Numerical Case Study
On
“Business Statistics”
By
Aditya Purohit
(BBA 2nd Year)
106/10 civil lines,
Ajmer 305001
Website: www.dezyneecole.com

NUMERICAL CASE STUDY ON TIME SERIES ANALYSIS:
(i) A Company produced Tea every economic year, the tea production of a
company are as follows:
Year Production
[‘000 lbs.]
Year Production
[‘000 lbs.]
1986 165 1998 280
1987 178 1999 351
1988 236 2000 320
1989 213 2001 370
1990 180 2002 366
1991 163 2003 325
1992 150 2004 256
1993 187 2005 304
1994 210 2006 291
1995 237 2007 271
1996 203 2008 274
1997 215 2009 272
Draw a time series graph on a graph paper relating to the following data and show
the trend by free hand curve and comment on the trend by giving emphasis in the
component of time series and business cycle and comment on the company’s
position and elaborate the stage or year of production according to the business
cycle.

(ii) Also find the trend of production by the method of a 3 yearly cycle and also
suggest the minimum and maximum level of production according to the time
series analysis and trend value for the company for the following data:
Year Production
[in tonnes]
2000 11
2001 12
2002 10
2003 8
2004 9
2005 10
2006 12
2007 11
2008 13
2009 14

SUMMARY
TOOLS and TECHNIQUES used in solving the case study:
Meaning of Analysis of Time Series:
“ A Time Series may be defined as a collection of magnitudes belonging to
different time periods, of some variable or composite of variables, such as
production of steel, per capita income, gross national product, production of
tobacco, or index of industrial production ”.
Utility of Time Series:
1. It helps in Understanding Past behavior.
2. It helps in forecasting.
3. It helps in evaluating Current Accomplishments.
4. It helps in Comparison.
Use of Long term or secular trend:
Ina time series secular trend means long term changes. In any time if we see the
changes between two periods, we will find increasing or decreasing or even a
constant trend.
Methods used in measuring long term or secular trend in case study:
(i) Free hand curve method.
(ii) Moving average method.

(i)
Comment on trend with emphasis on component of
time series
By observing the trend line and trend analysis from the graph, we can clearly
depict that it is a secular or long term trend component of time series and by
observation, we can analyze that an increasing trend has been seen in production of
the company from the starting year i.e. 1986 to 2009 (ignoring the short term
fluctuations) and high’s have been recorded in the year 1988, 1995, 1999(drastic),
2001, 2002, 2005 and 2007.

Comment according to the business cycle
According to the business cycle components, the years for different stages of
production are as follows:
YEARS IN
PROSPERITY STAGE: 1986, 1987, 1988, 1999, 2001 & 2002.
YEARS IN
DECLINE STAGE: 1989, 1990, 1991, 2000 & 2003.
YEARS IN
DEPRESSION STAGE: 1992, 1993 & 2004.
YEARS IN
IMPROVEMENT STAGE: 1994, 1995, 1996, 1997, 1998, 2005, 2006, 2007,
2008 & 2009.
By looking at the trend according to the business cycle, we observe that although
for five years company’s production declined, even it felt in depression stage for
three years but overall, company’s production have shown rapid improvement and
even prosperity.
Company has altogether managed to maintain its prosperity in production
and has shown remarkable improvement as compared to past years.

(ii)
Year Production
[in tonnes]
3 Yearly Totals 3 Yearly Moving
Average
2000 11 - -
2001 12 33 11
2002 10 30 10
2003 8 27 9
2004 9 27 9
2005 10 31 10
2006 12 33 11
2007 11 36 12
2008 13 38 13
2009 14 - -

Comment according to the trend observed
By watching the trend analysis from the graph, we can clearly depict that for the
original data, minimum level of production has been recorded in the year 2003
which was 8 tonnes and the maximum level of production has been recorded in the
year 2009 which was 14 tonnes.
In the same way, by watching the trend analysis for 3 yearly moving
average, we can depict that the minimum level of production has been recorded
consistently for two years i.e. 2003 and 2004 which was 9 tonnes for both the years
and the maximum level of production has been recorded in the year 2008 which
was 13 tonnes.
Comparison of the two Graphs
(I: Graph from 1986 to 2009)
(II: 3 Yearly m.a. graph from 2000 to 2009)
If we compare the trend lines and trend analysis for both the graphs, we can clearly
remark that if the company would have produced as per the 3 yearly m.a. graph,
then it would have produced more in tones as compared to the production done by
the company from years 1986 to 2009.
REASON: As per the 3 yearly m.a. graph is concerned, it clearly shows that the
trend line has shown rapid growth significantly both for 3 yearly m.a. as well as for
original data.

Bibliography
On completing this case study successfully, I would like to thank my
subject teacher Ma’am Neha who cleared all my doubts regarding the
case study and for supporting me in every step of this case study and I
would also like to thank my parents who were always there with me in
every phase of the case study.