Processing and graphing data

Results tables

Raw data goes in your logbook as you measure it. For the report, build a clear table:

• A numbered, descriptive title naming both variables ("Table 1: Mass of water lost from pots with different mulches over 7 days").
• The independent variable in the first column, then each trial, then the calculated mean.
• Units in the column headings only, in brackets: "Mass lost (g)".
• The same number of decimal places throughout a column, matching the instrument's resolution.
• A dash (–) for missing data, with a note explaining why, and outliers marked rather than deleted.

* Pot 3 was knocked over on day 4 and lost soil (see logbook p. 17). It was excluded from the mean and repeated afterwards.

Types of data

• Qualitative (categorical): names or categories, such as mulch type or eye colour.
• Quantitative discrete: counts that can only be whole numbers, such as number of seeds germinated.
• Quantitative continuous: measurements that can take any value in a range, such as mass, temperature or time.

The type of data decides the type of graph.

Choosing a graph

You met column and line graphs in Year 7 (1H). Two more are useful in research projects:

• A histogram shows how often values of one continuous variable fall in each range (class), such as the lengths of 60 oysters. The bars touch because the scale is continuous.
• A scatter graph plots pairs of measurements, such as the height and arm span of each student, to see whether two variables are related. You add a line of best fit if there is a trend.

Lines of best fit and outliers

Measured data always has scatter, so never join the dots. Draw a single straight line or smooth curve that follows the trend, with points scattered evenly on both sides. It doesn't have to pass through any particular point, including the origin, unless you know it must.

An outlier is a point well away from the trend. Don't just delete it. Check your logbook for a reason (a spill, a misread scale), repeat that measurement if you can, and leave the outlier out of the line of best fit only if you have a good reason, saying so in your report. Sometimes an "outlier" is the most interesting result in the whole project.

Gradient: what the slope tells you

The gradient (slope) of a straight line of best fit tells you how fast the dependent variable changes as the independent variable increases:

gradient = rise ÷ run = change in y ÷ change in x

Always give the gradient its units (units of y ÷ units of x) and say what it means. On a distance–time graph it is the speed; on a mass–volume graph it is the density; on a rate-of-reaction graph it is the rate. A gradient taken from a line of best fit uses all the data, so it is more reliable than a value calculated from any single pair of readings.

Interpolation means reading a value from the line within the range of your data (the pea was about 5.2 cm tall at day 3.5). Extrapolation means extending the line beyond your data, which is risky: the pea won't keep growing at 0.89 cm per day forever.

Using a spreadsheet

Spreadsheets save time and mistakes. Type raw data in columns, use =AVERAGE() for means and =MAX()−MIN() for ranges, and insert a scatter chart with a trendline (which can show the gradient). But check what the software does: spreadsheets often join dots, choose odd scales, leave off axis titles, or offer 3D charts that distort the data. You are responsible for the graph, not the program.