distribution is taken as a whole there are six possible divisions between what would be, for practical purposes, the maximum and the minimum values of the distribution. Therefore if the range of a data set i.e. the difference between the maximum and the minimum values, are taken and divided by 6 then this resultant number may be used as a heuristic for the standard deviation. Clearly the actual calculation of the standard deviation is better and with a spreadsheet this is easy to do. But sometimes this heuristic is useful.
2.4
The standard normal curve
Any variable a researcher is working with will have its own mean and standard deviation. All these means and standard deviations could be different and if every time we wanted to study a situation we had to work (i.e. make our calculations) with different means and standard deviations we would be faced with arithmetical challenges. However we are able to minimise this arithmetic work by standardising any variable to have a mean of zero and a variance or standard deviation equal to 1. Returning to Figure 2.8 the normal distribution shown here is called the standard norm al curve because the mean is zero and the standard deviation is 1. It is unusual for any normal distribution to have a mean of zero and a standard deviation of 1. However, any normal distribution variable can be standardised or transformed so that it may be considered to have a mean 0 and standard deviation 1. When this is done the resulting standardised variable is called the Z variable and the probability associated with the Z variable is shown in the Standard Normal Distribution Tables in Figure 2.10 (on page 86). Now to explore the idea of probability.
Ex am ple 1
Recall that having processed the results of the questionnaire in Part 1 we found the response to Question 1 to have a normal distribution 32 of mean 3.47 and a standard deviation of 2.05. We find an additional questionnaire (apparently a late submission) with a response rating of 8 to question 1. The quality of the lectures is excellent
Strongly Disagree 1.
2.
3.
4.
5.
6.
7.
Strongly Agree 8.
9.
32 In order to be able to use this type of logic it is necessary to make an assumption about how the data was distributed.
83