Welcome back to class! This week, we are diving into Chapter 2: Analysis of Growth. We are moving beyond simple numbers to look at the visual stories that data can tell. Sections 2-2 and 2-3 focus on constructing graphs, interpreting what they mean, and—crucially—learning when a graph might be tricking you.

Section 2-2: Picturing Growth

In this section, we focus on visualizing information to spot patterns that aren't obvious in a simple table. We look at three main ways to picture growth:

  • Scatterplots: Graphs consisting of isolated points, usually derived directly from raw data.
  • Line Graphs: Created by joining adjacent points in a scatterplot with straight line segments.
  • Smoothed Line Graphs: Created by joining points with smooth curves to show general trends.

Interpreting the Slope
The most important concept here is the relationship between the visual "steepness" of a line and the actual rate of growth:

  • Steepness: The steeper the graph, the greater the magnitude of the growth rate. A flat line implies little to no change.
  • Direction: An increasing graph (going up from left to right) indicates a positive growth rate. A decreasing graph indicates a negative growth rate.

Section 2-3: Misleading Graphs

Have you ever seen a news report where a small difference looked massive on a chart? In this section, we ask the question: Should I believe my eyes? We will analyze how media outlets sometimes manipulate visual data.

Common Manipulations

  • Axis Scale: By starting the vertical axis at a number other than 0 (truncating the axis), a small percentage difference can look like a massive gap. We review a real-world example involving political polling data where a 15% difference was visually manipulated to look like an 800% difference.
  • Default Ranges: Be careful when using calculators or Excel; the default settings often zoom in too far, distorting the perspective of the data.

Adjusting for Inflation
Graphs showing money over time can be misleading if they don't account for inflation. To compare prices fairly across decades, we convert old prices into "constant dollars" using the inflation rate ($r$).

The formula to adjust an old price to a current equivalent is:

$$ \text{Price}_{adjusted} = \text{Price}_{old} \times (1 + r) $$

Example from the notes: To compare gas prices from 1960 to 2000, knowing the inflation rate was $484\%$ (or $r = 4.84$), we calculate:

$$ \$0.31 \times (1 + 4.84) = \$1.81 $$

This tells us that $\$0.31$ in 1960 had the same buying power as $\$1.81$ in 2000.

Weekly Materials

Please review the detailed PDF notes and complete the quizzes for each section below.

Good luck with your analysis this week!