# Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 4 - Time Series [Latest edition]

## Solutions for Chapter 4: Time Series

Below listed, you can find solutions for Chapter 4 of Maharashtra State Board Balbharati for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board.

Exercise 4.1Miscellaneous Exercise 4
Exercise 4.1 [Pages 66 - 67]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 4 Time Series Exercise 4.1 [Pages 66 - 67]

Exercise 4.1 | Q 1 | Page 66

The following data gives the production of bleaching powder (in '000 tons) for the years 1962 to 1972.

 Year 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 Production 0 0 1 1 4 2 4 9 7 10 8

Fit a trend line by graphical method to the above data.

Exercise 4.1 | Q 2 | Page 66

Use the method of least squares to fit a trend line to the data in Problem 1 above. Also, obtain the trend value for the year 1975.

Exercise 4.1 | Q 3 | Page 66

Obtain the trend line for the above data using 5 yearly moving averages.

Exercise 4.1 | Q 4 | Page 66

The following table shows the index of industrial production for the period from 1976 to 1985, using the year 1976 as the base year.

 Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 Index 0 2 3 3 2 4 5 6 7 10

Fit a trend line to the above data by graphical method.

Exercise 4.1 | Q 5 | Page 66

Fit a trend line to the data in Problem 4 above by the method of least squares. Also, obtain the trend value for the index of industrial production for the year 1987.

Exercise 4.1 | Q 6 | Page 66

Obtain the trend values for the data in using 4-yearly centered moving averages.

 Year 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 Index 0 2 3 3 2 4 5 6 7 10
Exercise 4.1 | Q 7 | Page 66

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

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

Fit a trend line to the above data by the graphical method.

Exercise 4.1 | Q 8 | Page 66

Fit a trend line to the data in Problem 7 by the method of least squares. Also, obtain the trend value for the year 1990.

Exercise 4.1 | Q 9 | Page 66

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

Exercise 4.1 | Q 10 | Page 67

The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.

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

i. Obtain trend values for the above data using 5-yearly moving averages.
ii. Plot the original time series and trend values obtained above on the same graph.

Miscellaneous Exercise 4 [Pages 67 - 69]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board Chapter 4 Time Series Miscellaneous Exercise 4 [Pages 67 - 69]

Miscellaneous Exercise 4 | Q 1.01 | Page 67

Choose the correct alternative :

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

• Seasonality

• Cyclical

• Trend

• Mean

Miscellaneous Exercise 4 | Q 1.02 | Page 68

Choose the correct alternative :

The first step in time series analysis is to _______.

• perform regression calculations

• calculate a moving average

• plot the data on a graph

• identify seasonal variation

Miscellaneous Exercise 4 | Q 1.03 | Page 68

Choose the correct alternative :

Time-series analysis is based on the assumption that _______.

• random error terms are normally distributed.

• the variable to be forecast and other independent variables are correlated.

• past patterns in the variable to be forecast will continue unchanged into the future.

• the data do not exhibit a trend.

Miscellaneous Exercise 4 | Q 1.04 | Page 68

Moving averages are useful in identifying _______.

• Seasonal component

• Irregular component

• Trend component

• Cyclical component

Miscellaneous Exercise 4 | Q 1.05 | Page 68

Choose the correct alternative :

We can use regression line for past data to forecast future data. We then use the line which_______.

• minimizes the sum of squared deviations of past data from the line

• minimizes the sum of deviations of past data from the line

• maximizes the sum of squared deviations of past data from the line

• maximizes the sum of deviations of past data from the line

Miscellaneous Exercise 4 | Q 1.06 | Page 68

Choose the correct alternative :

Which of the following is a major problem for forecasting, especially when using the method of least squares?

• The past cannot be known.

• The future is not entirely certain.

• The future exactly follows the patterns of the past.

• The future may not follow the patterns of the past.

Miscellaneous Exercise 4 | Q 1.07 | Page 68

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

Miscellaneous Exercise 4 | Q 1.08 | Page 68

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 Rs). The estimated sales for 1984 (in 1000 Rs) is:

• Rs 500

• Rs 560

• Rs 1,040

• Rs 1,100

Miscellaneous Exercise 4 | Q 1.09 | Page 68

Choose the correct alternative :

What is a disadvantage of the graphical method of determining a trend line?

• Provides quick approximations

• Is subject to human error

• Provides accurate forecasts

• Is too difficult to calculate

Miscellaneous Exercise 4 | Q 1.1 | Page 68

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

• Trend

• Seasonal

• Cyclical

• Irregular

Miscellaneous Exercise 4 | Q 2.01 | Page 68

Fill in the blank :

_______ component of time series is indicated by a smooth line.

Miscellaneous Exercise 4 | Q 2.02 | Page 68

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

Miscellaneous Exercise 4 | Q 2.03 | Page 68

_______ component of time series is indicated by a long wave spanning two or more years.

Miscellaneous Exercise 4 | Q 2.04 | Page 68

Fill in the blank :

_______ component of time series is indicated by up and down movements without any pattern.

Miscellaneous Exercise 4 | Q 2.05 | Page 68

Fill in the blank :

Addictive models of time series _______ independence of its components.

Miscellaneous Exercise 4 | Q 2.06 | Page 68

Fill in the blank :

Multiplicative models of time series _______ independence of its components.

Miscellaneous Exercise 4 | Q 2.07 | Page 68

Fill in the blank :

The simplest method of measuring trend of time series is _______

Miscellaneous Exercise 4 | Q 2.08 | Page 68

Fill in the blank :

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

Miscellaneous Exercise 4 | Q 2.09 | Page 69

Fill in the blank :

The complicated but efficient method of measuring trend of time series is _______.

Miscellaneous Exercise 4 | Q 2.1 | Page 69

Fill in the blank :

The graph of time series clearly shows _______of it is monotone.

Miscellaneous Exercise 4 | Q 3.01 | Page 69

State whether the following is True or False :

The secular trend component of time series represents irregular variations.

• True

• False

Miscellaneous Exercise 4 | Q 3.02 | Page 69

State whether the following is True or False :

Seasonal variation can be observed over several years.

• True

• False

Miscellaneous Exercise 4 | Q 3.03 | Page 69

Cyclical variation can occur several times in a year.

• True

• False

Miscellaneous Exercise 4 | Q 3.04 | Page 69

Irregular variation is not a random component of time series.

• True

• False

Miscellaneous Exercise 4 | Q 3.05 | Page 69

State whether the following is True or False :

Additive model of time series does not require the assumption of independence of its components.

• True

• False

Miscellaneous Exercise 4 | Q 3.06 | Page 69

State whether the following is True or False :

Multiplicative model of time series does not require the assumption of independence of its components.

• True

• False

Miscellaneous Exercise 4 | Q 3.07 | Page 69

State whether the following is True or False :

Graphical method of finding trend is very complicated and involves several calculations.

• True

• False

Miscellaneous Exercise 4 | Q 3.08 | Page 69

State whether the following is True or False :

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

• True

• False

Miscellaneous Exercise 4 | Q 3.09 | Page 69

State whether the following is True or False :

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

• True

• False

Miscellaneous Exercise 4 | Q 3.1 | Page 69

State whether the following is True or False :

All the three methods of measuring trend will always give the same results.

• True

• False

Miscellaneous Exercise 4 | Q 4.01 | Page 69

Solve the following problem :

The following table shows the production of pig-iron and ferro- alloys (‘000 metric tonnes)

 Year 1974 1975 1976 1977 1978 1979 1980 1981 1982 Production 0 4 9 9 8 5 4 8 10

Fit a trend line to the above data by graphical method.

Miscellaneous Exercise 4 | Q 4.02 | Page 70

Solve the following problem :

Obtain trend values for data in Problem 19 using 3-yearly moving averages.

Miscellaneous Exercise 4 | Q 4.03 | Page 69

Solve the following problem :

Obtain trend values for the following data using 5-yearly moving averages.

 Year 1974 1975 1976 1977 1978 1979 1980 1981 1982 Production 0 4 9 9 8 5 4 8 10
Miscellaneous Exercise 4 | Q 4.04 | Page 69

Solve the following problem :

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

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

Fit a trend line to the above data by graphical method.

Miscellaneous Exercise 4 | Q 4.05 | Page 69

Solve the following problem :

Fit a trend line to data in Problem 4 by the method of least squares.

Miscellaneous Exercise 4 | Q 4.06 | Page 69

Solve the following problem :

Obtain trend values for data in Problem 4 using 4-yearly centered moving averages.

Miscellaneous Exercise 4 | Q 4.07 | Page 69

Solve the following problem :

The percentage of girls’ enrollment in total enrollment for years 1960-2005 is shown in the following table.

 Year 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Percentage 0 3 3 4 4 5 6 8 8 10

Fit a trend line to the above data by graphical method.

Miscellaneous Exercise 4 | Q 4.08 | Page 69

Solve the following problem :

Fit a trend line to the data in Problem 7 by the method of least squares.

Miscellaneous Exercise 4 | Q 4.09 | Page 69

Solve the following problem :

Obtain trend values for the data in Problem 7 using 4-yearly moving averages.

Miscellaneous Exercise 4 | Q 4.1 | Page 69

Solve the following problem :

Fit a trend line to the data in Problem IV (1) by the method of least squares.

Miscellaneous Exercise 4 | Q 4.11 | Page 70

Solve the following problem :

Fit a trend line to data by the method of least squares.

 Year 1977 1978 1979 1980 1981 1982 1983 1984 Number of boxes (in ten thousands) 1 0 3 8 10 4 5 8
Miscellaneous Exercise 4 | Q 4.12 | Page 70

Solve the following problem :

Obtain trend values for data in Problem 10 using 3-yearly moving averages.

Miscellaneous Exercise 4 | Q 4.13 | Page 70

Solve the following problem :

Following table shows the number of traffic fatalities (in a state) resulting from drunken driving for years 1975 to 1983.

 Year 1975 1976 1977 1978 1979 1980 1981 1982 1983 No. of deaths 0 6 3 8 2 9 4 5 10

Fit a trend line to the above data by graphical method.

Miscellaneous Exercise 4 | Q 4.14 | Page 70

Solve the following problem :

Fit a trend line to data in Problem 13 by the method of least squares.

Miscellaneous Exercise 4 | Q 4.15 | Page 70

Solve the following problem :

Obtain trend values for data in Problem 13 using 4-yearly moving averages.

Miscellaneous Exercise 4 | Q 4.16 | Page 70

Solve the following problem :

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

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

Fit a trend line to the above data by graphical method.

Miscellaneous Exercise 4 | Q 4.17 | Page 70

Solve the following problem :

Fit a trend line to data in Problem 16 by the method of least squares.

Miscellaneous Exercise 4 | Q 4.18 | Page 70

Solve the following problem :

Obtain trend values for data in Problem 16 using 3-yearly moving averages.

Miscellaneous Exercise 4 | Q 4.19 | Page 70

Solve the following problem :

Following tables shows the wheat yield (‘000 tonnes) in India for years 1959 to 1968.

 Year 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 Yield 0 1 2 3 1 0 4 1 2 10

Fit a trend line to the above data by the method of least squares.

Miscellaneous Exercise 4 | Q 4.2 | Page 69

Solve the following problem :

Following data shows the number of boxes of cereal sold in years 1977 to 1984.

 Year 1977 1978 1979 1980 1981 1982 1983 1984 No. of boxes in ten thousand 1 0 3 8 10 4 5 8

Fit a trend line to the above data by graphical method.

## Solutions for Chapter 4: Time Series

Exercise 4.1Miscellaneous Exercise 4

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 4 - Time Series

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Concepts covered in Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board chapter 4 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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