Data & Graphs

Problem

Compare line graphs that use different gridline scales

Two line graphs show daily cookie sales. Chocolate days 4-7 are 100, 150, 200, 150 (each small square = 50). Strawberry days 4-7 are 190, 150, 170, 230 (each small square = 10, with a wavy break below). For each cookie I find the difference between its highest and lowest day, then say which cookie has the larger difference.
Chocolate Cookies Sold 0 100 200 4 5 6 7 Day (cookies) Strawberry Cookies Sold 150 200 4 5 6 7 Day (cookies)
Measurement & data
Your answer
How to solve
Strategy Organize Information in More Ways — Because the graphs use different square sizes, comparing bar/point heights is misleading. I re-organize the data as actual numbers from each scale, then break the question into two subproblems: the chocolate range and the strawberry range, and compare those two numbers.
1STEP 1

Chocolate range

Reading the chocolate graph (each square = 50), the most was 200 on day 6 and the least was 100 on day 4: 200 - 100 = 100.

200 - 100 = 100
2STEP 2

Strawberry range

Reading the strawberry graph (each square = 10, axis cut by a wavy line), the most was 230 and the least was 150: 230 - 150 = 80.

230 - 150 = 80
3STEP 3

Compare the two ranges

Chocolate's range is 100 and strawberry's range is 80. Since 100 is greater than 80, chocolate has the larger difference.

100 is greater than 80
Answer
Chocolate cookies (range 100, vs strawberry's 80)
Strawberry's line looks taller and steeper, but that is only because its squares are worth 10 each; in true numbers its swing is just 80, while chocolate swings a full 100. Reading by scale, not by appearance, gives the correct winner.
Takeaway

When two graphs have different square sizes, read the real numbers first - a steeper line isn't always a bigger change!

  • Chocolate range
  • Strawberry range
  • Compare the two ranges
Where next?
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