Question

4. The Metropolis Public Library plans to expand with its first major branch library in the city's growing north side. The branch will serve six census tracts. Here are the coordinates of each tract and the population within it: Census Tract Center of Act Population in Tract 503-Logan Square (3,4) 45,000 519-Albany Park (4,5) 25,000 522-Rogers Park 62,000 (3,6) (4,7) 538-Kentwood 51,000 540-Roosevelt (2,3) (5,2) 32,000 29,000 561-Western Using the center-of-gravity method, what should be the coordinate location of the branch library? (30 points)

Answer 1

TRACT	LOCATION X	LOCATION Y	POPULATION
1	3	4	45000
2	4	5	25000
3	3	6	62000
4	4	7	51000
5	2	3	32000
6	5	2	29000

X BAR = SIGMA(Xi * Vi) / SIGMA(Vi)

(3*45000) + (4*25000) + (3*62000) + (4*51000) + (2*32000) + (5*29000) / (45000 + 25000 + 62000 + 51000 + 32000 + 29000) = 3.42

Y BAR = SIGMA(Yi * Vi) / SIGMA(Vi)

(4*45000) + (5*25000) + (6*62000) + (7*51000) + (3*32000) + (2*29000) / (45000 + 25000 + 62000 + 51000 + 32000 + 29000) = 4.87

LOCATION = XBAR, YBAR = 3.42, 4.87

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