Class 12 Statistics Notes · GSEB

Graphical Method

Time Series — learn the free-hand method and semi-average method for identifying trends. GSEB Class 12 Statistics notes.

Last updated: 22 Sep 2026

Notes

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.

TimeSalesEye-balled trend line through the middle
  • Merits: Simple, quick, visual — no calculation needed
  • Limitations: Subjective — two people may draw different lines. No formula for prediction.

Comparison

FeatureFree-HandSemi-Average
MethodDraw smooth line by eyeJoin means of two halves
CalculationNoneCompute two averages
ObjectivitySubjectiveMore objective
PredictionNo formulaLine equation available
Best forQuick visual impressionSimple 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.