1.1.6 Mathematical Analysis of Results Flashcards
How do you mathematically analyse results?
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
How do you compare results between two 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
How do you plot and interpret graphs?
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)
How do you use a tangent to find the rate of 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)
