Quantitative Investigations of Variation

Question 1

Standard deviation

Answer 1

is a measure of the spread or dispersion of data around the mean

Question 2

A small standard deviation indicates that the

a large standard deviation indicates that the

Answer 2

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

Question 3

Whether or not the standard deviations of different data sets overlap can provide a lot of information:

If there is an overlap

if there is no overlap

Answer 3

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

Question 4

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]

Question 5

You don’t need to include the range of values in your answer like we have done above. However we do recommend writing out the range of values for each data set before starting to answer the question. This way you can easily see any overlap in standard deviation!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.