The secular trend is measured by the method of the free hand curve in the following steps:

- Take the time periods along the $x$-axis by taking appropriate scaling
- Plot the points for observed values of the $Y$ variable as the dependent variable against the given time periods
- Join these plotted points by line segments to get a historigram
- Draw a free-hand smooth curve (or a straight line) through the histogram

In this method we draw the given times series data on graph paper, then we draw a free-hand trend line through the plotted graph according to the trend of the graph. Then we read trend values from this free-hand trend line.

It is generally preferred to use a curve instead of a straight line to show the secular trend.

**Merits (Free Hand Curve)**

- The free-hand curve method is simple, easy, and quick for measuring secular trends.
- A well-fitted trend line (or curve) approximates the trend closely based on a mathematical model.

**Demerits (Free Hand Curve)**

- It is a rough and crude method.
- It is greatly affected by personal bias as different persons may fit different trends to the same data.

The estimates are not reliable due to personal bias.

**Question: **The following time series shows the number of road accidents in Punjab from 1972 to 1978.

Year | 1972 | 1973 | 1974 | 1975 | 1976 | 1977 | 1978 |

No. of Accidents | 2493 | 2638 | 2699 | 3038 | 3745 | 4079 | 4688 |

- Obtain the historigram showing the number of road accidents and a free hand trend line by drawing a straight line
- Find the trend values for this time series

**Solution:**

Year | Value | Total | Mean | Trend Value |

1972 | 2493 | 2200 | ||

1973 | 2638 | 2550 | ||

1974 | 2699 | 2950 | ||

1975 | 3038 | 233380 | 3340 | 3340 |

1976 | 3745 | 3650 | ||

1977 | 4079 | 4050 | ||

1978 | 4688 | 4499 |

MCQs Intermediate Mathematics Part-I Quadratic Equations