• Quantitative investigations of variation can involve the interpretation of mean values and their standard deviations
• A?mean?value describes the average value of a data set
• Standard deviation?is a measure of the spread or dispersion of data around the mean
• A?small?standard deviation indicates that the results lie?close to the mean?(less variation)
• Large?standard deviation indicates that the results are?more spread out

Two graphs showing the distribution of values when the mean is the same but one has a large standard deviation and the other a small standard deviation

Comparison between groups

• When?comparing?the results from?different groups?or samples, using a measure of central tendency, such as the mean, can be quite misleading
• For example, looking at the two groups below
  • Group A: 2, 15, 14, 15, 16, 15, 14
  • Group B: 1, 3, 10, 15, 20, 22, 20

   

• Both groups have the same mean of 13
• However, most of the values in group A lie close to the mean, whereas in group B most values lie quite far from the mean
• For comparison between groups or samples it is better practice to use standard deviation in conjunction with the mean
• Whether or not the?standard deviations of different data sets overlap?can provide a lot of information:
  • If there is an?overlap?between the standard deviations then it can be said that the results are?not significantly different
  • If there is?no overlap?between the standard deviations then it can be said that the results are?significantly different

   

Step one: find the full range of values included within the standard deviations for each data set

Experimental group before: 0.67 to 0.71mm

Experimental group after: 0.71 to 0.77mm

Control group before: 0.69 to 0.73mm

Control group after: 0.67 to 0.77mm

Step two: use this information to form your answer

There is an?overlap?of standard deviations in the experimental group before and after the experiment (0.67~0.71mm and 0.71~0.77mm) so it can be said that the difference before and after the experiment is?not significant;?[1 mark]

There is also an?overlap?of standard deviations between the experimental and control groups after the eight weeks (0.71~0.77mm and 0.67~0.77mm) so it can be said that the difference between groups is?not significant;?[1 mark]

• Plotting data from investigations in the?appropriate format?allows you to more clearly see the?relationship?between two variables
• This makes the?results?of experiments much easier to?interpret
• First, you need to consider what?type of data?you have:
  • Qualitative?data (non-numerical?data e.g. blood group)
  • Discrete?data (numerical?data that can only take?certain values?in a range e.g. shoe size)
  • Continuous?data (numerical?data that can take?any value?in a range e.g. height or weight)

   

• For qualitative and discrete data,?bar charts?or?pie charts?are most suitable
• For continuous data,?line graphs?or?scatter graphs?are most suitable
  • Scatter graphs are especially useful for showing how two variables are?correlated?(related to one another)

   

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)

   

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