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 high school education (Less than HS), number of residents with high school education (HS), number of residents with some college (SC), number of residents with bachelor’s degree or higher (Bachelor), and median household income (Income).

a. Should Sanjay standardize the data before cluster analysis? Explain. 

b. Perform agglomerative clustering to group the community areas based on the standardized variables related to the education attainment of the population (i.e., Less than HS, HS, SC, and Bachelor). Use the Euclidean distance and the Ward clustering method. Inspect the dendrogram. How many clusters are generated if the minimum distance between clusters is 10? 

c. What are the size and average median household income of the largest cluster of community areas?

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