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 > 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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