. For instance, if we end up with something that is negative five over 128, we're just going to call it five because we just want to consider the positive difference here. The ratios that we are considering within the absolute value symbols, this lowercase bi, the lowercase bi stands for the number of black houses in a particular census tract. We're comparing that to the denominator, which is uppercase b. In this case, meaning all the black houses in the larger geographical area. For this example, that denominator will always be 128 because in this large geographical area, there are 128 black houses. And then same with this ratio, of course, it would follow that lowercase wi means the number of white homes in this census tract divided by the number of white homes represented with uppercase w. The number of white homes in the large geographical area. We'll take that difference and add it 16 times. And in the end, when we've taken that sum, we'll take half of the total of the differences of these ratios. So if I were to calculate from here the dissimilarity index, I will have 16 black houses in this census tract minus zero white houses in this census tract. So 16 divided by 128 plus how many black houses here? Zero. Minus how many white houses? 16. So again, I get 16 or negative 16, but remember we're taking the absolute value. 16 divided by 128 plus 16 divided by 128 plus 16 divided by 128 and so on. So we end up with a total of 256 divided by 128, which is two, but we're going to take half of that. And when we calculate, we see the dissimilarity index is one. A dissimilarity index of one is a completely segregated community. When I start to move houses and integrate neighborhoods, the dissimilarity index will change. So now in this case, we won't work all the way through it because I want you to do the work. But for example, now in this census tract, I have 12 black homes. That's bi divided by 128 minus four white homes. That's wi divided by 128. So that will be a difference of eight divided by 128. I'm going to add that to the next census tract, which will be four black homes for bi divided by 128 minus 12 white homes. That's wi divided by 128. So four minus 12 is negative eight. Remember, we're taking the absolute value, so eight divided by 128. And then I would do the same thing, replicate that for every census tract, depending on how I move houses, how I integrate these census tracts. And when you calculate, you will see the dissimilarity index is a little bit lower. So really a lower dissimilarity index means it's a more integrated geographical area. Now you try.