Methods of Measuring Seasonal Variations

Methods of Measuring Seasonal Variations

There are three methods such as:

1. Simple Average Method
2. Ratio-to-Moving Average Method
3. Ratio-to-Trend Method

1. Simple Average Method

This is the simplest method of measuring Seasonal Variation. In this method, the average of each month or quarter is calculated and compared with the overall average.

Main Idea

Suppose we have four years of quarterly data. For each year:

• Q1 = First Quarter
• Q2 = Second Quarter
• Q3 = Third Quarter
• Q4 = Fourth Quarter

A separate average is calculated for each quarter.

Formula

Seasonal Index = (Average of a Specific Season/Quarter ÷ Average of All Seasons) × 100

Example

The following quarterly sales data are given:

Step 1: Calculate the Average of Each Quarter

Q1 Average

(80 + 90 + 100 + 110) / 4 = 95

Q2 Average

(100 + 110 + 120 + 130) / 4 = 115

Q3 Average

(120 + 130 + 140 + 150) / 4 = 135

Q4 Average

(140 + 150 + 160 + 170) / 4 = 155

Step 2: Calculate the Average of All Quarterly Averages

(95 + 115 + 135 + 155) / 4 = 125

Step 3: Calculate the Seasonal Index

Interpretation

• Q1 = 76 → 24% below average
• Q2 = 92 → 8% below average
• Q3 = 108 → 8% above average
• Q4 = 124 → 24% above average

Check:

76 + 92 + 108 + 124 = 400

Since it is quarterly data, the sum of the Seasonal Indices is 400.

2. Ratio-to-Moving Average Method

This method is a more scientific and popular method for measuring Seasonal Variation.

In this method, the actual values are compared with the Moving Average.

Basic Formula

Ratio = (Actual Value / Moving Average) × 100

After that, the average of the ratios obtained for the same month or quarter is calculated.

Steps of the Method

Step 1: Write the given Time Series data.

Step 2: Determine the appropriate Moving Average.

For example, for quarterly data, a 4-quarter Moving Average is usually used.

Step 3: If the Moving Average period is even, calculate a Centered Moving Average.

Step 4: Determine the ratio of each Actual Value to the Moving Average.

(Actual Value / Moving Average) × 100

Step 5: Calculate the average of the ratios obtained for the same quarter or month.

Step 6: Make the necessary adjustments to the Seasonal Indices to obtain the final Seasonal Indices.

Simple Example

Suppose:

Actual Sales = ₹150 lakh
Moving Average = ₹125 lakh

Then:

Ratio = (150 / 125) × 100 = 120

Therefore, the Seasonal Ratio for that quarter is 120.

Meaning:

A Seasonal Index of 120 means that sales in that quarter are 20% higher than the average.

Advantages of the Ratio-to-Moving Average Method

1. The effect of the trend is reduced.
2. Seasonal Variation can be measured more accurately.
3. It is useful for large Time Series datasets.
4. A direct comparison between the actual value and the Moving Average is possible.

Limitations

1. The calculation is more complex than that of the Simple Average Method.
2. Moving Averages are not available for some of the initial and final observations.
3. An even-period Moving Average requires centering.

3. Ratio-to-Trend Method

In this method, actual values are compared with trend values.

First, the trend in the Time Series is determined, and then the ratio of the Actual Value to the Trend Value is calculated.

Formula

Seasonal Ratio = (Actual Value / Trend Value) × 100

The Seasonal Index is then obtained by calculating the average of the ratios for the same month or quarter.

Example

Suppose:

Actual Sales = ₹180 lakh
Trend Sales = ₹150 lakh

Then:

Seasonal Ratio = (180 / 150) × 100 = 120

Therefore, the Seasonal Ratio is 120.

Interpretation:

Sales during this period are 20% higher than the Trend Value.

Steps of the Ratio-to-Trend Method

Step 1: Take the Time Series data.

Step 2: Determine the Trend Equation or Trend Values.

For example:

Y = a + bX

Step 3: Determine the Trend Value for each period.

Step 4: Calculate the ratio of the Actual Value to the Trend Value.

(Actual Value / Trend Value) × 100

Step 5: Calculate the average of the ratios for the same month or quarter.

Step 6: Adjust the Seasonal Indices.

Comparison of All Three Methods

Important Formulas for the Exam

Simple Average Method

Seasonal Index = (Seasonal Average / Grand Average) × 100

Ratio-to-Moving Average Method

Seasonal Ratio = (Actual Value / Moving Average) × 100

Ratio-to-Trend Method

Seasonal Ratio = (Actual Value / Trend Value) × 100

FAQ – Frequently Asked Questions

Q1. What are the major methods for measuring Seasonal Variation?
Answer:

1. Simple Average Method
2. Ratio-to-Moving Average Method
3. Ratio-to-Trend Method

Q2. Which is the simplest method?
Answer: Simple Average Method.

Q3. What is compared in the Simple Average Method?
Answer: The average of a particular season or quarter is compared with the Grand Average.

Q4. What is the formula for the Simple Average Method?
Answer:
(Seasonal Average / Grand Average) × 100

Q5. What are the two components compared in the Ratio-to-Moving Average Method?
Answer: Actual Value and Moving Average.

Q6. What is the formula for the Ratio-to-Moving Average Method?
Answer:
(Actual Value / Moving Average) × 100

Q7. What are the two components compared in the Ratio-to-Trend Method?
Answer: Actual Value and Trend Value.

Q8. What is the formula for the Ratio-to-Trend Method?
Answer:
(Actual Value / Trend Value) × 100

Q9. What is the total sum of Quarterly Seasonal Indices?
Answer: 400

Q10. What is the total sum of Monthly Seasonal Indices?
Answer: 1200

Q11. What does a Seasonal Index of 120 mean?
Answer: The value in the relevant period is 20% higher than the average.

Q12. What does a Seasonal Index of 80 mean?
Answer: The value in the relevant period is 20% lower than the average.

Q13. Which Moving Average is used for quarterly data in the Moving Average Method?
Answer: Usually, a 4-quarter Moving Average is used.

Q14. What process is required for an even-period Moving Average?
Answer: Centering is required.

Q15. What is determined first in the Ratio-to-Trend Method?
Answer: Trend Values.

MCQ – Methods of Measuring Seasonal Variations

1. What is the simplest method for measuring Seasonal Variation?

A) Ratio-to-Trend Method
B) Ratio-to-Moving Average Method
C) Simple Average Method
D) Least Squares Method

Answer: C) Simple Average Method

2. What is the Seasonal Index based on in the Simple Average Method?

A) Median
B) Seasonal Average and Grand Average
C) Mode
D) Standard Deviation

Answer: B) Seasonal Average and Grand Average

3. What is the formula for the Simple Average Method?

A) Trend / Actual × 100
B) Actual / Moving Average × 100
C) Seasonal Average / Grand Average × 100
D) Moving Average / Actual × 100

Answer: C) Seasonal Average / Grand Average × 100

4. What is the numerator in the Ratio-to-Moving Average Method?

A) Trend Value
B) Actual Value
C) Average
D) Median

Answer: B) Actual Value

5. What is the formula for the Ratio-to-Moving Average Method?

A) Actual / Moving Average × 100
B) Moving Average / Actual × 100
C) Actual / Trend × 100
D) Trend / Actual × 100

Answer: A) Actual / Moving Average × 100

6. What is the denominator in the Ratio-to-Trend Method?

A) Actual Value
B) Seasonal Average
C) Trend Value
D) Median

Answer: C) Trend Value

7. What is the formula for the Ratio-to-Trend Method?

A) Actual / Trend × 100
B) Trend / Actual × 100
C) Average / Trend × 100
D) Trend / Average × 100

Answer: A) Actual / Trend × 100

8. Which Moving Average is generally used for quarterly data?

A) 2-quarter
B) 3-quarter
C) 4-quarter
D) 12-quarter

Answer: C) 4-quarter

9. Which Moving Average is generally used to measure Seasonal Variation for monthly data?

A) 2-month
B) 4-month
C) 6-month
D) 12-month

Answer: D) 12-month

10. What is required for an even-period Moving Average?

A) Regression
B) Centering
C) Median
D) Mode

Answer: B) Centering

11. What does a Seasonal Index of 125 mean?

A) 25% less
B) 25% more
C) 125% less
D) No change

Answer: B) 25% more

12. What is the Ratio if the Actual Value is ₹150 and the Moving Average is ₹125?

A) 100
B) 110
C) 120
D) 125

Answer: C) 120

13. If the Actual Value is ₹180 and the Trend Value is ₹150, what is the Seasonal Ratio?

A) 110
B) 115
C) 120
D) 130

Answer: C) 120

14. What is the expected total sum of Quarterly Seasonal Indices?

A) 100
B) 200
C) 400
D) 1200

Answer: C) 400

15. What is the expected total sum of Monthly Seasonal Indices?

A) 100
B) 400
C) 600
D) 1200

Answer: D) 1200

16. What is the main purpose of the Moving Average in the Ratio-to-Moving Average Method?

A) To reduce the effect of trend and short-term fluctuations
B) To calculate the population
C) To calculate the median
D) To calculate the mode

Answer: A) To reduce the effect of trend and short-term fluctuations

17. What is the first operation performed in the Ratio-to-Trend Method?

A) The Seasonal Index is calculated
B) Trend Values are calculated
C) The median is calculated
D) The mode is calculated

Answer: B) Trend Values are calculated

18. What is a major limitation of the Simple Average Method?

A) It is very complex
B) The effect of the trend is not completely eliminated
C) An average cannot be used
D) Seasonal data cannot be used

Answer: B) The effect of the trend is not completely eliminated

19. What does a Seasonal Index of 90 indicate?

A) 10% increase
B) 10% decrease
C) 90% increase
D) 90% decrease

Answer: B) 10% decrease

20. What does a Seasonal Index of 140 indicate?

A) 14% increase
B) 40% increase
C) 40% decrease
D) 140% increase

Answer: B) 40% increase

21. If the Actual Value equals the Moving Average, what is the Seasonal Ratio?

A) 0
B) 50
C) 100
D) 200

Answer: C) 100

22. If the Actual Value is greater than the Trend Value, what is the Ratio-to-Trend?

A) Less than 100
B) 100
C) More than 100
D) 0

Answer: C) More than 100

23. If the Actual Value is less than the Trend Value, what is the Ratio-to-Trend?

A) Less than 100
B) 100
C) More than 100
D) 200

Answer: A) Less than 100

24. Which of the following is not a method of calculating the Seasonal Index?

A) Simple Average Method
B) Ratio-to-Moving Average Method
C) Ratio-to-Trend Method
D) Simple Regression Method only

Answer: D) Simple Regression Method only

25. What is done with the ratios of the same season or quarter in the Ratio-to-Moving Average Method?

A) Addition
B) Average
C) Subtraction
D) Squaring

Answer: B) Average

Exam Quick Revision

Simple Average Method

Seasonal Average ÷ Grand Average × 100

Ratio-to-Moving Average Method

Actual Value ÷ Moving Average × 100

Ratio-to-Trend Method

• Actual Value ÷ Trend Value × 100
• Quarterly Data → 4-Quarter Moving Average
• Monthly Data → 12-Month Moving Average
• Quarterly Seasonal Indices Sum → 400
• Monthly Seasonal Indices Sum → 1200
• Index > 100 → Positive Seasonal Effect
• Index < 100 → Negative Seasonal Effect
• Index = 100 → Average Level