Todd’s direct Todd\'s Direct, a major TV sales chain headquartered in New Orlean

Question

Todd’s direct Todd's Direct, a major TV sales chain headquartered in New Orleans, is about to open its first outlet in Mobile, Alabama, and wants to select a site that will place the new outlet in the center of Mobile's population base. Todd examines the seven census tracts in Mobile, plots the coordinates of the center of each from a map, and looks up the population base in each to use as a weighting. The information gathered appears in the following table. Census Tract 101 102 103 104 105 106 107 Population in Census Tract 2,000 5,000 10,000 7,000 10,000 18,000 12,000 (25,45) (25,24) (52,48) (52,20) (84,52) (68,18) a) The center-of-gravity coordinates for the location of the proposed outlet in Mobile, Alabama should be: (round your response to two decimal places)

Explanation / Answer

To be calculated:

The centre-of-gravity coordinates for the location of the proposed outlet in Mobile, Alabama

Given values:

7 census tracts, population in census tract and X,Y map coordinates

Solution:

The centre-of-gravity coordinates can be calculated as;

X-coordinate = Sum of [Xi x Population] / Total population in census tract

Total population in census tract = 2000 + 5000 + 10000 + 7000 + 10000 + 18000 + 12000

Total population in census tract = 64,000

X-coordinate = [(25 x 2000) + (25 x 5000) + (52 x 10000) + (52 x 7000) + (84 x 10000) + (68 x 18000) + (90 x 12000)] / 64000

X-coordinate = [(50000) + (125000) + (520000) + (364000) + (840000) + (1224000) + (1080000)] / 64000

X-coordinate = 4203000 / 64000

X-coordinate = 65.67

Y-coordinate = Sum of [Yi x Population] / Total population in census tract

Y-coordinate = [(45 x 2000) + (24 x 5000) + (48 x 10000) + (20 x 7000) + (52 x 10000) + (18 x 18000) + (28 x 12000)] / 64000

Y-coordinate = [(90000) + (120000) + (480000) + (140000) + (520000) + (324000) + (336000)] / 64000

Y-coordinate = 2010000 / 64000

Y-coordinate = 31.41

The centre-of-gravity coordinates for the location of the proposed outlet in Mobile, Alabama is (X, Y) =  (65.67, 31.41)

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