In the most varied fields of practical and scientific experience, cases occur where certain observations or trials may be repeated a large number of times under similar circumstances. Our attention is then directed to a certain quantity, which may assume different numerical values at successive observations. In many cases each observation yields not only one, but a certain number of quantities, say k, so that generally we may say that the result of each observation is a definite point X in a space of k dimensions (k ≥ 1), while the result of the whole series of observations is a sequence of points: X1, X2, ….

Thus if we make a series of throws with a given number of dice, we may observe the sum of the points obtained at each throw. We are then concerned with a variable quantity, which may assume every integral value between m and 6m (both limits inclusive), where m is the number of dice. On the other hand, in a series of measurements of the state of some physical system, or of the size of certain organs in a number of individuals belonging to the same biological species, each observation furnishes a certain number of numerical values, i.e. a definite point X in a space R of a fixed number of dimensions.

In certain cases, the observed characteristic is only indirectly expressed as a number.