Following data shows the number of bags of cereals sold in years 1977 to 1984.Years19771978197919801981198219831984No. of bags (in ten thousands)103810458Fit a trend line to the above data by graphical method.

Answer: Plot the eight points and draw a free-hand straight trend line through them; the trend is upward (rising).

Method:

1. Take years on the X-axis (1977 to 1984) and number of bags (in ten thousands) on the Y-axis (scale 0 to 10).
2. Plot the points (1977, 1), (1978, 0), (1979, 3), (1980, 8), (1981, 10), (1982, 4), (1983, 5), (1984, 8) and join them by line segments to show the actual data.
3. Draw a straight line by eye through the middle of the plotted points so that roughly equal numbers of points lie above and below it and the line follows the general direction of the graph. This line is the trend line.

A good guide for the line: the average of the first four years is \(\frac{1+0+3+8}{4}=3\) (centred between 1978 and 1979) and of the last four years is \(\frac{10+4+5+8}{4}=6.75\) (centred between 1982 and 1983). A straight line through these two points rises by about 0.94 (ten thousand bags) per year.

[Rough sketch: the actual data graph zig-zags (low in 1977–78, a peak in 1981, a dip in 1982), while the trend line rises steadily from about 1.6 in 1977 to about 8.2 in 1984.]

Conclusion: the sale of cereal bags shows an upward (increasing) trend over 1977–1984.