Minggu, 19 April 2015

# 72 Graphs and other ways of displaying data

When you have collected your data and completed your results table, you will generally want to display the data so that anyone looking at them can see any patterns.









1. Line graphs 

Line graphs are used when both the independent variable and the dependent variable are continuous. This is the case for the potato strip data on the table below.


The graph can help you to decide if there is a relationship between the independent variable and the dependent variable. This is what a line graph of these data might look like.


Notice:
• The independent variable goes on the x-axis, and the dependent variable goes on the y-axis.
• Each axis is fully labelled with units. You can just copy the headings from the appropriate columns of your results table.
• The scales on each axis should start at or just below your lowest reading, and go up to or just above your highest reading. Think carefully about whether you need to begin at 0 on either of the axes, or if there is no real reason to do this.
• The scales use as much of the width and height of the graph paper as possible. If you are given a graph grid on the exam paper, the examiners will have worked out a sensible size for it, so you should find your scales will fit comfortably. The greater the width and height you use, the easier it is to see any patterns in your data once you have plotted them.
• The scale on each axis goes up in regular steps. Choose something sensible, such as 1s, 2s, 5s or 10s. If you choose anything else, such as 3s, it is practically impossible to read off any intermediate values. Imagine trying to decide where 7.1 is on a scale going up in 3s...
• Eachpoint is plotted very carefully with a neat cross. Don't usejust a dot, as this may not be visible once you've drawn the line. You could, though, use a dot with a circle round it.
• A smooth best-fit line has been drawn. This is what biologists do when they have good reason to believe there is a smooth relationship between the independent and dependent variables. You know that your individual points may be a bit off this line (and the fact that the two repeats for each concentration were not always the same strongly supports this view), so you can actually have more faith in there being a smooth relationship than you do in your plots for each point.

Sometimes in biology (it doesn't often happen in physics or chemistry!) you might have more trust in your individual points than in any possible smooth relationship between them. If that is the case, then you do not draw a best-fit curve. Instead, join the points with a very carefully drawn straight line, like this:


Tips

During your course:

• Get plenty of practice in drawing graphs,so that it becomes second nature always to choose the correct axes. To label them fully and to choose appropriate scales.

In the exam:

• Take time to draw your graph axes and scales - you may need to try out two or even three different scales before finding the best one.
• Take time to plot the points - and then go back and check them.
• Use a sharp HB pencil to draw the line, taking great care to touch the centre of each cross if you are joining points with straight lines. If you go wrong, rub the line out completely before starting again.
• If you need to draw two lines on your graph, make sure you label each one clearly.

You may be asked to read off an intermediate value from the graph you have drawn. It is always a good idea to use a ruler to do this - place it vertically to read a value on the x-axis, and horizontally to do the same on the y-axis. You can draw in faint vertical and horizontal pencil lines along the ruler. This will help you to read the value accurately.

You could also be asked to work out the gradient of a line on a graph. This is explained on The post #20.

Tips

During your course:

• Make sure you know how to read off an intermediate value from a graph accurately, and how to calculate a gradient.

In the exam:

• Take time over finding intermediate values on a graph - If you rush it is very easy to read off a value that is not quite correct.

2. Histograms

A histogram is a graph where there is a continuous variable on the x-axis, and a frequency on the y-axis. For example, you might have measured the length of 20 leaves taken from a tree. You could plot the data like this:


Notice:

• The numbers on the x-ails scale are written on the lines. The first bar therefore includes all the leaves with a length between 30 and 39 mm. The next bar includes all the leaves with a length between 40 and 49 mm, and so on.
• The bars are all the same width.
• The bars are all touching - this is important, because the x-axis scale is continuous, without any gaps in it.

3. Bar charts

A bar chart is a graph where the independent variable is made up of a number of
different, discrete categories and the dependent variable is continuous. For example, the independent variable could be type of fruit juice, and the dependent variable could be the concentration of glucose in the juice.


Notice:
• The x-axis has an overall heading (type of fruit), and then each bar also has its own heading (orange, apple and so on on).
• The y-axis has a normal scale just as you would use on a line graph.
• The bars are all the same width.
• The bars do not touch.