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Statistics · Class 12 Commerce

Ch 4Time Series — Class 12 Statistics, concept-first.

The Gujarat Std-12 Statistics syllabus (Business Mathematics & Statistics) takes up time series right after correlation and regression, because most real business data — sales, production, profit, price — is recorded over successive periods, and a time series is exactly that: a set of numerical values arranged in chron…

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Key concepts

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Time Series and Its Components

A time series is a set of values of a variable recorded in chronological order at successive points or intervals of time.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

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Meaning and Utility of Time Series

The Gujarat Std-12 Statistics syllabus (Business Mathematics Statistics) takes up time series right after correlation and regression, because most real business data — sales, production, profit, pri…

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Components of a Time Series

A time series observed in the real world is rarely a single smooth movement — it is the combined effect of several distinct forces acting together.

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Measurement of Trend: The Moving Average Method

Short illustration. For five years 2018-2022 with values , the 3-yearly moving averages are:

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Measurement of Trend: The Method of Least Squares

Meaning and Principle The method of least squares fits a straight-line trend where is the estimated (trend) value, is the value of at , and is the trend's slope — the average change in per unit of .

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Uses of Time Series Analysis in Business

Time series analysis is not an abstract statistical exercise — it is a tool a business, a trading house, or a government department genuinely uses for planning.

Exercises

+Show 4 questions4 questions
  1. Q1Define a time series. State and briefly explain its four components.Free
  2. Q2Distinguish between seasonal variation and cyclical variation in a time series.Free
  3. Q3Explain the additive and multiplicative models used to describe a time series. When is each considered appropriate?Preview
  4. Q10Discuss the uses of time series analysis in business decision-making.Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 31 questions31 questions
  1. Q1Which types of variations are produced in the time series variable due to seasonal component? (a) Long-term (b) Irregular (c) Regular (d) Ze…Preview
  2. Q2What is meant by analysis of time-series?Preview
  3. Q3Write any two limitations of the method of moving average.Preview
  4. Q4Fit a linear equation from the following data for variable $(y)$ of a time series $n = 4$, $\Sigma y = 270$, $\Sigma ty = 734$.Preview
  5. Q5The birth rates of a state in different years are given in the following table. Fit a linear trend for these data. Also find the estimate of…Preview
  6. Q6Which variation is shown in 'decrease in production of company' due to strike? (a) Random (b) Trend (c) Seasonal (d) CyclicalPreview
  7. Q7Which method of finding trend is best to eliminate the effect of repetitive short-term variations? (a) Graphical method (b) Method of least…Preview
  8. Q8What is a time-series?Preview
  9. Q9State the limitations of graphical method to measure trend.Preview
  10. Q10Obtain the linear equation for trend for a Time Series with $n = 8$, $\Sigma y = 344$, $\Sigma ty = 1342$.Preview
  11. Q11The information about death rate of a state in different years is given in the following table. Fit a linear equation to find trend and henc…Preview
  12. Q12Find the trend using four monthly moving averages for the following data showing monthly sales (in lakhs ₹) of a shop. | Month | Sales (lakh…Preview
  13. Q13Which variation is shown in “decrease in the agricultural production due to floods”? (a) (A) Random (b) (B) Trend (c) (C) Seasonal (d) (D) C…Preview
  14. Q14Which of the components of time-series produce short-term variation?Preview
  15. Q15State the limitations of the method of moving average. (Any two)Preview
  16. Q16Obtain the linear equation for trend for a time series with $n = 7$, $\sum y = 145.2$, $\sum ty = 637.3$.Preview
  17. Q17The number of two wheelers registered (in thousand) in a city in different years is as follows. Use the method of fitting linear equation to…Preview
  18. Q18Which variation is shown in increase in the sale of umbrellas of a company due to monsoon? (a) RANDOM (b) Trend (c) Seasonal (d) CyclicalPreview
  19. Q19State the independent variable of time series. (a) $y_t$ (b) $S_t$ (c) $t$ (d) $x_t$Preview
  20. Q20The linear equation fitted using the data of 7 weeks for a variable $y$ is $\hat{y} = 25.1 - 1.5t$. Estimate the value of $y$ for the eighth…Preview
  21. Q21State the components of time series.Preview
  22. Q22State any three merits of graphical method of time series.Preview
  23. Q23The birth rates of a state in different years are given in the following table. Fit a linear trend for these data. Also find the estimates f…Preview
  24. Q24Find the trend using four yearly moving averages for the following data showing yearly sales (in lakh ₹) of a shop : | Year | 2015 | 2016 |…Preview
  25. Q25Which component of the time series is impossible to predict? (a) Random component (b) Trend (c) Seasonal component (d) Cyclical componentPreview
  26. Q26Which method of finding trend is best to eliminate the effect of repetitive short-time variations? (a) Graphical method (b) Method of least…Preview
  27. Q27What is the notation to show the cyclical component of the time series?Preview
  28. Q28State the limitations of graphical method.Preview
  29. Q29Write a short note on seasonal component.Preview
  30. Q30The profit earned (in lakh $\text{\rupee}$) by a company making computers is as follows. Find the linear equation for the trend from these d…Preview
  31. Q31The number of students studying in a college are shown in the following table. Find the trend by four yearly moving averages: | Year | 2006…Preview

More questions

6 Q
+Show 5 questions5 questions
  1. Example 4From the following data on the production of a factory (in '000 units) for 2016-2022, calculate the trend values by the method of 3-yearly m…Free
  2. Example 5From the following data on a company's sales (Rs lakh) for 2015-2022, compute the trend values by the method of 4-yearly moving averages. |…Free
  3. Example 6Fit a straight-line trend by the method of least squares to the following data on a firm's profit (Rs '000) for 2018-2022, and estimate the…Preview
  4. Example 7Fit a straight-line trend by the method of least squares to the following data on a company's sales (Rs lakh) for 2019-2022. | Year | 2019 |…Preview
  5. Example 8Using the trend equation obtained for the firm's profit data in the earlier example ($Y_c = 18 + 4.6X$, origin 2020, $X$ in years), estimate…Preview
+Show 1 question1 question
  1. Q9Which component of a time series best explains the regular rise in demand for umbrellas every monsoon? (a) Secular Trend (b) Seasonal Variat…Preview