In this note the Nearest Neighbour Index is investigated in three cases, linear, 2-dimensional and 3-dimensional. In each case the formula is investigated and the numerical values for the data points to be viewed as attracting each other, repelling each other or being randomly distributed are justified. Also, in each of the three cases mentioned above, when we have a random distribution of data points we have created an approximate (exact in the linear case) probability density function for D, the distance from a point to its nearest neighbour, and obtained its mean and variance. In each case a rough statistical test is devised to be able to conclude if the data points are clustered, avoiding or randomly distributed. (Contains 8 figures.)