Graphing Data

Tables, charts and graphs are all ways of representing data, and they can be used for two broad purposes. 

1. To support data collection, organisation and analysis as part of the process of scientific investigation.

2. To help present the conclusions of an investigation to a wider audience. 

The choices of how we represent data are influenced by both the nature of the data (what type of data are we dealing with) and the kinds of questions about the data that are of interest to our investigation.

We covered data tables extensively in previous Knowledge Areas. Here, we focus on charts and graphs as a way of representing data. 

Graphs are a very useful way of presenting numerical data visually to compare relative sizes of values and display any patterns or trends that may not be visible from a table; when data is more complicated or when there is a relationship you want to show with a large amount of data points. Graphs are less useful in communicating actual values, because people tend to focus on the patterns rather than the numbers. To emphasise the actual values, a table is more effective. 

When choosing a good scale, we must fit the range to the graph paper and avoid making our data points hard to read.  A simple rule of thumb is that each large square (main division) should have a value of 1, 2 or 5 multipled by some power of 10. Other values may be suitable, but this rule works well whether the main squares on the graph paper are further divided into 5 or 10 sub-divisions. For this rule, each main square should have one of these values - we'll call this The Scale Ladder.

This makes it easier to work out the values of the small squares. For example, suppose the range of values to be plotted on the horizontal x-axis is from 2 metres to 14 metres. Figure 4.5 shows some possible scales following this rule. Here, the scale in Figure 4.5(c) would be the best choice. Figures (a) and (b) don't completely fit all of the data points on the graph paper, while Figure (d) squashes all of the data points to just a small part of the graph paper. 

In general, the range of the data on each axis should be OVER half of the space avaiable. A graph with the data points squashed together makes it hard to read accurate values when interpolating or finding a gradient. 

You can think of the hcoice of values for each square (1, 2, 5, 10, 20, 50 and so on) as a ladder where each step is about twice the previous one. If the range of the data occupies less than half of the space on an axis, go up the ladder until it does; if it doesn't fit on the grpah paper, go down a step. 

Graphing not only displays any trend or pattern, but also allows you to:

• interpolate - take readings from the graph line for intermediate values of the independent variable.

• extrapolate - extend the line beyond the values used for the independent variable to predict further trends. 

Prior teaching or discussions with your teacher will guide you as to the correct type of graph to draw (for pattern seeking investigations, kite diagrams may be appropriate). The most common type of graph drawn for a fair test investigation is a line grraph - used when both variables are continuous. It is a good idea to use a pencil for initial graph work. 

Graphs must conform to the following:

• Be drawn on graph paper (or a grid) or you may be able to use a computer program (check with your teacher).

• Have a title linking the independent and dependent variables.

• Have ruled axes - the dependent variable always goes on the vertical (y) axis while the independent variable always goes on the horizontal (x) axis. 

• Write the name of the dependent variable and its units alongside the vertical axis and write the name and units of the independent variable underneath the horizontal axis. 

• Each axis must have a scale - this can be different for each axis. Make sure the scale goes up evenly.

• Plot the points (averages for the dependent variable) on the graph and then connect them with a smooth line. This line will either:

  • • go through most or all of the points; or;

    • go through the 'middle' of the points so that it (usually) has as many points on one side as it has the other - this is the line of best fit (or trendline); it can be straight (linear) or curved (check with your teacher as to whether a line of best fit is appropriate for your results). 

• Unless the results give a (0,0) reading, do not take the line back to the origin (a common mistake when graphing). 

• If you have more than one set of results on the graph (i.e. two or more lines), you must either clearly label each line or use a key. 

Outliers can be a problem with graphs. Outliers are points that don't appear to fit the trend. There are two types of outliers:

• data that result from incorrect measurements - these need to be ignored

• data that result from the dependent variable having a wider range than expected - these have to be taken into account in the interpretation of the data. 

Analysing the graph to look for a trend or pattern means considering the shape and slope of the line on the graph - i.e. describe the shape and slope of the line supported by figures from the graph, then explain what the shape and slope of the graph tell about the relationship between the dependent variable and the independent variable. From this analysis, a conclusion may be made. 

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Graphs provide a visual representation of trends in data that may not be evident from a table. It is useful to plot your data as soon as possible, even during your experiment, as this will help you to evaluate your results as you proceed and make adjustments as necessary (e.g. to the sampling interval). The choice between graphing or tabulation in the final report depends on the type and complexity of the data and the information that you want to convey. Usually, both are appropriate. 

• Graphs (called figures) should have a concise explanatory title. If several graphs appear in your report, they should be numbered consecutively. 

• Label both axes and provide appropriate units of measurement if necessary. 

• Place the dependent variable (e.g. biological response, on the vertical (Y) axis (if you are drawing a scatter graph, it does not matter). 

• A break in the axis allows economical use of space if there are no data in the "broken" area. A floating axis (where zero points do not meet) allows the data points to be plotted away from the vertical axis. 

• Place the independent variable on the horizontal (X) axis. 

• Measures of spread (e.g. standard deviation and the 95% confidence intervals) about the plotted mean value can be shown on the graph. The values are plotted as error bars and give an indication of the reliability of the mean value. If the 95% confidence intervals do not overlap between points, then these means will be significantly different. 

• Each axis should have an appropriate scale. Decide on the scale by finding the maximum and minimum values for each variable. 

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A graph provides a picture of information more clearly than any table can. If data are entered into a spreadsheet such as Microsoft Excel, the Chart Wizard function will draw graphs for you - but you still need to decide what kind of graph will best suit your purpose.