Statistics and Research Methods Assignment - Business Analysis

This assignment delves into the application of statistical techniques for business decision-making. It begins with an analysis of Australian exports, employing graphical techniques to compare values and percentages over time. The assignment then explores frequency and relative frequency distributions, cumulative distributions, and histogram plotting to analyze a given dataset. Furthermore, the analysis extends to descriptive statistics, investigating the relationship between final consumption expenditure and retail turnover per capita, including the calculation of correlation coefficients and the development of a regression equation. The document provides detailed interpretations of statistical measures, including mean, standard deviation, kurtosis, and quartiles, offering a comprehensive understanding of the data and its implications for business analysis.

STATISTICS AND
RESEARCH METHODS
FOR BUSINESS DECISION
MAKING

Table of Contents
INTRODUCTION...........................................................................................................................1
Question 1........................................................................................................................................1
a. Using an appropriate graphical technique to compare the value of Australian exports..........1
b. Using an appropriate graphical technique to compare the percentage value of Australian
exports (in %)..............................................................................................................................2
c. Commenting on observation (200)..........................................................................................2
QUESTION 2...................................................................................................................................3
a. Constructing a frequency and relative frequency distribution for the data set given..............3
b. Construct a cumulative frequency and relative distribution...................................................3
c. Plotting a relative frequency histogram for the data...............................................................4
d. Ogive chart .............................................................................................................................4
e. Stating proportion of the grades which is less than 60............................................................4
f. Stating proportion of the grades which is more than 70..........................................................5
QUESTION 3...................................................................................................................................5
a. Using an appropriate graphical descriptive measure for describing two variables ................5
b. Investigating the relationship between final consumption expenditure and retail turnover
per capita.....................................................................................................................................5
c. Descriptive statistics ...............................................................................................................5
d. Calculating coefficient of correlation (r) between two concerned variables..........................8
e. .................................................................................................................................................8
f. .................................................................................................................................................9
g...................................................................................................................................................9
h. ...............................................................................................................................................10
CONCLUSION .............................................................................................................................11
REFERENCES..............................................................................................................................12

INTRODUCTION
Statistics referred as the form of the mathematical analysis in which scientific methods
are used for collecting, summarizing, analysing, organising, presenting, the data for deriving the
valid conclusions so that reasonable decisions can be taken based on the analysis. It is mainly
concerned with systematic collection of the numerical data with its interpretation. It is used for
referring to the numerical facts like the number of persons living in the specific area. Statistics in
business relates with the growing size and the increased competition, it is the tool that helps in
resolving the business problems (Kong, and Zhao, 2016). In today's competitive world it
becomes essential for the top executives to adopt statistical methods and the data for assessing
the results with relevancy and accuracy. The present study is based on the various statistical
techniques that helps in resolving the problems of the business and application of the techniques
effectively to generate the results. Furthermore, various scenarios are also created that fits best in
the solution of the problems.
Question 1
a. Using an appropriate graphical technique to compare the value of Australian exports
1
China
Japan
United States
Republic of Korea
India
New Zealand
Singapore
United Kingdom
0
10
20
30
40
50
60
70
80
90
100
A$ bn 2004-05
2014-15

b. Using an appropriate graphical technique to compare the percentage value of Australian
exports (in %)
2004-
05 (A$
bn)
2014-
15 (A$
bn)
China 15.39% 40.40%
Japan 27.30% 20.85%
United States 13.46% 9.17%
Republic of
Korea 10.65% 9.17%
India 6.87% 5.68%
New Zealand 11.81% 5.50%
Singapore 5.61% 5.37%
United
Kingdom 8.91% 3.85%
2

c. Commenting on observation (200)
From the above analysis it can be interpreted that the graph that is showing the value of
the Australian exports in money terms are resulting an increasing trend over the years from
2004-05 to 2014-15. This means that the demand for the Australian products in the other
countries has been increased which indicated as the goods sign for the overall economy of the
Australia as more and more exports brings larger amount of the funds in the country. China and
the Japan are the two major countries in which the export of Australian goods has been made
with a greater value that is from 15.9 to 90.3 in china and 28.2 to 46.6 in japan (Karni, and
Safra, 2016). In other countries also the value is increasing but in united kingdom it is reflecting
the lower value over the years.
From the graphical analysis in the b part, it has been observed that the percentage value
of the Australian export in majority of the countries is showing the decreasing trend which
means the percentage demand of the products and services of the exports has been declined over
the years which in turn results in lower percentage of the returns (Rees, 2018). China is only the
country in which the export increases from 15.39% to 40.40% whereas in other countries that are
Japan, Korea, India, New Zealand, Singapore, UK and US, it reflects the declining trend.
Thus, it could be clearly concluded from the analysis that the export in terms of monetary value
is increasing however the value of percentage of the export in Australian economy is decreasing.
3
China
Japan
United States
Republic of Korea
India
New Zealand
Singapore
United Kingdom
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
40.00%
45.00%
2004-05 (A$ bn)
2014-15 (A$ bn)

QUESTION 2
a. Constructing a frequency and relative frequency distribution for the data set given
Class interval Frequency Relative frequency
30-39 2 5.0%
40-49 4 10.0%
50-59 8 20.0%
60-69 11 27.5%
70-79 8 20.0%
80-89 5 12.5%
90-100 2 5.0%
Grand Total 40
b. Construct a cumulative frequency and relative distribution
Class interval Cumulative Frequency Cumulative Relative frequency
30-39 2 5.0%
40-49 6 15.0%
50-59 14 35.0%
60-69 25 62.5%
70-79 33 82.5%
80-89 38 95.0%
90-100 40 100.0%
c. Plotting a relative frequency histogram for the data
4
30-39 40-49 50-59 60-69 70-79 80-89 90-100
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
Relativ e frequenc y

d. Ogive chart
e. Stating proportion of the grades which is less than 60
Row
Labels
Count of umbrella
sales
30-39 2
40-49 4
50-60 8
>60 26
Grand
Total 40
= 26 / 40 * 100
= 65%
f. Stating proportion of the grades which is more than 70
Row
Labels
Count of umbrella
sales
<70 25
70-79 8
80-89 5
5

90-100 2
Grand
Total 40
Proportion: 25 / 40 * 100
= 62.5%
QUESTION 3
a. Using an appropriate graphical descriptive measure for describing two variables
b. Investigating the relationship between final consumption expenditure and retail turnover per
capita.
X (independent variable): Final consumption expenditure
Y (Dependent variable): Retail turnover per capita - Chain Volume Measures
c. Descriptive statistics
6

Retail
turnover
per
capita -
Chain
Volume
Measures
; Total
(State) ;
Unit $
FINAL
CONSUMPTION
EXPENDITURE:
Chain volume
measures ; $
Millions
Mean 2205.76 146019.855
Standard Error 47.4591 4098.05042
Median 2180.2 139137
Mode 2852.8 #N/A
Standard
Deviation 543.194 46904.331
Kurtosis -1.612 -1.2960945
Range 1558.7 151259
Minimum 1455.9 81889
Maximum 3014.6 233148
Interpretation- As per above table it has been analyzed that the mean value obtained is
2205.76 from the Retail turnover per capita which is considered as dependent variable and
146019.855 from final level of consumption expenditure which is counted as independent
variable respectively. Through detection of the standard error, it has been evaluated that the
sample mean of Retail turnover per capita and final consumption expenditure has been resulted
as 47.4591 and 4098.05042 respectively. The value of the Standard deviation is determined from
the actual and true mean value which states the relationship between the increased Retail
turnover per capita figure and the consumption expenditure change (Silverman, 2018). The
value of Kurtosis depicts the peak distribution of data set whereas the positive value of Skewness
reflects that the value of the mean and median are greater than the value of mode. The difference
between highest and smallest sales figure defines the value of the range which is resulted as
1558.7 in case of retail turnover per capita and in case of consumption expenditure it has been
determined as 151259. Sales in value of 2852.8 has been attianed most of the time as per the
7

calculation of mode. The minimum and the maximum value evaluated from the analysis is
1455.9 and 81889 however 3014.6 and 233148 is the maximum value calculated in the retail
turnover per capita and final consumption.
Particular
s
Figures: Retail
turnover per
capita - Chain
Volume
Measures ;
Total (State) ;
Unit $
Figures:
Final
consumptio
n
expenditure
: Chain
volume
measures ; $
Millions
Quartile 1
and 25th
percentile
1652.95 103558.5
Quartile 2
and 50th
percentile
2180.2 139137
Quartile 3
and 75h
percentile
2793.4 192800.5
Interpretation- Quartile refers to the statistical term that describes the division of the data
into the four stated intervals (Gravetter and Wallnau, 2016). From the above table it can be has
been analyzed that in the first quarter the value for the retail turnover per capita and the final
consumption resulted as 1652.95 and 103558.5. In the second quarter, the value for the
dependent and the independent variable equates to 2180.2 and 139137. The results of the
variables in the third quarter determined as 2793.4 and 192800.5. The value of the Quartile
computed for Retail turnover per capita and final consumption expenditure is showing an
increasing trend over the certain period. The change in percentile level at different stages is also
8

reflecting the positive trend as it rises from 1652.95 to 2793.4 in Retail turnover per capita and
103558.5 and 192800.5 in respect to consumption expenditure level. This means that better
division is been made and positive outcomes has been gained.
d. Calculating coefficient of correlation (r) between two concerned variables
Correlation coefficient is the statistical measure that measures the degree or the extent to
which the change in the value of the one variable to predict the changes with that of the value of
the another value (Otto, 2016). The value equals to -1 depicts the negative correlation, which
means that the resulting value of the one variable predict the changes in opposite direction under
the second variable (Berman and Wang, 2016). In other words it refers to the measure that shows
the linear relationship between different variables that include the dependent and the independent
variable.
Particulars Retail turnover per capita -
Chain Volume Measures ;
Total (State) ; Unit $
FINAL CONSUMPTION
EXPENDITURE: Chain
volume measures ; $
Millions
Retail turnover per capita 1 .987 or .99
Final consumption
expenditure
.987 or .99 1
Interpretation- From the above calculation it is interpreted that the relationship between
the dependent variable that is retail turnover and the independent variable that is final
consumption is resulting a positive correlation which that both the variable are directly related
with each other (Rohatgi, and Saleh, 2015). This means that change in one variable predicts the
change in the other variable in a common direction and not opposite direction. Retail turnover
per capita and final consumption expenditure level are highly correlated as the value of the
correlation calculated as same in both the variables. Both the factors are showing positive
correlation between each other. Any change in the value of one factor will bring in change in the
value of other as well, that is both will move in the same direction.
e.
Regression equation: y = a + bx
Retail turnover per capita = a + b final consumption expenditure
Retail turnover per capita = 535.52 + .011 (Final consumption expenditure)
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f.
Regression
Statistics
Multiple R 0.987697
R Square 0.975546
Adjusted R
Square 0.975356
Standard Error 85.2727
Observations 131
Interpretation- The R square define the movement of dependent variable with regards to
the independent variable (Devore, 2015). It depicts the fitness of good which means the value to
which the dependent variable best fit to the independent variable. Under this study, the
independent variable is consumption expenditure and dependent variable is retail turnover per
capita. The value of R square for the above two variable have calculated as 0.98 or 98 %, which
is more than 0.05 that means no difference is present between the variables. The regression
between the two variable depicts the dependability of one variable over other. From the present
calculation it can be stated that both consumption expenditure and retail turnover per capita are
significantly related and have a high dependability over each other.
g.
Null hypothesis (H0): There is no statistical significant difference in the mean value of
dependent and independent variable.
Alternative hypothesis (H1): There is a statistical significant difference in the mean value
of dependent and independent variable.
Regression analysis- It is the series of the process under statistics that is made for
estimating relationship between the different variables (Frankfort-Nachmias and Leon-Guerrero,
2017). This technique is used to determine or in understanding the extent to which the dependent
variable is dependent on the independent variable and also helps in exploring the forms of the
relationship present among the variables. Regression analysis helps in developing the predictions
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