Maths (commerce) Solve the Following Question.(5 Marks)

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

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

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

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

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

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

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

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

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

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

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

The following table shows the all India infant mortality rates (per ‘000) for the years 1980 to 2000.

YEAR	1980	1985	1990	1995
IMR	10	7	5	4
YEAR	2000	2002	2010
IMR	3	1	0

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

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

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

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

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

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

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

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

The following table shows the productivity of pig-iron and ferro-alloys (‘000 metric tonn

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

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

The following table gives the production of steel (in millions of tonnes) for the 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 to the above data by the graphical method.

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.

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
Index	0	2	3	3	2
Year	1981	1982	1983	1984	1985
Index	4	5	6	7	10

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

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

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

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

(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.

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

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

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