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

## 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 yearlymoving total 3-yearly movingaverage(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 centeredmoving 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 – –

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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

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.

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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.

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