The accompanying data set contains the school level average SAT critical reading (CR), math (M), and writing (W) scores for the graduating seniors from 100 high schools in New York City. The data set also records the number of SAT test takers (Test Takers) from each school. 

a. Perform k-means clustering to group the 100 high schools into four clusters on the critical reading, math, and writing scores. Is data standardization necessary in this case? What are the size and cluster center values of the largest cluster? Which cluster has the fewest average number of test takers? 

b. Select only the schools with at least 200 SAT test takers and repeat the cluster analysis performed in part a. What are the size and cluster center values of the largest cluster?  

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School Name A. Philip Randolph Campus High School Abraham Lincoln High School I Williamsburg Preparatory School Test Takers CR M 228 430 456 475 ⠀ 113 456 423 W 396 437 I 393. 397 410 380