Bayesian Statistics and Data Mining Applications

This assignment delves into the world of Bayesian statistics and its practical applications in diverse fields. It examines theoretical concepts, nonparametric and semiparametric methods, and real-world applications spanning risk management, econometrics, and network analysis. The provided resources encompass textbooks, research papers, and online materials that shed light on various statistical techniques and their practical implementations.

Statistics for Management

Table of Contents
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
A): i) Gross annual earnings in the public and private sector ...............................................1
TASK 2............................................................................................................................................5
a): Analyse raw business data by using statistical methods...................................................5
TASK 3..........................................................................................................................................12
Statistical methods used in business planning......................................................................12
TASK 4..........................................................................................................................................14
Communicating finding though using charts and tables......................................................14
CONCLUSION..............................................................................................................................18
REFERENCES..............................................................................................................................19

INTRODUCTION
Statistics is said to be the science of collection, presentation and evaluation and analysis
of numerical as well as mathematical data. It is necessary to have a correct data which will be
helpful in analyzing the positive conclusion from the available resources which are collection for
the various sources. The main objective of these data is to reach out to a solution which is further
required to achieve the organizational objectives. This project report consists of various tasks
which are explaining the nature and process of economical data from different published sources
(Yalagandula and KimCurtis, 2012). Evaluation of various sources of implement techniques for
the analysis. Under of using qualitative and quantitative data in the concern business is also
discussed under this report. Some of the major tools are also used in order to know the right
results from the given situation. All the information and data are collected are presented through
allying various charts.
TASK 1
A): i) Gross annual earnings in the public and private sector
In an organization, the employees are working in order to achieve their individual as well
as group goals. In return of their work they are getting some annual earning after the net profit a
company get during the year. It is the amount which is earned annually. Gross annual income is
said to be that amount of fund a person or employees earn in a one financial year from all the
related sources before any taxes levied on it. While, preparing an income tax return during the
accounting period, the gross annual income total is taken as the base amount with which to
operate (Reaves and Hickman, 2015).
How to determine gross annual salary:
To examine the total gross annual salary firstly, to find out exact amount of pay, multiply
it with the hourly wages by the total number of hours an employees is working in a week then
multiply it with 52. It will come out as gross annual income and after that divide it by 12 to
determine monthly pay they are getting.
1

Gross annual earnings for Male
Year Public sector Private sectors Changes
2009 30638 27362 3276
2010 31264 27000 4264
2011 31380 27233 4147
2012 31816 27705 4111
2013 32541 28201 4340
2014 32878 28442 4436
2015 33685 28881 4804
2016 34011 29679 4332
Gross Annual earnings of Female
Year Public sector Private sectors Changes
2009 25224 19551 5673
2010 26113 19532 6581
2011 26470 19565 6905
2012 26636 20313 6323
2013 27338 20698 6640
2014 27705 21017 6688
2015 27900 21403 6497
2016 28053 22251 5802
2

From the above drawn column charts, it has been found that in case of female they are
earning more than male since 2009 (Embrechts and FreyMcNeil, 2014). Under this situation,
both public and private sectors are dominated by the female groups as they are earning more than
male which is indicated in 2011. From, 2013 to 2015 they are getting maximum earning while
males are at that point not able to get that much of income from the company.
ii): The difference among male and female gross annual earning for public sector
Year
Public
sector
for male
Public
sectors
for
female
Differe
nce
2009 30638 25224 55862
2010 31264 26113 57377
2011 31380 26470 57850
2012 31816 26636 58452
2013 32541 27338 59879
2014 32878 27705 60583
2015 33685 27900 61585
2016 34011 28053 62064
3

2. The difference among male and female gross annual earning for private sector
Year
Private sector for
male
Private
sectors
for
female Difference
2009 27362 19551 46913
2010 27000 19532 46532
2011 27233 19565 46798
2012 27705 20313 48018
2013 28201 20698 48899
2014 28442 21017 49459
2015 28881 21403 50284
2016 29679 22251 51930
4

According to the above used line charts, it has been found that if we combine both public
and private sectors income in order to calculated total earning. For male, it has been seen that
line charts are starting at very constant stages and fall some time and then after reached at the
maximum with highest point (Wright and Goodwin, 2013). Likewise, in case of female it has
been found that they are receiving income from very low stages and stiff down sometime and
then after increases at increasing rate and reached out at maximum level.
TASK 2
a): Analyse raw business data by using statistical methods
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i: Earning of various employees
Hourly
Earning
% of
employees CF Cf
Below
10 8 8 8.00%
10 but
under 15 22 30
30.00
%
15 to 20 24 54
54.00
%
20 to 25 14 68
68.00
%
25 to 30 12 80
80.00
%
30 to 40 14 94
94.00
%
40 to 50 6 100
100.0
0%
100
Median 41.25
Quartile
25th 17
6

Median= L1 + (N/2) – C/ F* I
Mean= Number of frequency / 2 = 100/2= 50
It falls into the range of 15-20
Median: 15 + [(50-8) / 24*15]
: 15+(42/24*15)=41.25
Q1 = 100/4 = 25 which is fall under the category of 10-15
Q1= 10+(25-8)/22*10
= 10+17/22*10=17
Q3= 3(N/4)
= 3(100/4)=75 fall under the category of 25-30
=25+ (75-54)/ 12*10 =42.5
According to the calculated results, median of hourly earning is 41.25. while quartile first
was determined to 17 and Q3 is found 42.5. It seems to be that reaction which indicate that only
6employes are less paid those are linked to 40-50 class.
ii) calculation of standard deviation and mean
Hourly Earning
Frequenc
y Mid value F* M
Below 10 8 5 40
10 but under 15 22 12.5 275
15 to 20 24 17.5 420
20 to 25 14 22.5 315
25 to 30 12 27.5 330
30 to 40 14 35 490
40 to 50 6 45 270
Total 2140
Mean 21.4
7

Working note:
The above calculation is done through using below mentioned formula:
Mean: = ∑F*x /∑F
= 2140 /10
= 21.40
Calculation for standard deviation
Hourly Earning Frequency Mid value F* M Dx = X-A Fdx Fdx2
Below 10 8 5 40 -17.5 -140 19600
10 but under 15 22 12.5 275 -10 -220 48400
15 to 20 24 17.5 420 -5 -120 14400
20 to 25 14 22.5 315 0 0 0
25 to 30 12 27.5 330 5 60 3600
30 to 40 14 35 490 12.5 175 30625
40to 50 6 45 270 22.5 135 18225
100 2140 -110 134850
Assume mean 22.5
Standard deviation: √ ∑Fdx2/N – (∑F d*x/N)2
= √ 134850 / 100 - (- 110/100)^2
= √ 1348.5- 12100 / 10000
= √ 1348.5-1.21 =√1347.29= 36.7
b) Comparison of two results:
In case of A In case of B
In the above mentioned case of A it has been found
that median of following data are £68.
But in the other situation of north east health
professional it was come out to be £14.55. Which is
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very much low as compare to the A situation.
Mean values from the given observation in which the
employees are hourly paid are 21.4 of the total.
While in case of B, it low with 16.75 which means
that the company is paying very less amount to them
for their work.
If we look into the standard deviation it has more
risk with 141 to the company.
In case of Company B, they are recorded very less
risk as their standard deviation is much lower with
only 7.14.
According to the above comparison it has been found that in case of A they are much
satisfying with the facilities from that of the company. They are earning more than as compare to
other company. The best result is provided from the A (Ripley and Venables, 2014). The quartile
ranges at 25th percentage is around 8 which is again a positive sign for the company. The
statistical data of A is more effective from that of B. The information which are collected in
order to determine the total changes and impacts on the company as well as employee’s
performance through changes in the earning. This survey from the health professionals is more
effective to analyses the best alternative which is providing more accurate results to the
employees of an organization.
B):
a): Scattered diagram: It is refers as the study and determine best possible relationship among
the changes that are observed in various two sets of variables. It is that value which indicates the
two variables those are plotted on the two axes, this pattern is used to identify correlation
present. It consists of numerical data, the point on that graphs are either fall along the line or in
curve manner.
Outlet size(S) Turnover(T)
A 22 3.3
B 12 2
C 15 2.5
D 20 3.8
E 25 4.1
F 24 3.5
G 10 1.8
H 26 5
I 12 2.5
9

J 18 2.5
From the above scattered diagram, it has been found the size of flour areas is much
higher side as compare to that of average weekly turnover (Cochran and et. al., 2011). It means
the most of the clusters are observed in above in the graphs. The turnover is summarized at the
same point with various sizes at the common level. The diagram is perfect to demonstrate the
changes which are seen in the flour or average weekly turnover. Both are gather in their
respective places.
b): Equation on scatter line
10

11

Y= 0.0727x+18.8 on the size of the flour
Y= 0.133x+3.0267 on the total turnover.
c) Calculation of total turnover if the new outlet of 30 sqm is to be designed.
From the above equation,
Y=0.133x+3.0267
= 0.133*30+3.0267
= 3.99+3.0267=7.0167. sqm
d): Calculation of Correlation coefficient
Outle
t size(S)
Turnover
(T)
A 22 3.3
B 12 2
C 15 2.5
D 20 3.8
E 25 4.1
F 24 3.5
G 10 1.8
H 26 5
I 12 2.5
J 18 2.5
Coefficient
correlation
0.913767
28
Range
Minimum 1.8
Maximum 5
e): Statistical validity is the extent to which various data are represented in order to know the
cause and effect relationship rather than its failure. It represents that result as whether any kind
of relationship exist and what is the best possibility to chance which are arises by using various
data. It is more similar to the internal validity. The reliability of measure is high. The statistical
data must establish that an outcome has very less chance of possibility of occurrence (Linoff and
et. al., 2011). There is also no guarantee that the selected data is random error in sampling of the
information or its measurement. The two important factors which are affecting the internal or
external validity of turnover are:
12

Testing effects: these are related with the chosen situation which is used in order to
determine the overall values from the mentioned variables. The necessary testing possibility can
be used so that more accurate chance of getting right results is generated from weekly turnover.
Selection effects: The other factors which are affecting the turnover are the selection of
variable for the evaluation. It is based on the hypothetical situation whether the selection has the
best possible chance to provided better results. The effects can be determined by using right kind
of methods and techniques in the analysis of statistical values.
TASK 3
Statistical methods used in business planning
These kind of methods are more helpful in analyzing positive results and more reliable
outcome. Such information are essential for determining the average and accurate frequency of
the outcomes. There are different number of numerical values which are identified by using
statistical methods. As, it has been found that comparing with settled techniques, which are
accurate whereas, observations are reproducible. In that situation where the distribution of data is
inclined statistical handling is more complex (Dey, 2012). The most effective parameters used
under this method are mean or average and the standard deviation is being used. Some of other
important tools are F-test, T-test and regression and correlation analysis. Few of the statistical
methods are:
Analysis of variances(ANOVA): It is used to compare values of two variables which are
present in a situation. If the results are come out as odd value then these techniques are known as
analysis of variances (Curtis, 2016).
Chi- square test: It is considered as written test which is based on the hypothetical test
wherein the sampling distribution of the statistic which is a chi-squared distribution is case null
hypothesis is true.
Correlation: The mutual relationship and more that two variables are represented with
the use of this method. It is that methods which is used to compare two sets of data that are
connected together in that situation they are representing high correlation.
13

Factor analysis: It refers as a statistical techniques which is used to determine variability
among ascertained and correlated variables in terms of a specific low number of unseen data
presented as factors (Factor Analysis, 2017).
There are various planning tools which are used by the company in order to ascertain large
number of targets which is followed in an organization. Some of them are:
Financial accounting: With the use of company's financial statements and estimation of
right kind of factors are need to be supported in forming its targets and those of plans. The major
targets of company is to promote it growth and performance in order to gain more competitive
advantages over the others. It will help to achieve its long and short term goals.
Management and operations: In an organization, most of the department are working in
for the individual as well as organization goals which are needed to be achieved in as soon as
possible. For this process, proper maintenance of operational department are overlooks so that
more effective results can be drawn.
R and D: The other aspects of this planning tools are research and development team.
They are responsible for determining the proper skills and knowledge of an employees whether
they require any training and development to improvise its capabilities (Heizer, 2011).
For the demand of client c with the situation provided into the case.
a) The total number of delivery made in each year
Total days=365
No. of days not working=5 days
Total working days= 365-5 =360 days
one deliveries takes = 12 days time.
So, the total number of deliveries = 360/12= 30 days.
b) Total number of bottles of olive oils which are currently delivered with each delivery
The demand of total bottle of olive oils = 450,000
Total delivery time = 30 days
So, for per unit = 450,000/30= 15000 bottles
c) EOQ:
Economic order quantity is the total amount of units that a company is added to its
inventory with the each order to reduce the total costs of stocks such as carrying cost, ordering
14

costs, and holding cost. It is seen that mostly they are calculated at the one year and than
expressed as in the form of percentages of the cost of products (Hinkelmann, 2014). It is known
as one of the most oldest production cost methods which is used by the company to control its
inventory.
EOQ=√2RO/C
=√2*450000*20/0.50
=6000 bottles
d) Determine the variations in every above cases and provide recommendations
In financial accounting system, total cost is considered as those cost which are associated
with the production process and those which is made up of with variable costs. It is mainly
linked to the direct labour, material and other costs and in addition of fixed cost in this. All those
expenses which are related with the development of products or supply a services that alter in
direct proportion to the total quantity manufactured or generated during the year. The more is the
production done by the company less cost will be incurs respectively. Hence, the management
need to have proper understanding about the reactions which are seen at the time of production
process (Neave, 2012). It will directly impact the cash inflows and also to the productivity.
Economic order quantity is right kind of techniques which is more useful in determine current
position of the stocks which are available with the company. Before making any effective plan or
strategies the management need to analyse the proper mode and reports whether they are getting
positive outcomes from that of investments.
TASK 4
Communicating finding though using charts and tables
a) Gross annual earnings for Male
Year Public sector Private sectors Changes
2009 30638 27362 3276
2010 31264 27000 4264
2011 31380 27233 4147
2012 31816 27705 4111
2013 32541 28201 4340
2014 32878 28442 4436
15

2015 33685 28881 4804
2016 34011 29679 4332
Gross Annual earnings of Female
Year Public sector Private sectors Changes
2009 25224 19551 5673
2010 26113 19532 6581
2011 26470 19565 6905
2012 26636 20313 6323
2013 27338 20698 6640
2014 27705 21017 6688
2015 27900 21403 6497
2016 28053 22251 5802
16

From the above mentioned line chart which is generated from the total gross annual
earning of males and female. In case of male the line starts from the 3000 of earning and keep
increasing till 4264 and there after starts fluctuating and in 2015 it gain reached at the highest
position. Likewise, in case of female they start getting earning from 5673 and increases till 6905
and thereafter decline and after that it starts increasing constantly (Hofert and Embrechts, 2015).
So the best part of this charts is producing right results as they females are getting more earning
as compare to male.
b) Use of Ogive charts for cumulative %
Hourly Earning % of employees CF
Below 10 8 8
10 but under 15 22 30
15 to 20 24 54
20 to 25 14 68
25 to 30 12 80
30 to 40 14 94
40 to 50 6 100
17

According to this o give chart presented through taking hourly earning which is paid to
both female and male employees those are working in an organization. The above graphs is
indicating that the line begun from cumulative frequency of 8 and goes increasing at 54 and after
than it little bends and thereafter again starts increasing constantly (Haimes and et. al., 2012).
The best recommendation is to stop paying those who are below 10 and increase the earning of
20 to 25 range of employed as they are more skilled and experiences.
c) Scatter diagram
Outlet size(S) Turnover(T)
A 22 3.3
B 12 2
C 15 2.5
D 20 3.8
E 25 4.1
F 24 3.5
G 10 1.8
H 26 5
I 12 2.5
J 18 2.5
18

According to the above data based on the size and turnover which are incurred from
various number of outlets. It has been found that lot size are above the turnover. The sizes are too
much fluctuating in the above scatter diagram as compare to turnover as they are constantly
move. The recommendation to this analyze the deviation which are taking in different aspects of
both size and turnovers (Roger, 2013). The relationship among both of them are represented at
positively but the size is at most higher side as compare to turnover as it is constantly deviating
at each stages.
CONCLUSION
From the above project report it has been concluded that statistical management is more
effective tool which is used by an organisation in order to analyse there financial data. This
project report consists of various information related with company performance. Such as gross
annual earnings of male and female during the coming years. Likewise, various information is
presented with the help of charts and graphs. Al the measures of central tendency are evaluated
under this projects. On the basis of above charts necessary recommendation is been made in
order to reach at a valid solution.
19