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Three districts hold 5,000, 15,000 and 30,000 people. On a Dorling cartogram scaled by area, how do the circle radii compare, taking the smallest as 1?

  • A.about 1, 1.7 and 2.4
  • B.1, 3 and 6
  • C.1, 9 and 36
  • D.about 1, 1.4 and 2

Answer: A

Correct answer: about 1, 1.7 and 2.4

Scaling by area means the radius goes with the square root of the value: \[ \sqrt{1} = 1, \qquad \sqrt{3} = 1.73, \qquad \sqrt{6} = 2.45. \] The 1, 3 and 6 offered is what results from scaling the radius directly by the value, which would make the largest circle 36 times the area of the smallest instead of 6 - the standard error in proportional symbol work, and always in the direction of exaggeration.

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