A sketched graph is a hand-drawn graph used to show the qualitative relationship between two variables. Unlike a plotted (processed) graph, a sketched graph:
A sketched graph tells you how variables relate (e.g., proportional, inversely proportional) but not by how much.
Sketched graphs are used when:
They are particularly useful in chemistry for showing:
If two variables are directly proportional, the sketched graph is a straight line through the origin.
If two variables are inversely proportional, the sketched graph is a hyperbolic curve that approaches but never touches either axis.
Some variables show an exponential increase or decrease:
A straight line that does not pass through the origin indicates a linear but non-proportional relationship:
| Feature | Sketched Graph | Plotted Graph |
|---|---|---|
| Axes | Labeled, unscaled | Labeled, scaled with numbers |
| Data points | Not plotted | Plotted from measurements |
| Purpose | Show qualitative trends | Show quantitative relationships |
| Precision | General shape only | Precise values readable |
| Error bars | Not included | May be included |
Sketched graphs are closely related to the distinction between qualitative and quantitative data:
Key point: Because quantitative data always carries uncertainty, plotted graphs include error bars and lines of best fit. Sketched graphs avoid this issue by showing only the trend.
A straight line with a negative slope, showing concentration decreasing linearly with time. Axes labeled "[A]" and "Time" — no numbers on axes.
A straight line through the origin, showing rate is directly proportional to concentration. Axes labeled "Rate" and "[A]".
A parabolic curve starting from the origin, curving upward, showing rate increases with the square of concentration.
An exponential decay curve starting from an initial concentration and decreasing toward zero, never quite reaching it.