Q.Explain the freehand (graphical) method of measuring the trend of a time series, and state one merit and one limitation of the method.

Describe how the series is plotted and a smoothing line is drawn by eye, then give one advantage and one drawback.

The method. In the freehand (graphical) method we first plot time (years) on the $X$-axis and the observed values on the $Y$-axis, mark each observation $(t_i, y_i)$ as a point, and join the points to get the actual curve. We then draw — by hand and by eye — a smooth curve or straight line that runs through the general middle of these points, so that roughly as many points lie above the line as below it. This smoothing averages out the seasonal, cyclical and irregular ups and downs, and the smooth line that remains is taken as the trend.

One merit. It is the simplest and quickest method: it needs no calculation at all and gives an immediate visual impression of the direction of the series.

One limitation. It is subjective — the position and shape of the line depend on the judgement of the person drawing it, so two people can obtain different trend lines from the same data. The result is therefore not unique and cannot be trusted for precise measurement or forecasting.

Describing the freehand line as passing through the first and last points only, or through every point. It should pass through the middle of the scatter of points, balancing those above and below it, not connect specific points.