Maharashtra State BoardHSC Commerce 12th Board Exam
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SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 - Time Series [Latest edition]

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12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 - Shaalaa.com
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Chapter 2: Time Series

Q.1Q.2Q.3Q.4Q.5
Q.1

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Time Series Q.1

MCQ [1 Mark]

Q.1 | Q 1

Choose the correct alternative:

Which of the following can’t be a component of a time series?

  • Seasonality

  • Cyclical

  • Trend

  • Mean

Q.1 | Q 2

Choose the correct alternative: 

Which component of time series refers to erratic time series movements that follow no recognizable or regular pattern?

  • Trend

  • Seasonal

  • Cyclical

  • Irregular

Q.1 | Q 3

Choose the correct alternative:

The following trend line equation was developed for annual sales from 1984 to 1990 with 1984 as base or zero year.

Y = 500 + 60X (in 1000 ₹). The estimated sales for 1984 (in 1000 ₹) is

  • 500

  • 560

  • 1,040

  • 1,100

Q.1 | Q 4

Choose the correct alternative:

An overall upward or downward pattern in an annual time series would be contained in which component of the times series?

  • Trend

  • Cyclical

  • Irregular

  • Seasonal

Q.1 | Q 5

Choose the correct alternative:

Moving averages are useful in identifying

  • Seasonal component

  • Irregular component

  • Trend component

  • cyclical component

Q.2

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Time Series Q.2

Fill in the blanks [1Markl]

Q.2 | Q 1

______ components of time series is indicated by a smooth line

Q.2 | Q 2

______ component of time series is indicated by periodic variation year after year.

Q.2 | Q 3

The complicated but efficient method of measuring trend of time series is ______

Q.2 | Q 4

The simplest method of measuring trend of time series is ______

Q.2 | Q 5

The method of measuring trend of time series using only averages is ______

Q.3

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Time Series Q.3

Q.3 | Q 1

State whether the following statement is True or False:

The secular trend component of time series represents irregular variations

  • True

  • False

Q.3 | Q 2

State whether the following statement is True or False: 

Seasonal variation can be observed over several years

  • True

  • False

Q.3 | Q 3

State whether the following statement is True or False: 

Cyclical variation can occur several times in a year

  • True

  • False

Q.3 | Q 4

State whether the following statement is True or False: 

Moving average method of finding trend is very complicated and involves several calculations

  • True

  • False

Q.3 | Q 5

State whether the following statement is True or False:

Least squares method of finding trend is very simple and does not involve any calculations

  • True

  • False

Q.4

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Time Series Q.4

Solve the followoing problems. [4 Marks]

Q.4 | Q 1

Following table shows the amount of sugar production (in lac tons) for the years 1971 to 1982

Year 1971 1972 1973 1974 1975 1976
Production 1 0 1 2 3 2
Year 1977 1978 1979 1980 1981 1982
Production 4 6 5 1 4 10

Fit a trend line by the method of least squares

Q.4 | Q 2

Obtain trend values for data, using 4-yearly centred moving averages

Year 1971 1972 1973 1974 1975 1976
Production 1 0 1 2 3 2
Year 1977 1978 1979 1980 1981 1982
Production 4 6 5 1 4 10
Q.4 | Q 3

The following table gives the production of steel (in millions of tons) for years 1976 to 1986.

Year 1976 1977 1978 1979 1980 1981
Production 0 4 4 2 6 8
Year 1982 1983 1984 1985 1986  
Production 5 9 4 10 10  

Fit a trend line by the method of least squares. Also, obtain the trend value for the year 1990

Q.4 | Q 4

Obtain the trend values for the data, using 3-yearly moving averages

Year 1976 1977 1978 1979 1980 1981
Production 0 4 4 2 6 8
Year 1982 1983 1984 1985 1986  
Production 5 9 4 10 10  
Q.4 | Q 5

Use the method of least squares to fit a trend line to the data given below. Also, obtain the trend value for the year 1975.

Year 1962 1963 1964 1965 1966 1967 1968 1969
Production
(million barrels)
0 0 1 1 2 3 4 5
Year 1970 1971 1972 1973 1974 1975 1976  
Production
(million barrels)
6 8 9 9 8 7 10  
Q.4 | Q 6

The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.
Obtain trend values for the above data using 5-yearly moving averages.

Year 1962 1963 1964 1965 1966 1967 1968 1969
Production
(million barrels)
0 0 1 1 2 3 4 5
Year 1970 1971 1972 1973 1974 1975 1976  
Production
(million barrels)
6 8 9 9 8 7 10  
Q.5

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 Chapter 2 Time Series Q.5

Activity based question [4 Mark]

Q.5 | Q 1

Following table shows the all India infant mortality rates (per ‘000) for years 1980 to 2010

Year 1980 1985 1990 1995
IMR 10 7 5 4
Year 2000 2005 2010  
IMR 3 1 0  

Fit a trend line by the method of least squares

Solution: Let us fit equation of trend line for above data.

Let the equation of trend line be y = a + bx   .....(i)

Here n = 7(odd), middle year is `square` and h = 5

Year IMR (y) x x2 x.y
1980 10 – 3 9 – 30
1985 7 – 2 4 – 14
1990 5 – 1 1 – 5
1995 4 0 0 0
2000 3 1 1 3
2005 1 2 4 2
2010 0 3 9 0
Total 30 0 28 – 44

The normal equations are

Σy = na + bΣx

As, Σx = 0, a = `square`

Also, Σxy = aΣx + bΣx2

As, Σx = 0, b =`square`

∴ The equation of trend line is y = `square`

Q.5 | Q 2

Obtain trend values for data, using 3-yearly moving averages
Solution:

Year IMR 3 yearly
moving total
3-yearly moving
average

(trend value)
1980 10
1985 7 `square` 7.33
1990 5 16 `square`
1995 4 12 4
2000 3 8 `square`
2005 1 `square` 1.33
2010 0
Q.5 | Q 3

Fit equation of trend line for the data given below.

Year Production (y) x x2 xy
2006 19 – 9 81 – 171
2007 20 – 7 49 – 140
2008 14 – 5 25 – 70
2009 16 – 3 9 – 48
2010 17 – 1 1 – 17
2011 16 1 1 16
2012 18 3 9 54
2013 17 5 25 85
2014 21 7 49 147
2015 19 9 81 171
Total 177 0 330 27

Let the equation of trend line be y = a + bx   .....(i)

Here n = `square` (even), two middle years are `square` and 2011, and h = `square`

The normal equations are Σy = na + bΣx

As Σx = 0, a = `square`

Also, Σxy = aΣx + bΣx2

As Σx = 0, b = `square`

Substitute values of a and b in equation (i) the equation of trend line is `square`

To find trend value for the year 2016, put x = `square` in the above equation.

y = `square`

Q.5 | Q 4

Complete the table using 4 yearly moving average method.

Year Production 4 yearly
moving
total
4 yearly
centered
total
4 yearly centered
moving average
(trend values)
2006 19  
    `square`    
2007 20   `square`
    72    
2008 17   142 17.75
    70    
2009 16   `square` 17
    `square`    
2010 17   133 `square`
    67    
2011 16   `square` `square`
    `square`    
2012 18   140 17.5
    72    
2013 17   147 18.375
    75    
2014 21  
       
2015 19  

Chapter 2: Time Series

Q.1Q.2Q.3Q.4Q.5
12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 - Shaalaa.com

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 - Time Series

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 (Time Series) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. SCERT Maharashtra Question Bank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 chapter 2 Time Series are Introduction to Time Series, Uses of Time Series Analysis, Components of a Time Series, Mathematical Models, Measurement of Secular Trend.

Using SCERT Maharashtra Question Bank 12th Board Exam solutions Time Series exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in SCERT Maharashtra Question Bank Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board 12th Board Exam prefer SCERT Maharashtra Question Bank Textbook Solutions to score more in exam.

Get the free view of chapter 2 Time Series 12th Board Exam extra questions for 12th Standard HSC Mathematics and Statistics (Commerce) Maharashtra State Board 2022 and can use Shaalaa.com to keep it handy for your exam preparation

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