Final answer:
The dis-similarity index for the city, calculated based on the racial composition of each neighborhood compared to the city as a whole, is approximately 29.13%.
Step-by-step explanation:
The dis-similarity index is a measure of segregation that represents the percentage of a racial group that would have to move to different neighborhoods in order to achieve complete integration. In the given scenario, we have two races and three neighborhoods. We calculate the dis-similarity index by comparing each neighborhood's racial composition to that of the city, and then summing the absolute differences divided by two.
The city's racial composition is 200 white households and 100 black households, giving us a total of 300 households. We break down each neighborhood as follows:
- Neighborhood 1: 100 white, 20 black
- Neighborhood 2: 60 white, 60 black
- Neighborhood 3: 40 white, 20 black
We then perform the calculations:
- Determine the proportion of white and black households in the city.
- Calculate the proportion of each race that would need to move from each neighborhood to match the city-wide proportions.
- Sum these proportions and divide by two to get the dis-similarity index.
Using the proportions of the city's racial makeup (2/3 white, 1/3 black), we calculate the dis-similarity index for each neighborhood:
Neighborhood 1: |(100/120) - (2/3)| + |(20/120) - (1/3)| = 0.167 + 0.083
= 0.25
Neighborhood 2: |(60/120) - (2/3)| + |(60/120) - (1/3)| = 0.167 + 0.167
= 0.334
Neighborhood 3: |(40/60) - (2/3)| + |(20/60) - (1/3)| = 0.111 + 0.111
= 0.222
We now add these up for each neighborhood and divide by the total number of households to find the city-wide dis-similarity index:
(0.25 * 120 + 0.334 * 120 + 0.222 * 60) / 300 = 0.29133
Therefore, the dis-similarity index for the city is approximately 29.13%.