Sanjay Johnson is working on a research paper that studies the relationship between the education level and the median income of a community. The accompanying table shows a portion of the data that he has collected on the educational attainment and the median income for 77 areas in the city of Chicago. Sanjay plans to cluster the areas using the educational attainment data and compare the average median incomes of the clusters. For each community area, the measures include total number of residents 25 years and over (25 or Over), number of residents with less than a high school education (Less than HS), number of residents with a high school education (HS), number of residents with some college (SC), number of residents with a Bachelor’s degree or higher (Bachelor), and median household income (Income, in $). The accompanying table shows a portion of the data.

a. Does Sanjay need to standardize the data before performing cluster analysis? Explain. 

b. Perform k-means clustering to group the community areas into three clusters based on the variables related to educational attainment of the population (i.e., Less than HS, HS, SC, and Bachelor). Plot the three clusters using the cluster and silhouette plots. What is the average silhouette width? What are the size and cluster center values of the largest cluster? Which cluster of community areas has the highest average median household income?

Transcribed Image Text:

Community Area 25 or Over 32541 7327 ⠀ 15267 Albany Park Archer Heights E Woodlawn Less than HS 11347 2669 ⠀ 2738 I Income 46198 42571 E 27413