17.3 Normal distributions
A suitable model for the heights of all Australian adult males may be described (Fig. 17.1) as having:
- An approximately normal shape,
- With a mean height of \(\mu=175\) cm, and
- A standard deviation of \(\sigma=7\) cm.
This model for the heights of Australian adult males is a theoretical idea about the unknown population: it does not represent any particular sample of data. The model can be thought of as an ‘average’ of the histograms of the data from many samples.
Indeed, if this model turns out to be poor at describing what appears in these many samples, the parameters of the model (that is, the values of \(\mu\) and \(\sigma\)) can be adjusted so the model does describe the sample data well.
In fact, sample evidence suggests that the average height of Australians has been increasing (Loesch et al. 2000) and so the mean of the model may need to be changed at various times to remain a good model for heights of Australian adult males.