Index NumbersMCQPYQ July 21Question 3883 of 197
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If in an additive model, O refers to original data as 875, T refers to trend 700, S refers to seasonal variations 200, C refers to cyclical variations 75 then the value of I which refers to irregular variation is:

Options

A−100\displaystyle -100
B−170\displaystyle -170
C140\displaystyle 140
D150\displaystyle 150
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Correct Answer

✅ Option a — −100\displaystyle -100

All Options:

  • A−100\displaystyle -100
  • B−170\displaystyle -170
  • C140\displaystyle 140
  • D150\displaystyle 150

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Detailed Solution & Explanation

In the **additive model** of time series analysis, the observed value (O\displaystyle O) is the sum of trend (T\displaystyle T), seasonal variation (S\displaystyle S), cyclical variation (C\displaystyle C), and irregular variation (I\displaystyle I): O=T+S+C+IO = T + S + C + I We are given: - O=875\displaystyle O = 875 - T=700\displaystyle T = 700 - S=200\displaystyle S = 200 - C=75\displaystyle C = 75 Substitute these values to solve for I\displaystyle I: 875=700+200+75+I875 = 700 + 200 + 75 + I 875=975+I875 = 975 + I I=875−975=−100I = 875 - 975 = -100 Thus, the value of irregular variation is −100\displaystyle -100. Hence, **Option A** is the correct answer.

About This Chapter: Index Numbers

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Construction of Index Numbers, Time Series

This chapter covers Construction of Index Numbers, Time Series and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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