Page 22 - Applied Statistics Using SPSS, STATISTICA, MATLAB and R

1 Introduction

1.1 Deterministic Data and Random Data

Our daily experience teaches us that some data are generated in accordance to
known and precise laws, while other data seem to occur in a purely haphazard way.
Data generated in accordance to known and precise laws are called deterministic
data. An example of such type of data is the fall of a body subject to the Earth’s
gravity. When the body is released at a height h, we can calculate precisely where
the body stands at each time t. The physical law, assuming that the fall takes place
in an empty space, is expressed as:

2
h = h − ½gt ,
0

where h 0 is the initial height and g is the Earth s gravity acceleration at the point
’
where the body falls.
Figure 1.1 shows the behaviour of h with t, assuming an initial height of 15
meters.

16
h
14 t h
12 0.00 15.00
0.20 14.80
10
0.40 14.22
8
0.60 13.24
6 0.80 11.86
1.00 10.10
4
1.20 7.94
2
t 1.40 5.40
0 1.60 2.46
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Figure 1.1. Body in free-fall, with height in meters and time in seconds, assuming
2
g = 9.8 m/s . The h column is an example of deterministic data.