Statistical Analysis in Business Decision Making

This assignment delves into the significance of statistical analysis in aiding business managers in decision-making processes. It emphasizes the role of descriptive statistics in summarizing datasets effectively and highlights the value of graphical presentations for data visualization and understanding. Furthermore, it showcases how statistical tools and techniques contribute to robust business planning, particularly in areas like quality management, capacity optimization, and inventory control.

Statistics for Management

TABLE OF CONTENTS
INTRODUCTION......................................................................................................................3
MAIN BODY.............................................................................................................................3
P1 and M1 Evaluating the nature and process of business & economic information............3
P2 Evaluating data set from a variety of sources...................................................................5
P3 Analyzing qualitative and quantitative data using statistical methods.............................8
P4 Applying range of business methods that can be used for business planning................13
P5 Communicating findings regarding the given variables.................................................16
M2 Presenting differences take place in application between measuring association,
descriptive and inferential statistics.....................................................................................16
M3 Justifying the use of appropriate statistical methods.....................................................17
M4 Stating rationale pertaining to the chosen method of communication..........................18
D1 Critically evaluating differences in the application of descriptive, exploratory and
confirmatory analysis...........................................................................................................18
D2 Giving recommendations in relation to making improvement in business planning
through the means of statistical method...............................................................................19
CONCLUSION........................................................................................................................19
REFERENCES.........................................................................................................................20

INTRODUCTION
In the current times, for ensuring effectual management business units lay high level
of emphasis on undertaking statistical tool and techniques. This in turn helps in evaluating
and summarizing large data set in a meaningful manner and thereby aid in decision making.
Statistical assessment also focuses on presenting data in a graphical format which in turn
develops high level of understanding regarding data set. Statistical evaluation mainly includes
collection, recording, analysis and evaluation of data using multiple tools. By applying such
tools manager of the firm can make appropriate estimation and thereby develops competent
framework which makes contribution in the goal attainment. The present report is based on
different case situations which will provide deeper insight about the manner in which
statistical techniques assist in evaluating trend. It also depicts how inventory, quality and
capacity management can be ensured through the means of statistical evaluation.
MAIN BODY
P1 and M1 Evaluating the nature and process of business & economic information
Bain (2017) analyzed in their study that business related information contributes in
the attainment of goals significantly. Moreover, information pertaining to operations assists
company in taking decision about selling & marketing, promotional aspects and cost control.
For instance: Increasing level of expenses gives clear indication to the manager in relation to
taking initiative for cost control and thereby enhances the level of profit margin. Further,
Crowder (2017) presented in their study that business information helps in assessing products
or services of the firm, making improvement in the existing offerings and sales process. Thus,
referring such aspects it can be mentioned that business information is highly vital which in
turn helps in developing suitable strategic and policy framework.
Now, with the motive to take suitable decisions business units make focus on the
collection and analysis of data set. According to the views of Hussain and et.al., (2018),
significant difference takes place between data and information. Data implies for the figures
that is recorded by the company for further analysis and evaluation. It is raw in nature and
considered for evaluation purpose. However, on the critical note, O'Mahony (2017) stated
one can generate suitable information from data set only when they have ability to process
and analyze the data set. Hence, suitability of information and decision making is highly

influenced from the ability of manager in relation to analyzing information. Further, another
Valiullin, Legros and Tkachenko (2017) stated that using statistical techniques manager of
the firm can analyze information and thereby aid in decision making aspects.
On the basis of given case situation, considering the data set pertaining to net income
and sales expenses client wishes to take suitable business decisions. In this regard, given data
set from the year of 2009 to 2017 can be processed or analyzed using statistical tools and
techniques. Hence, by evaluating such data set manager of the firm can take decision about
the funds that need to be allocated for selling & promotional aspects. In addition to this,
outcome of statistical assessment also gives input to the company about the manner through
which net income can be enhanced (Lazar, 2017). For example: through evaluation it has
assessed that sales & promotional expenses place positive impact on the net income of firm.
Moreover, promotional activities develop awareness among the customers and thereby entice
their decision making. In accordance with such aspect, for enhancing revenue and profit
margin client should make focus on doing promotional activities.
In addition to this, now client also wishes to use a courier firm for their deliveries and
operations. Reviews presented by the customers clearly show that courier services offered by
Hermes UK are average. By evaluating reviews, it has found that clients are waiting for their
deliveries. It shows that such courier firm failed to deliver services on time as per the
promises made by them. In addition to this, concerned customers can contact company only
through the means of web chat. Hence, in the case of technical errors customers cannot
contact to the company regarding their deliveries. In addition to this, other people have also
given negative reviews regarding Hermes courier services. By taking into account such
information it can be mentioned that client should make focus on identifying and approaching
other courier service provider.
Data collection: In the context of business unit, data can be gathered from two
sources such as primary and secondary. Primary sources include interview, focus group,
observation, survey etc which helps in gathering data as per the concerned issue. On the basis
of cited case scenario, client wants to get information about the effectiveness of courier
services offered by Hermes. Thus, for collecting reviews about the services primary data has
been gathered via interview. Further, secondary data can be gathered by the researcher for
resolving business issues via books, journals and scholarly articles.

Qualitative data: It implies for the data set in which objects are classified on the basis
of attributes and properties. Such data lays emphasis on using subjective approach which
helps in developing initial understanding about issue. Examples of qualitative data set include
characteristics which can be defined or presented theoretically such as colour etc.
Quantitative data: It contains type of data which can be measured and expressed in a
numerical format. Sales, income trend etc may be served as the main examples of quantitative
data assessment.
Qualitative data
Advantages Disadvantages
 Assists in conducting social and
behavioural studies prominently
 Helps in obtaining rich descriptive
data set about social phenomena
through the means of interview etc.
 Under qualitative evaluation,
conscious and unconscious biasness
affects researcher’s conclusion.
 It lacking rigorous scientific control
and numeric evaluation.
Quantitative data
Advantages Disadvantages
 Presents solution by reducing the
level of biasness
 Helps in finding suitable solution of
issues by including statistical
techniques
 Includes complexity in relation to
hypothesis framing and inclusion of
suitable tools
P2 Evaluating data set from a variety of sources
There are several statistical modes or techniques that can be used for data analysis
regarding sales expense and net income. Statistical evaluation provides high level of
assistance in evaluating data set more effectually and thereby helps in taking appropriate
decisions. Main techniques that client can undertake for analyzing information is as follows:\
Computation of mean, mode and median:

Expenses Income
Mean 21777.78 39444.44
Median 20000 40000
Mode 20000 45000
Mean: It renders information about the average value of data set. By dividing sum of
all the values from the total count of number analyze can derive or assess mean value.
Mean = sum of all the values / number of units
Tabular presentation depicted above clearly shows average expenditure incurred
within the period of 9 years imply for £21777.78. In addition to this, mean income generated
over expenses within the concerned time frame accounted for £39444.44 significantly.
Mode: This reflects the number which is occurred repeatedly or more frequently in the data
set (Suresh and Joshi, 2017). Hence, referring mode value analyst can evaluate the impact of
same on the performance level. Quantitative evaluation shows that within the period of 9
years, figure related to expenses and income occurred repeatedly accounts for £20000 &
£45000 respectively.
Median: By doing median analysis client can get information about and evaluate 50%
value of data set. Hence, median analysis helps in decision making prominently by presenting
information about half or majority of the data set.
Median = Value of ($\frac{N+1}{2})^{th}\ item$.\
Statistical evaluation presents that 50% value pertaining to the expenses and income
imply for £20000 & £40000 significantly.
Trend analysis: This statistical measure helps in assessing whether concerned
variable will incline in the near future or not (Wang and et.al., 2017). Hence, conducting
trend analysis, manager of the firm can make proper forecast about the future aspects and
thereby would become able to develop competent framework for the future growth or
success.

2009 2010 2011 2012 2013 2014 2015 2016 2017
0
10000
20000
30000
40000
50000
60000
70000
f(x) = 1050 x + 16527.7777777778
R² = 0.419851904090268
f(x) = 4333.33333333333 x + 17777.7777777778
R² = 0.74014598540146
Expenses
Linear (Expenses)
Income
Linear (Income )
The above depicted trend line shows that in the near future both selling
expenses and net income will incline significantly. Movement of selling expenses are neither
too high nor too lower. However, trend of net income presents that it will be increased to a
great extent.
Correlation: Such statistical tool indicates relationship which takes place between
two variables. By doing correlation analysis, manager of the firm can measure or evaluate the
impact of one variable on another (Arostegui and et.al., 2018). Correlation can be presented
in three ways high, moderate and negative. In the case of positive and high relationship both
the concerned variables move in a similar direction.
Correlation between sales expenses and net income on the basis of information given by the
client:
Sales Expenses Net Income
Sales Expenses 1 .84
Net Income .84 1
The above depicted table shows that .84 correlations takes place between sales
expenses and net income. On the basis of such outcome, net income of client’s firm will
increase or decrease in the similar direction according to selling expenses. In other words, it
can be mentioned that net income increases when client spends high money in selling
expenses.

Quartile and percentile: Statistical measure such as quartile and percentile
represents information regarding each quarter. The main difference between the two is
quartile presents information in numeric terms, whereas percentile exhibits data set in the
form of percentage.
Particulars Expenses (in £) Income (in £)
Quartile 1 and 25th
percentile 20000 30000
Quartile 2 and 50th
percentile 20000 40000
Quartile 3 and 25th
percentile 24000 45000
Statistical assessment presents that, in quarter 1 and 2, selling expenses accounts for
£20000 respectively. On the other side, in the third quarter, expenses incurred by the
company for selling purpose implied for £240000. Further, income level increased over the
each quarter. As per quarter 1, net income was £30000 whereas at the end of 3rd one it
reached on £45000 respectively.
Evaluation of quantitative tools
Quantitative techniques Positives Negatives
Mean Easy to compute Highly sensitive to the most
extreme values
Mode It assists in assessing most
frequent data
In the discrete data series mode
is difficult to assess
Median Such tool is not highly sensitive
to outliers
In this, more than one
dimension is difficult to
generalize
Trend analysis Helps in gathering information
about future
It is based on historical data set
which may not provide clear
view of future aspects.
P3 Analyzing qualitative and quantitative data using statistical methods
Data pertaining to income and expenses from the period of 2009 to 2017 is as follows:
Year
Expense
s
Incom
e

2009 15000 20000
2010 20000 25000
2011 24000 30000
2012 20000 40000
2013 18000 35000
2014 25000 50000
2015 20000 45000
2016 30000 65000
2017 24000 45000
Descriptive statistics
Expenses Income
Mean 21777.78 39444.44
Standard Error 1479.281 4598.04
Median 20000 40000
Mode 20000 45000
Standard Deviation 4437.842 13794.12
Sample Variance 19694444 1.9E+08
Kurtosis 0.311663 0.131387
Skewness 0.421339 0.423326
Range 15000 45000
Minimum 15000 20000
Maximum 30000 65000
Sum 196000 355000
Count 9 9
Confidence Level (95.0%) 3411.228 10603.1

The above depicted table shows that average expenses incurred by the firm accounts
for £21778 respectively. On the other side, median and mode pertaining to sales expenditure
accounted for £20000 significantly. It shows that average expense level of the company is
higher. Thus, company should make focus on undertaking budgetary control tools and
techniques which in turn help in exerting control on expenses and attaining profit margin.
Hence, through continuous monitoring of expenses firm can avoid spending on undesirable
spending. Further, outcome of descriptive evaluation shows that in the upcoming time period
mean value of expense will deviate from the figure of £4437. Hence, at the time of
formulating strategies and policy framework manager of the company should keep in mind
such figure.
In the context of net income, mean, mode and median implied for £39444, £40000 &
£45000. Overall evaluation shows that average income of the firm is less over other
measures. Hence, for enhancing income level company needs to make focus on controlling
both direct and indirect expenses. Further, results of evaluation present that minimum and
maximum level of income is £20000 & £65000. Thus, focus needs to be placed on
developing competent strategies that helps in reaching to the maximum level or limit.
Inferential statistics
Regression tool has been applied, a part of inferential statistics, with the motive to
ascertain the influence of sales expenditure on net income. This tool is highly prominent
which in turn helps in evaluating the extent to which one variable affects another
(Hadjisolomou and et.al., 2018).
Null hypothesis (H0): There is no significant difference in the mean values of sales expenses
and net income.
Alternative hypothesis (H1): There is a significant difference in the mean values of sales
expenses and net income.
Regression Statistics
Multiple R 0.814509
R Square 0.663425
Adjusted R Square 0.615343

Standard Error 8555.21
Observations 9
ANOVA
df SS MS F
Significan
ce F
Regressi
on 1
1.01E+
09
1.01E+
09
13.797
77 0.00751
Residual 7
5.12E+
08
731916
18
Total 8
1.52E+
09
Coefficie
nts
Standa
rd
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Interce
pt -15691.1
15114.
66
-
1.0381
4
0.333
73
-
51431.
6
20049.
37
-
51431.
6
20049.
37
Expens
es 2.531735
0.6815
75
3.7145
35
0.007
51
0.9200
65
4.1434
04
0.9200
65
4.1434
04
Residual output
Observat
ion
Predict
ed
Residu

Income als
1
22284.
91
-
2284.9
1
2
34943.
58
-
9943.5
8
3
45070.
52
-
15070.
5
4
34943.
58
5056.4
17
5
29880.
11
5119.8
87
6
47602.
26
2397.7
43
7
34943.
58
10056.
42
8
60260.
93
4739.0
69
9
45070.
52
-
70.521
9
Probability output’
Percenti
le
Incom
e

5.55555
6 20000
16.6666
7 25000
27.7777
8 30000
38.8888
9 35000
50 40000
61.1111
1 45000
72.2222
2 45000
83.3333
3 50000
94.4444
4 65000
5.55555555555554
16.6666666666667
27.7777777777778
38.8888888888889
50
61.1111111111111
72.2222222222222
83.3333333333333
94.4444444444447
0
40000
80000
Normal Probability Plot
Series1
Sample Percentile
Income

10000 15000 20000 25000 30000 35000
-20000
-15000
-10000
-5000
0
5000
10000
15000
Expenses Residual Plot
Expenses
Residuals
Interpretation: From evaluation, it has assessed that r square implies for .66 or 66%.
This in turn entails that variability of data set revolves around its mean. In other words, if one
variable will change then other also influences. Further, regression evaluation presents that
p<0.05 which means null hypothesis is true and other one false. Referring the results of
overall evaluation it can be presented that mean values of expenses and net income varies. On
the basis of such aspect, it can be presented that expenses made by the company having
impact on its net income.
Qualitative evaluation pertaining to the reviews of Hermes UK is as follows:
From investigation it has assessed that one can chat with Hermes via web chat.
Further, it has identified that after a pop-up message no parcel and card was found. Through
evaluation, it has found that sometimes customer need to do house to house enquiries for
getting or receiving the concerned parcel. Apart from this, reviews of customers present that
they never had good experiences with the business unit. In relation to the parcel delivery,
numerous emails and complaints are received by Hermes. Only 30% chances take place in
relation to getting delivery of parcels on time. Given case scenario presents that after
numerous web-chats and telephone conversation customers are receiving their parcels.
Hence, referring overall evaluation it can be presented that customer services offered by
Hermes are poor. Thus, client should make focus on assessing courier service provider who
make deliveries on time.
P4 Applying range of business methods that can be used for business planning
In the context of business organization, quality, capacity and stock management is
highly essential for the attainment of goals & objectives. Moreover, quality is the main
factors that have significant impact on customer satisfaction and thereby sales revenue as
well as profit margin. In this regard, control chart is highly effectual which in turn helps in

making evaluation of quality aspect and thereby helps in taking appropriate measure for the
improvement purpose (Quality control charts, 2018).
Quality management
Sample X-bar Range
1 15.91 0.19
2 15.99 0.27
3 15.92 0.17
4 15.93 0.46
5 15.98 0.47
6 16.03 0.2
7 15.96 0.46
8 15.93 0.2
9 15.96 0.21
10 15.83 0.3
11 15.99 0.29
12 15.96 0.43
13 15.83 0.24
14 15.91 0.37
15 16.05 0.31
16 15.99 0.29
17 15.86 0.33
18 16.01 0.34
19 15.98 0.28
20 16.02 0.2
21 16 0.23
22 15.9 0.16
23 15.86 0.32
24 15.94 0.15
25 15.94 0.3
Mean of all the means 15.95
Standard deviation 0.14
Control limit 15.95
Upper control limit 15.95 + 3 * (.14 / SQRT of 4) = 16.16
Lower control limit 15.95 - 3 * (.14 / / SQRT of 4) = 15.74
Range chart

Inventory management: Economic order quantity is recognized as the most effectual
tools that can be used for the purpose of inventory management. EOQ presents the number of
inventory that firm should add into its inventory for reducing the level of holding, order and
shortage cost (Economic order quantity, 2018). Such stock management tool assists in
determining the units which should be purchased on the basis of ordering and carrying cost.
Thus, it clearly exhibits the stock level that firm should maintain and place order for each
times. EOQ technique of stock management provides high level of assistance in minimizing

holding cost. Along with this, optimal inventory level also avoids the situation of deficiencies
and thereby ensures smooth functioning of the operations.
Economic order quantity (EOQ) = SQRT (2 × Quantity × Cost Per Order / Carrying
Cost Per Order)
Particulars
Figure
s
Demand (in units) 360
holding cost 0.8
ordering cost 100
Days in a year 250
EOQ: SQRT (2 × 360 × 100 / 0.8)
= 300 units
Orders should be processed in a year
= 360 / 300
= 1.2 per annum
On the basis of assessed outcome, firm should place order 1 time for 300 units and
then for remaining 60. This in turn helps company in maintaining both holding as well as
ordering cost and thereby maximizes profitability.
Expected time between the order
s= Quantity demanded / days in a year
= 360 / 250
= 1.44 per day
T = 300 / 1.44

= 208.33 days
Total cost for EOQ policy: [Demand / EOQ (ordering cost)] + [EOQ / 2 (holding cost)]
360/300 (100) + 300/2 (0.8)
= 120 + 120
= £240
Capacity management: This implies for the process which is used to make
appropriate planning about resources. The main objective of the firm behind undertaking the
practices of capacity management is to ensure proper management of resources which in turn
meets business demands or requirements (Capacity management, 2018). It includes capacity
forecasting, planning, monitoring and performance analysis. Hence, such planning tool
enables firm to attain success by making optimum use of limited resources available to it.
Design capacity = [10 workers * 7 hours per day / 1 hours per customer call out] * 5 working
days
70 * 5 = 350 days
Effective capacity = [10 workers * 5.6 hour day / 1 hours per customer call out] * 5
= 56 * 5
= 280 customers per week
Efficiency: Actual output 200 / effective capacity 280
In this case, efficiency of operations account for 71%.
Utilisation: Actual output 200 /design capacity 350
From assessment, it has identified that process utilisation account for 57%
respectively.
P5 Communicating findings regarding the given variables
In order to communicate findings related to quality aspect graphical presentation
technique of statistics has been used. The rationale behind using such statistical tool of
communication is that it presents information in a clear and presentable manner. In addition

to this, graphical presentation also enables analyst to do comparison of data set with other
variables more effectually (Advantages and Disadvantages of Graphical Representation of
Data, 2018). Along with this, graphs also facilitate quick decision making as compared to the
descriptive report. By viewing the graphs manager can evaluate trend and thereby become
able to develop effectual strategies for performance enhancement. Further, graphical
assessment includes less cost and time. In the context of quality management, x bar and range
chart clearly presents control limit. Hence, using such graphical presentation business entity
can take decision about further improvement or management. Referring all such aspects, it
can be mentioned that graphical evaluation helps in highlighting the main aspects and thereby
aid in decision making.
M2 Presenting differences take place in application between measuring association,
descriptive and inferential statistics
Descriptive statistics Inferential statistics Measures of
association
It is used for describing
a situation or
population under study.
By using inferential
statistics analyst can
present or figure out
chances pertaining to
the occurrence of an
event.
Helps in assessing and
defining relationship
takes place between
two or more variables.
M3 Justifying the use of appropriate statistical methods
There are several statistical methods which can be used by the business organization
for the purpose of decision making such as:
Trend analysis:
Through performing trend analysis business unit can assess whether it will grow in
the near future or not.
Advantages Disadvantages
 Offers input for developing strategic
and policy framework
 Facilitates comparative analysis
 Under inflationary conditions such
statistical tool do not offer suitable
solution

 Lacking analytical and informative
evaluation
Correlation
By doing correlation analysis ABC can assess the extent to which one variable has an
impact on another.
Advantages Disadvantages
Provides help in doing experimental research by
clearly exhibiting relationship between two
factors
Such statistical tool does not help in establishing
cause and effect relationship between the
variables.
M4 Stating rationale pertaining to the chosen method of communication
From assessment, it has identified that graphical presentation is the most effectual
way which helps in communicating findings in the best possible way. Moreover, graphical
presentation includes chart which in turn presents data appropriately. Along with this,
attractive graphs grab the attention of users and develop better understanding about results.
Referring all such aspects it can be presented that graphical presentation help in
communicating finding appropriately.
D1 Critically evaluating differences in the application of descriptive, exploratory and
confirmatory analysis
Descriptive analysis
Advantages Disadvantages
 Helps in analyzing and evaluating
large data set more effectually.
 Descriptive evaluation includes
median which is not affected by
extreme results.
 Mode measure of descriptive
evaluation helps in presenting suitable
solution when data is in categories or
 In the case of having nominal data set
mean measure of descriptive statistics
cannot be used
 Range measure pertaining to
descriptive evaluation is affected
from extreme values.

having nominal value
Exploratory analysis
Advantages Disadvantages
 It assists in exploring data set
prominently
 Facilitates discovery of structural
secrets pertaining to the concerned
data set
 Helpful in conclusive research
projects or studies
 It is based on the usage of modest
sample
Confirmatory analysis
Advantages Disadvantages
 Helps in testing hypothesis and
generating an estimation in an
appropriate manner
 Provides suitable results or solutions
from quantitative data set
 In this, result recognition is hard as
compared to the expectations.
 Such analysis lays emphasis on the
inclusion of theories and methods that
are firmly established.
D2 Giving recommendations in relation to making improvement in business planning through
the means of statistical method
Business units can do effectual planning by undertaking statistical tools and
techniques. Moreover, tools such as descriptive statistics, correlation, quartile, trend analysis
etc helps in evaluating large data set pertaining to business operations effectually. Thus, by
taking into account the results of statistical evaluation firm would become able to develop
competent plan.
CONCLUSION
By summing up this report, it has been concluded that statistical evaluation offers
valuable input to the managers for decision making. Besides this, it can be inferred that
descriptive statistics helps in summarizing data set in the best possible way. It can be seen in

the report that graphical presentation reflects better view of data set and helps in
understanding the same prominently. Further, it also has been articulated that statistical tools
and techniques provide high level of assistance in business planning. Using techniques of
statistics business units can make suitable plan regarding quality, capacity and inventory
management.

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