Graphs and Modelling
Core concepts
Graphs display relationships visually so patterns and comparisons become clear. Know how to read and construct: coordinate-plane plots, bar graphs, line graphs, scatterplots, and histograms. For scatterplots, describe the association (positive, negative, or none), its strength, and whether it is linear. A line of best fit summarises the trend and supports prediction; interpolation (predicting inside the data range) is more reliable than extrapolation (predicting beyond it). Interpret slope and intercept in context: slope is the change per unit, intercept is the value when the input is zero. Understand axes: labels, units, and scale choices that can exaggerate or hide change. Distinguish correlation from causation - a strong association does not prove one variable causes the other.
Traps to expect
- Misreading a broken or non-zero axis as showing a huge change.
- Confusing which variable is independent (x, horizontal) and dependent (y, vertical).
- Claiming causation from a correlation.
- Using extrapolation confidently far outside the data.
- Choosing a histogram (numerical data binned) when a bar graph (categories) is appropriate, or vice versa.
Worked example
A scatterplot shows study hours (x) versus test score (y) with a line of best fit y = 55 + 6x. The slope 6 means each additional hour is associated with about 6 more points; the intercept 55 is the predicted score with zero study hours. Predicting a score for 4 hours gives 55 + 24 = 79 - an interpolation if the data range includes 4 hours.
Rule of thumb
Before reading any graph, check the axis labels, units, and scale; then state the trend in a full sentence with both variables.