GSEB Class 12 Statistics Solutions Chapter 4 Time Series Exercise 4.3

GSEB Solutions

Gseb Solutions Class 12 Statistics Part 1 Chapter 4 Time Series Exercise 4.3

Gujarat Board Textbook Solutions Class 12 Statistics Part 1 Chapter 4 Time Series Exercise 4.3

Question 1. Find the trend by three yearly moving averages from the following data about the sales (in ten lakh Rs.) of a company:
Answer: For this problem, the total number of periods (n) is 10. The time variable (t) will take values from 1, 2, 3, up to 10. The variable 'y' represents the sales figures.

In simple words: To find the sales trend, we calculate the average sales over three consecutive years. This helps to smooth out short-term ups and downs, showing the general direction of sales over time.

The table for calculating three yearly moving average is prepared as follows:

🎯 Exam Tip: Ensure correct calculation of the moving total and precise division for the moving average. Pay attention to centering the average for odd-period moving averages.

Question 2. The average monthly closing prices of shares of a company in the year 2016 are given in the following table. Find the trend using four monthly moving averages.
Answer: For this problem, 'n' represents 12 months in total. The time variable 't' will run from 1, 2, 3, up to 12. The variable 'y' corresponds to the share price.

In simple words: To find the trend in share prices using four-monthly moving averages, we first calculate the total of prices for four consecutive months. Then, we sum these totals in pairs and divide by eight to get a centered moving average, which helps smooth out monthly fluctuations.

To calculate four monthly moving average, the table is prepared as follows:

🎯 Exam Tip: For even-period moving averages, remember to center the moving total by taking a two-period average of the moving totals and then dividing by the total number of periods (e.g., 4x2=8 for four-monthly data).

Question 3. Find the trend using five yearly moving averages from the following data of profit (in lakh Rs.) of a trader in different years:
Answer: For this scenario, the total number of years ('n') is 9. The time periods ('t') will range from 1, 2, ..., up to 9. The variable 'y' represents the profit figures.

In simple words: To determine the profit trend, we calculate the average profit over five consecutive years. This method helps to smooth out yearly variations and reveal the underlying long-term movement of the trader's profits.

To calculate five yearly moving average the table is prepared as follows:

🎯 Exam Tip: Remember to center the moving average values correctly, especially for odd-period averages, aligning them with the middle year of the period. Be careful with calculations for each step.

Question 4. The wholesale price index numbers for different quarters (9) of a year are obtained as follows. Find the trend by four quarterly moving averages.
Answer: In this problem, we have 12 quarters, with each quarter covering a period of three months. The variable 'y' represents the index number. Since there are four quarters in a year, we need to calculate the trend by using a four-quarterly moving average method.

In simple words: To find the trend in wholesale price index numbers, we use a four-quarterly moving average. This involves calculating the sum of index numbers for four consecutive quarters, then pairing these sums, and finally dividing by eight to get a smoothed trend value.

The table for calculating four quarterly moving average is prepared as follows:

🎯 Exam Tip: When dealing with quarterly data for even-period moving averages, ensure correct centering by calculating the average of two consecutive moving totals before dividing by the total number of periods (e.g., 4x2=8). Label your columns clearly for easy understanding.