# Plotting Points on a Graph

## Key Concepts

• A graph is a way of presenting lots of information in a very condensed form.

• Features common to graphs based on experimental data:

(a) title

(b) x axis labelled with the independent variable

(b) y axis labelled with the dependent variable

(d) data points plotted

• To draw a graph you will need the following equipment:

(a) graph paper

(b) sharp pencil

(c) eraser (rubber)

(d) ruler

## Labelled Axes

The horizontal axis, the x axis, is used for the independent variable, that is, the variable which you control (set at several known intervals).
The independent variable is also sometimes referred to as the controlled variable.

The vertical axis, the y axis, is used for the dependent variable, the variable that you observe or measure when you change the independent variable.

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Units of measurement are written after the name of the quantity in the labels of each axis.
This can be done in several different ways:

• units in round brackets after the name:
example: time (min) and mass (g)

• units separated from name with a comma:
example: time, min and mass, g

• units separated from name using a forward slash:
example: time / min and mass / g
This is now the most acceptable format.

Each axis should be marked off in regular intervals, referred to as the scale.

• Horizontal axis:
eg, if you measure time every minute during the experiment, mark off 1 minute intervals on the x axis and label each mark as 1 then 2 etc.
A suitable scale might be to let 1 cm on the graph paper be equal to 1 minute.

• Vertical axis: inspect the values of the dependent variable then
(a) round up the highest value to a convenient number (eg, 14.12 g might become 15 g or even 20 g)
(b) round down the lowest value to a convenient number (eg, 2.92 g might become 2 g or even 0 g)
(c) calculate the range of values you need to plot
(ie, highest value minus smallest value, eg, 20 - 0 = 20)
(d) decide on a suitable scale: metric graph paper might have lighter ruled divisions every 2 mm and darker divisions to mark every 1 cm.
For a range of 20 g, every 1 cm on the graph paper could represent 1 g

You do not need to start either the x axis or the y axis at zero, unless zero has some special significance.

## Title

The title of a graph is usually in the format of "y-axis label (without units) versus x-axis label (without units)".
The word "versus" is Latin for "against".

The first step in writing a title for the graph is to remove the units from the labels on the x and y axes:

• y-axis = mass
• x-axis = time

Then we construct the title of the graph in the format y-axis versus x-axis, that is, "mass versus time".
The word versus is often abbreviated to vs
Using this abbreviation, the title of the graph becomes "mass vs time"

If you are including more that one graph in your lab report, it is a good idea to number the graphs as well.
You can use the phrases Graph 1., Graph 2., etc
or you can use the more general phrases Figure 1., Figure 2., etc

When you refer to a graph in your lab report, you write, "Figure 1. Mass versus time".
When you are talking to someone about your graph, you might say, "Figure one, mass versus time", or you might say, "Figure one, mass against time".

## Plotting Data Points

The data obtained from an experiment is plotted on the graph using a suitable symbol.
The symbol used must be large enough to be seen, but small enough so that there is no uncertainty about where the centre of the point is.
For this reason, the first choice for plotting points on a graph is a cross, x (the point is located where the two lines forming the x crossover, but, the two lines themselves make the point easy to see on the graph).

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If the points on the graph form the pattern of a straight line or a smooth curve, draw the line of best fit through the points.

The line will

• start at the x value of the first data point

• end at the x value of the last data point

If you need to include more than one set of data points on the same graph, use two different symbols, that is, use one symbol (x) for the first set of data but use a circle (o) for the second set of data points.

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