Graphical Method
Time Series — Chapter 4, GSEB Class 12 Statistics
Overview
Graphical methods are the simplest way to identify trends — no complex calculations needed. You plot the data and visually draw or calculate the trend line.
Free-Hand Method
Plot the time series data on graph paper. Then draw a smooth line by eye that passes through the middle of the points — balancing points above and below the line.
- Merits: Simple, quick, visual — no calculation needed
- ✗Limitations: Subjective — two people may draw different lines. No formula for prediction.
Comparison
| Feature | Free-Hand | Semi-Average |
|---|---|---|
| Method | Draw smooth line by eye | Join means of two halves |
| Calculation | None | Compute two averages |
| Objectivity | Subjective | More objective |
| Prediction | No formula | Line equation available |
| Best for | Quick visual impression | Simple trend estimation |
Key Takeaways
Key Takeaways
- Free-hand: draw a smooth line through the data by eye — simplest method, no calculation.
- Semi-average: divide data into two halves, find mean of each, join with a straight line.
- Free-hand is subjective; semi-average is more objective but uses only two points.
- Both are preliminary methods — for precise forecasting, use least squares or moving averages.
- Graphical methods are best for getting a quick visual impression of the trend.