Constructing Scatter Plots
Learn to draw scatter plots for NSW Year 12 Mathematics Standard 1 (NESA outcome MST-12-S1-06). A scatter plot shows a bivariate dataset as separate dots — one for each pair of values — so you can see at a glance whether two quantities are related.
You will put the independent variable across and the dependent variable up, label each axis with its name and units, choose a scale with equal steps, plot each pair and read values back off the graph — a practical way to show data such as study hours and test marks.
Theory
A scatter plot shows bivariate data as separate dots — one dot for each pair of values — plotted at (across, up) on two evenly scaled, labelled axes. This Year 12 Standard 1 (NSW) guide shows how to choose the axes and a sensible scale, plot each point and read values back off the graph.
A scatter plot shows bivariate data as separate dots — one dot for each pair of values. Do not join the dots.
Put the independent variable on the horizontal axis and the dependent variable on the vertical axis. Label each axis with its name and units, and choose a scale with equal steps that reaches past the largest value.
To plot the pair \((x,y)\), start at the origin, move \(x\) across, then \(y\) up, and mark a dot. To read a dot, go straight down to the horizontal axis and straight across to the vertical axis.
Every point is written with the across value first:
How to construct a scatter plot
- Decide the axes: independent variable across, dependent variable up.
- Choose a scale with equal steps that reaches past the largest value on each axis.
- Label each axis with its name and units.
- Plot each pair \((x,y)\): \(x\) across, then \(y\) up. Do not join the dots.
| \(h\) | 2 | 3 | 5 | 6 | 8 | 9 |
|---|---|---|---|---|---|---|
| \(M\) | 11 | 12 | 15 | 14 | 18 | 19 |
One dot for each pair; write each point as (across, up).
| \(\text{(i) } 6 \text{ pairs}\) | \(\Rightarrow\) | \(6 \text{ dots}\) |
| \(\text{(ii) at } h=6\) | \(\Rightarrow\) | \(M=14\) |
| \(\text{point}\) | \(=\) | \((6,\,14)\) |
(i) 6 dots. (ii) \(\mathbf{(6,14)}\).
The scale must reach past \(47\) with equal, easy steps.
| \(0 \text{ to } 10\) | \(\Rightarrow\) | \(\text{does not reach } 47\) |
| \(0 \text{ to } 500\) | \(\Rightarrow\) | \(\text{dots squashed at the bottom}\) |
| \(\text{steps of } 7\) | \(\Rightarrow\) | \(\text{awkward; } 47 \text{ is not a multiple of } 7\) |
Use 0 to 50 in steps of 10.
| \(t\) | 16 | 20 | 24 | 28 | 32 |
|---|---|---|---|---|---|
| \(C\) | 15 | 25 | 30 | 45 | 50 |
\(t\) is independent (across, steps of \(4\)); \(C\) goes up to \(50\) (steps of \(10\)).
| \(\text{points}\) | \(=\) | \((16,15),\ (20,25),\ (24,30)\) |
| \(\) | \(\) | \((28,45),\ (32,50)\) |
\(5\) dots, not joined.
Go up from the axis to the dot, then across to the other axis.
| \(\text{(i) up from } 24, \text{ across}\) | \(\Rightarrow\) | \(C=30\) |
| \(\text{(ii) largest } t\) | \(=\) | \(32,\ \text{height } 50\) |
| \(\text{point}\) | \(=\) | \((32,\,50)\) |
(i) \(C=\mathbf{30}\). (ii) \(\mathbf{(32,50)}\).
Common pitfalls
Frequently asked questions
How do you construct a scatter plot?
Put the independent variable on the horizontal axis and the dependent variable on the vertical axis, choose scales with equal steps that reach past the largest values, label both axes with names and units, then plot one dot for each pair of values. Do not join the dots.
How do you plot a point on a scatter plot?
Start at the origin, move across by the first value, then up by the second value, and mark a dot. For the point (4, 6) go 4 across and 6 up.
How do you choose a scale for a scatter plot?
Use equal steps such as 0, 5, 10, 15 that are easy to read and reach just past the largest value in the data. Never write the data values themselves along the axis.
Do you join the dots on a scatter plot?
No. A scatter plot shows each pair as a separate dot. Joining them would suggest values between the dots that were never measured.
How many dots should a scatter plot have?
One dot for each pair of values, so the number of dots equals the number of pairs in the table.