ABSTRACT
In Section 1.4, we developed a simple mechanical model for the arithmetic mean of a set of observations based on a chemical balance in a state of equilibrium. Given a set of n direct observations on a single variable Y , we represented these n observations as a scatter of points on the y-axis in the horizontal plane and treated this line as if it were a horizontal beam with unit weights suspended from the given points. Our problem was to locate the point of balance of the weighted beam. Arbitrarily selecting a point on the line and placing a fulcrum at this point, we found that weights to the right of this point will cause the beam to rotate in a clockwise direction about the fulcrum whilst weights to the left will cause it to rotate in an anticlockwise direction. We have thus to multiply the value of the ith weight by the distance from the fulcrum to the point of suspension to determine the ith weight’s contribution to the net clockwise couple. Summing these contributions, we may determine the net clockwise couple of the system as a whole about the fulcrum. If this value is positive then the beam will rotate in an
anticlockwise direction, see Figure 10.1a. Zero values of this function will identify the point of balance of the system of unit weights. This point of balance is usually known as the centre of gravity or the centroid of the system and is located at the Arithmetic Mean of the n given observations, see Figure 10.1b.
