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Tales by Dots and Lines

Two honest pictures, one truth

A bus had 48, 50 and 52 seats filled on three Mondays. The same three numbers can be drawn two ways. The side scale is the row of numbers up the side.

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Scale from 0 to 56: the rise looks small.
Step 1 of 2
  1. Scale from 0 to 56: the rise looks small.
  2. Scale from 44 to 56: the same rise looks big.

The side scale is a choice

The rise from 48 to 52 is 4 seats.

On a 0 to 56 scale, the rise is 4 of 56. That is 4 ÷ 56, one fourteenth. On a 44 to 56 scale, the height is 56 − 44 = 12. The rise is 4 of 12. That is 4 ÷ 12, one third.

On the short scale, each seat takes more height. So the same rise looks bigger.

Neither chart has a wrong number. The picture changes, and the seat counts do not.

Rule: A line graph may start above zero. Say where it starts.

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This track

  1. 0 Start here
  2. 1 The mean is a balance point
  3. 2 The two sides always match
  4. 3 Move one reading, move the mean
  5. 4 A new reading joins the set
  6. 5 Two groups, one true mean
  7. 6 When joining dots is allowed
  8. 7 Steepness is a number
  9. 8 Two honest pictures, one truth
  10. 9 The big picture
  11. 10 Track quiz

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