Graphing in Biology (SL IB Biology)

Sketch graphs

• Sketch graphs are a way to represent qualitative trends where the variables shown are often proportional or inversely proportional

A simple sketch graph

A sketch graph of the relationship between time and volume of gas given off, these two variables show a proportional relationship trend

General guidance on drawing graphs

• The types of graphs that students are expected to be able to draw include:
  • Bar charts
  • Histograms
  • Scatter graphs
  • Line / curve graphs
  • Logarithmic graphs
  • Pie charts
  • Box-and-whisker plots

Tips for plotting data

• Whatever type of graph you use, remember the following:
  • The data should be plotted with the independent variable on the x-axis and the dependent variable on the y-axis
  • Plot data points accurately
  • Use appropriate linear scales on axes
  • Choose scales that enable all data points to be plotted within the graph area
  • Label axes, with units included
  • Make graphs that fill the space the exam paper gives you
  • Draw a line of best fit. This may be straight or curved depending on the trend shown by the data. If the line of best fit is a curve make sure it is drawn smoothly. A line of best-fit should have a balance of data points above and below the line
  • In some cases, the line or curve of best fit should be drawn through the origin (but only if the data and trend allow it)

Continuous data represented in a line graph

Discontinuous data represented in a bar chart

The line graph has been used to display continuous data over time while the bar chart has been used to display grouped data

• Remember: The independent variable is the one you control or manipulate and the dependent variable is the one that changes as a result of your manipulation
• Always draw data points in pencil as it makes it easier to make corrections and adjustments

Best fit lines

• Students often confuse the term lines of best fit with straight lines
• Lines of best fit can be straight lines or curves and:
  • They show the trend of the data
    • It does not have to go through all the points, but shows the general trend
  • They must go through the majority of the points
  • Where the data is scattered the points should be evenly distributed on either side of the best fit line

Graph to show use of a best fit line

Other features of graphs

Using a tangent to find the initial rate of a reaction

• For linear graphs (i.e. graphs with a straight-line), the gradient is the same throughout

  • This makes it easy to calculate the rate of change (rate of change = change ÷ time)
• However, many enzyme rate experiments produce non-linear graphs (i.e. graphs with a curved line), meaning they have an ever-changing gradient
  • They are shaped this way because the reaction rate is changing over time
• In these cases, a tangent can be used to find the reaction rate at any one point on the graph:
  • A tangent is a straight line that is drawn so it just touches the curve at a single point
  • The slope of this tangent matches the slope of the curve at just that point
  • You then simply find the gradient of the straight line (tangent) you have drawn
• The initial rate of reaction is the rate of reaction at the start of the reaction (i.e. where time = 0)

Step 1: Estimate the extrapolated curve of the graph

Step 2: Find the tangent to the curve at 0 seconds (the start of the reaction)

The tangent drawn in the graph above shows that 72 cm³ of product was produced in the first  20 seconds.

Step 3: Calculate the gradient of the tangent (this will give you the initial rate of reaction):

Gradient = change in y-axis ÷ change in x-axis

Initial rate of reaction = 72 cm³ ÷ 20 s

Initial rate of reaction = 3.6 cm³ s^-1

Changes in gradient

• Graphs with curves of best fit have changing gradients
• This means that multiple gradients can be calculated to show:
  • The progressing rate of a reaction
  • The effects of factors, such as concentration, on the rate of reaction 

Intercepts

• Intercepts are the points where a line / curve of best fit crosses an axis on a graph

Maxima and minima

• The maxima and minima are the high and low points on a graph
  • Maxima are:
    • high points, or peaks, on a graph
    • points at which the gradient of the line passes from positive, though 0, to negative
  • Minima are:
    • low points, or troughs, on a graph
    • points at which the gradient of the line passes from negative, through 0, to positive

Uncertainty bars

• The uncertainty in a measurement can be shown on a graph as an uncertainty bar
• Uncertainty bars are plotted on graphs to show the absolute uncertainty of values plotted
  • Usually, these bars will be in the vertical direction for y-values, but they can be plotted horizontally for x-values
• The size of the uncertainty bar can be used as an indication of the amount of uncertainty in the measurement

Graph with uncertainty bars

Uncertainty bars show the uncertainty in a specific measurement 

Extrapolation and interpolation

• Extrapolation is extending a line of best fit to estimate values that lie beyond the data points of a graph
• Interpolation is using a line of best fit to estimate values that lie between data points of a graph

Extrapolation and interpolation on a graph

Interpolation uses the line of best fit between the plotted points and extrapolation extends the best fit line beyond the plotted points

Some additional graph skills 

• In addition to plotting standard graphs like the examples above, there are some biology-specific examples that you need to have an understanding of
• These are as follows:
  • Designing dichotomous keys
  • Representing energy flow in the form of food chains, food webs and pyramids of energy
  • Representing familial genetic relationships using pedigree charts