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
A group of scientists wanted to investigate the effects of a specific diet on the risk of coronary heart disease. One group was given a specific diet for 8 weeks, while the other group acted as a control. After the 8 weeks scientists measured the diameter of the lumen of the main artery in the arm of the volunteers. The results of the experiment are shown in Table 1 below:
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]
The standard deviations of a data set are not always presented in a table, they can also be represented by standard deviation error bars on a graph.
The graph below shows the results of an enzyme rate reaction. Using this graph, calculate the initial rate of reaction.
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
When drawing tangents: always use a ruler and a pencil; make sure the line you draw is perfectly straight; choose the point where the tangent is to be taken and slowly line the ruler up to that point; try to place your ruler so that none of the line of the curve is covered by the ruler (it is much easier if the curve is entirely visible whilst the tangent is drawn).There is a handy phrase to help you remember how to calculate the gradient of a tangent or line. Rise over run means that any increase/decrease vertically should be divided by any increase/decrease horizontally.