Home > Topics > Business Statistics – II > Method of Semi-Averages
← PreviousNext →

Method of Semi-Averages ➗

This method involves dividing the data into two equal parts and fitting a straight line through the averages of these parts.

Procedure 📝

  1. Divide Data: Split the time series into two equal halves.
    • If N is Even: Example 10 years → 5 years + 5 years.
    • If N is Odd: Example 9 years → 4 years + (ignore middle year) + 4 years.
  2. Calculate Averages: Find the arithmetic mean of the Y-values for each half.
    • Let Target 1 be average of first half.
    • Let Target 2 be average of second half.
  3. Plot & Join: Plot these two average points against the mid-time of their respective halves and join them with a straight line.

Example 1: Even Number of Years

Data: Year: 2010, 2011, 2012, 2013, 2014, 2015 Sales: 20, 24, 22, 30, 28, 32

Step 1: Divide (N=6)

  • Part I: 2010, 2011, 2012
  • Part II: 2013, 2014, 2015

Step 2: Averages

  • Avg I: (20 + 24 + 22) / 3 = 66 / 3 = 22
  • Avg II: (30 + 28 + 32) / 3 = 90 / 3 = 30

Step 3: Plot Trend

  • Point A: Year 2011 (mid of Part I), Value 22.
  • Point B: Year 2014 (mid of Part II), Value 30.
  • Join A and B.

Example 2: Odd Number of Years

Data: Year: 2010, 2011, 2012, 2013, 2014, 2015, 2016 Sales: 10, 12, 15, 18, 20, 22, 25

Step 1: Divide (N=7)

  • Part I: 2010, 2011, 2012
  • (Ignore middle year 2013)
  • Part II: 2014, 2015, 2016

Step 2: Averages

  • Avg I: (10 + 12 + 15) / 3 = 37 / 3 = 12.33
  • Avg II: (20 + 22 + 25) / 3 = 67 / 3 = 22.33

Step 3: Trend Values The line passing through these averages gives the secular trend.

Advantages & Limitations

  • Pros: Simple, Objective (unlike freehand).
  • Cons: Assumes linear trend (not good for curves), Uses only arithmetic mean (affected by outliers).

Loading quiz…

← PreviousNext →