Statistics for Management: Data Analysis, Interpretation, and Findings

This report provides a comprehensive analysis of statistical techniques applicable to management. It begins with hypothesis testing, comparing income levels between male and female employees in both public and private sectors using T-tests. The report further explores the creation of earnings-time charts to visualize income trends and calculates annual growth rates for different sectors. Task 2 includes pictorial data presentation and analysis of student marks, emphasizing measures to improve performance. The report also delves into economic order quantity (EOQ) calculations and data analysis related to deliveries. Finally, it examines the relationship between the number of bedrooms and property prices. The report offers valuable insights into applying statistical methods for effective decision-making in various management scenarios.

Statistics for Management

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
A) Hypothesis testing on income of employees in public industry........................................1
B) Producing T test based on income level of male and female in the private sectors..........2
C) Producing Earnings – Time chart for male and female in private as well as public sector3
D) Annual growth rate............................................................................................................4
TASK 2............................................................................................................................................6
2.1 Pictorial presentation of data............................................................................................6
2.2 Data analysis.....................................................................................................................7
B) Discussing measures of dispersion....................................................................................9
2.3 Producing report and interpretation of measures of central tendencies...........................9
SECTION B...................................................................................................................................10
2.4 Preparing Best fit line chart............................................................................................10
TASK 3..........................................................................................................................................12
A) Producing deliveries made in a particular period............................................................12
B) Presenting number of deliveries accomplish in various rounds......................................13
C) Finding the economic order quantity using precise statistical formula..........................14
TASK 4..........................................................................................................................................15
4.1 Data Analysis..................................................................................................................15
4.2 Relationship between number of bedrooms and their prices in varied streets...............18
CONCLUSION..............................................................................................................................19
REFERENCES..............................................................................................................................20

INTRODUCTION
Statistics is useful as it shows relationship between dependent and independent variables
to arrive at meaningful conclusions. It is quite useful technique for statistician to draw concrete
results in the best possible way. The enclosed reports deals with statistics for management and
provides useful techniques of statistics to be used by the management to arrive at results quite
easily. This report discusses testing of hypothesis to show difference between two variables and
also computations of mean, mode and standard deviation is also done. EOQ model is also
discussed so that overall cost may be reduced while purchasing stock by the organisation.
Moreover, correlation method and chi square technique are also discussed being used by
statistician for arriving at valid conclusions with much ease. These statistics techniques and
methods are quite useful for managers to arrive at concrete results and resolve the problem quite
effectively and take better and enhanced decisions.
TASK 1
A) Hypothesis testing on income of employees in public industry
The ranges of hypothesis testing are as follows-
H 0 : No significant difference between income level of men in public sector and income level of
women in public entities.
H 1 : Significant difference observed between income level of men in public entities and income
level of women in public entities
Table – 1 T test table showing difference of income level of male and female in public entities
Men Public
Entities
Women Public
Entities
Value of mean calculated 32276.625 26929.875
Value of variance calculated 1449962.268 977868.4107
Observations drawn from sector 8 8
Hypothesized Mean showing difference 0
df 13
t Stat 9.705673424
P(T<=t) one-tail 1.27E-007
t Critical one-tail 1.770933396
P(T<=t) two-tail 2.54E-007
t Critical two-tail 2.160368656
Interpretation -
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The calculations shown above interpret about significant difference between income level
of male and female in public industry. For showing out such difference, T test is being used for
carrying out difference in income level. The T test shows difference between value of mean and
value of variance obtained. From the calculations carried out in the above table, it can be
observed that level of significant difference is in the range 1.27 > 0.05 which highlights that
there is not much difference observed between income level of men and women in the public
sector quite effectively (Chatterjee and et.al, 2017). This is shown by performing T test
calculation which highlights that no significant difference is analysed. It means that salaries
earned by both male and female workers are almost same at various job position. Moreover, it
can be said that government is not biased on gender and it can be said that gender inequality is
not observed that is a good sign as same salaries are drawn by men and women at the workplace.
Furthermore, T test shows how mean value is deviated from the variable value. Thus,
difference is shown by this technique and is useful for statistician for drawing about conclusions
quite effectively. As the table shows that income level of men in public sector is 32276 and
besides this income level of women in public entities is around 26929. Thus, no significant
difference is observed in income level of both male and female. This is evident that income of
male is around 5347 more than that of women in the public industry at the same position. Apart
from this, value of variance of male is 1449962 and that of women is 977868 which shows that
variance of male is more than that of female by much margin. Thus, variance value of men is
much deviating than that of women in the public sectors.
B) Producing T test based on income level of male and female in the private sectors
Table – 2 T test table showing difference of income level of male and female in private entities
Men Private Entities
Women Private
Entities
Value of mean calculated 28062.875 20541.25
Value of variance calculated 840242.6964 988729.9286
Observations drawn from industry 8 8
Hypothesized Mean showing difference 0
df 14
t Stat 15.73088181
P(T<=t) one-tail 1.35387E-10
t Critical one-tail 1.761310136
P(T<=t) two-tail 2.70773E-10
2

t Critical two-tail 2.144786688
Interpretation -
The table shows significant difference on the basis of income level of men and women at
private sector. For achieving this, T test is applied so that difference can be highlighted with
much ease in the best possible way. The value of significance shown in above calculation ranges
from 1.35 > 0.05. This range shows that not much difference is observed in the salaries earned
by male and female in private entities. As such, mean value of male in private industry is 28062
and in addition to this, mean value of female is 20541. This shows that male income is only 7521
more than that of female at the workplace (Huang, Wu and Yi, 2017). Now coming to variance
value, men has 840242 and value of variance of women is 988729 which have only minor
difference in both income levels. This shows that variance value of men is slightly deviated than
that of women. It can be said that salaries are provided on equal basis to both employees which
is being highlighted by the calculation and as such, private industries are not biased while giving
remuneration to female employees. As such, no gender biasness is observed. Minor difference
can be ignored as not much deviation is observed and this is provided by applying T test which is
a reliable technique used by statistician to draw out meaningful conclusions with much ease from
the statistical data.
C) Producing Earnings – Time chart for male and female in private as well as public sector
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Illustration 1: Earnings - Time Chart
The above chart shows difference of income level of male and female in private as well
as public sectors. The difference is shown by earnings-time chart. The above chart shows that
income level of men in public sector is on increasing trend from 2009 to 2016 financial years.
This is evident from the figures that income level in 2009 was 30638 that raised to 34011 in the
financial year 2016. This means that income is increased up to 3373 in recent years. On the other
hand, private sector has also observed increasing income level in recent years as in 2009 was
27632 which increased in 2016 as figure was 29679. This provides clarity that income level of
men in both sectors has increasing trend which is a good sign. Now coming to salaries of women
in private industry (Kumar, and Bhargava, 2017). The income level is increasing in this sector as
in 2009 was 19551 and in 2016 was 22251. This shows that income has considerably increased
in recent years. In public industry, income level in 2009 was 25224 and that in 2016 was around
28053. Thus, the analysis concludes that women income is more in public sector and men has
more income in public sector as well.
D) Annual growth rate
Table – 3 Percentage change in income level in both sectors
2010 2011 2012 2013 2014 2015 2016
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Males in Public
entities 2.00% 0.4% 1.4% 2.3% 1.0% 2.5% 1.0%
Males in Private
entities -1.30% 0.9% 1.7% 1.8% 0.9% 1.5% 2.8%
Females in Public
entities 3.5% 1.4% 0.6% 2.6% 1.3% 0.7% 0.5%
Females in Private
entities -0.1% 0.2% 3.8% 1.9% 1.5% 1.8% 4.0%
Illustration 2: Chart showing annual growth
From the above charts and table, difference of annual growth of income level of male and
female is highlighted in both sectors such as private and public sectors. The income level of men
in public sector is in the range between 1 % to 2 % which is highly deviated in the past years.
While, in private sector, range is between 1.5 % to 2.5 %. These figures clearly shows that
income level in public entities was more than private ones. Now coming to women in private
sector, range was between 3.5 % to 0.5 %. This means that income has gone down significantly
in recent years. On the other hand, income level of women in public industry was between 0.2 %
to 4 %. Thus, it can be conveyed that there is ample of difference between income level of men
and women in both sectors. As income of male in public sector is more and in contrary to this,
female had more income in private sector than public one. Both sectors are considerably
different for male and female.
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TASK 2
2.1 Pictorial presentation of data
The above column graph provides marks scored by students in KCB school. This shows
that marks scored by students are not good as there are less high scorers while rest of the
students have scored poorly. Majority of students has scored between 72 and 75 as shown by the
column graph. This range was the highest marks attained by them. However, the lowest marks
scored were between 30 to 37 which shows that students are not performing well and teachers
have to take measures so that problems may be resolved as soon as possible. The students should
score well in next exam so that they can at least more than 50 marks in the subjects quite easily.
The faculty need to be strict with the students and should take weekly tests so that they may be
able to perform and score well in the subjects (Searle and Khuri, 2017).
Moreover, certain measures be taken by teachers and students so that overall grade may
be increased up to higher extent. For achieving this, certain steps need to be taken. Among this,
concentration power of students may be increased by engaging them in group activities and
discussing queries with teachers. For this, students should study at home and if they do not
understand the lectures delivered in the class, then they can ask from teachers to resolve queries.
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Illustration 3: Marks trend

This way grades may be increased effectively. Proper time management may be made by
students so that they may study each subject within stipulated time and this way, syllabus can be
completed within time and students can do revision of the same. Moreover, notes should be
written down by them and this helps to grab things quickly and effectively and students may
scored well in the future. Furthermore, it is not only duty of faculty to make understand value of
studies but parents are equally under duty to guide children so that they may perform well and
achieve good grades.
2.2 Data analysis
Serial order
Marks
attained
1 20
2 72
3 60
4 41
5 37
6 32
7 43
8 46
9 45
10 62
11 64
12 30
13 39
14 58
15 75
16 45
17 58
18 56
19 39
20 40
21 21
22 29
23 68
24 59
25 54
26 42
27 37
28 30
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29 70
30 45
31 46
32 36
33 43
34 33
35 48
36 39
37 41
38 48
39 44
40 57
41 52
42 55
43 32
44 46
45 40
46 48
47 68
48 40
49 48
50 56
Value of mean 46.74
Value of mode 48
Value of Standard
deviation 12.82187226
Interpretation-
From the table it may be interpreted that mean is 46.74, mode is 48. The range of scores
are between 45 to 50. As such, scores are not good.
Average
Strengths Weaknesses
1. It provides fast and effective calculations. 1. Main weakness is that it is unsuitable in case
of extreme values. In such circumstances,
median is most suitable to draw results quite
effectively.
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Mode
Strengths Weaknesses
1. It provides data which has occurred most
frequently in the whole data set. This eases to
analyse data in effective way especially, when
data is large enough.
2. It is relevant for qualitative data analysis and
not useful for quantitative data.
1. It does not provide specific range that from
which part value comes most frequently.
2. It is unsuitable for further analysis of data as
it is only once used and not suitable for further
calculations.
B) Discussing measures of dispersion
The measure of central tendency is useful tool but does not provide variable information
of the data. To overcome this shortcoming, measures of dispersion is a useful for statistician to
draw results quite effectively (Measures of Dispersion). Measures of dispersion is the difference
between the smallest score in a data and that of the largest data. It provides better relationship
and combination of data by providing difference between largest and smallest data with much
ease. It has basically two types of it such as absolute and relative measures of dispersion. From
the calculation, it may be analysed that standard deviation calculated is 12 which is deviated
from mean value but moderately only. This makes harder to predict scores of the students. As a
result, it is evident from the fact that measures of dispersion is quite helpful technique to draw
concrete conclusions with much ease.
2.3 Producing report and interpretation of measures of central tendencies
To
The Director of KCB Business School
Subject: Performance of students in the subjects
Mean and mode interpretation
It can be interpreted that mean value obtained is 46. On the other hand, value of mode is 48.
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This clearly shows that on average, 46 marks have been obtained by students and mode implies
that 48 marks have been scored by most of the students.
Standard deviation
The standard deviation being obtained is 12.82 which can be interpreted that it is moderately
deviated from mean value of 46. This makes prediction of marks to be obtained in future
difficult as standard deviation is moderate and as such, to predict marks is much difficult.
Ways to effectively compare between various subjects
For comparison of subjects, T test can be applied as it provides effective results to easily
compare variables with much ease. Apart from this, ANOVA technique is also useful tool to
compare variables and draw concrete results. This is technique is used to assess difference
between group means. As such, it is good for comparison purpose.
Different ways to assess association
For this, correlation method is quite useful as it provides relationship between two variables and
this is helpful for measuring association with much ease. Another method which can be used is
Chi square test. It is useful tool to measure association and also known as test of independence.
SECTION B
2.4 Preparing Best fit line chart
Illustration 4: Line chart
10

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The above computations provide value of intercept and value of beta quite effectively. It
can be observed that beta value computed is 2.15 in the above table. While, intercept value
calculated is 7.65. Moreover, beta value obtained is a representation of weight of babies in
different months. This means that beta is 2.15 and this makes clear that weight is changed by
2.15. In addition to this, intercept value is different from beta value (Murphy and et.al, 2017).
This value means that if independent value remains constant, dependent value will be 7.65
analysed by the table. This is evident from the fact that age of babies is 7 months, then weight is
9.155. While, when age is 8 months, then mean weight of babies is 9.37 and in case of age of 9
months, weight will be 9.58. Thus, when age changes, weight of babies also consecutively
changes. The value of level of significance comes around 2.15 > 0.05 which implies that there is
not much significant difference between weight and age of babies. Besides this, multiple R
calculated is 0.97 which implies perfect correlation among variables. Moreover, correlation
among variables undergoes changes, when independent variables are changed. In addition to
this, value of R is 0.95. This clarifies that dependent variable is changed up to 95 %, when
independent variables undergoes alteration.
TASK 3
A) Producing deliveries made in a particular period
The deliveries made by the company according to the data provided is 450000. It can be
said that sales amount is based on mere estimation and is relevant to organisation (Revelle,
2017). By taking into account such estimation or assumption, full computation is accomplished
by taking same value and no alterations are made to arrive at results.
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B) Presenting number of deliveries accomplish in various rounds
Table – 4 Number of bottles transported
Quantity demanded annually 450000
Number of trips 30
Bottles per delivery in round 15000
Interpretation -
It can be interpreted from the above table that total number of bottles in each delivery
comes to 15000. This figure is obtained by taking annual demand and then dividing the same
with number of trips in transportation of the goods. The annual demand of bottles amounts to
450000 and number of trips is 30. As such, by dividing both, bottles per delivery that is 15000 is
obtained quite easily.
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C) Finding the economic order quantity using precise statistical formula
Quantity 450000
Cost per order 2
Carrying cost per order 0.5
EOQ 6000
The economic order quantity is the amount of units that an organisation should add to the stock
with each order in order to reduce the total cost of inventory. The economic order quantity is
utilised as part of ceaseless monitor inventory system in which the level of inventory is being
reviewed at all times and a fixed quantity is ordered each time the inventory level reaches
specific reorder point (Roger and et.al., 2012). From the above table, it can be understood that
the business organisation requires purchasing 6000 units of the olive oil in order to keep the
inventory under control. There are numerous benefits of economic order quantity technique
which are listed below:
Reduced storage and holding cost: It is considered as one of the best advantage of economic
order quantity as it aid the organisation to reducing the storage of goods in the company. As
it eventually decrease the carrying cost as fewer products are stored at the warehouse of the
organisation. All the events helps the management of the organisation to reduce their
holding cost and it can be enunciates that economic order quantity holds huge important in
the organisation.
Specific to business: Economic order quantity is the method which are used by the managers to
determine the quantity firm must purchase and time at which the order must place to
increase the inventory of the business (Cressie, 2015). This helps the management of the
business organisation to increase the profits and sales level adequately and the firm will able
to maximise their turnover eventually.
Minimize strong holding cost: Strong inventory of business would be more expensive for all
type of small business. The major benefits of the EOQ model is the modified the
recommendation furnished concerning the major economical number of units each order.
This model might suggest purchasing a larger quantity in lowest orders taking benefits of
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discounts in buying in bulk quantity and decrease the order cost of the products.
Alternatively, it could be point to large quantity of fewer items to decreasing cost if they are
broad and ordering cost are comparatively lowest.
Comparison of economic order quantity and cost
Quantity 450000 450000 450000 450000 450000
Cost per order 2 2 2 2 2
Carrying cost per
order 0.5 0.52 0.54 0.56 0.58
EOQ 1897.367 1860.521 1825.742 1792.84 1761.661
Interpretation: From the above analysis it can be considered that carrying cost is inversely
proportional from EOQ. As carrying cost declined EOQ increased. More quantity may be
purchased so that carrying cost declined and EOQ can be increase.
TVC
CD/Q+HQ/2= 20*450000/15000+0.5*6000/2= 600+3750=4350
CD/Q+HQ/2= 20*450000/6000+0.5*6000/2= 1500+1500=3000
TASK 4
4.1 Data Analysis
(I) Bar Chart
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(II) Pie Chart
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Illustration 5: Number of bedrooms in varied areas

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Illustration 6: Number of homes having specific number of bedrooms in
Church Lane
Illustration 7: Number of homes having specific number of bedrooms in
Green Street

From the above chart, it can be understood that there are 8 houses in Green Street with only one
bedroom, 28 housed with 2 bedrooms, 37 housed with 3 bedroom, 17 houses with 4 bedrooms
and 10 houses with 5 bedrooms. In Church lane, there are 6 houses with 1 bedroom, 18 houses in
2 bedrooms, 24 houses with 3 bedrooms, 9 houses with 4 bedrooms and 3 houses with 5
bedrooms. Further, in Eton Avenue, there were 4 houses with 1 bedroom, 20 houses in 2
bedrooms, 32 houses with 3 bedrooms, 12 houses with 4 bedrooms and 12 houses with 5
bedrooms. Thus, it can be understood that there are more houses in Green Street as compared to
Church Lane and Eton Avenue. Further, the number is more in Eton Avenue with 5 bedrooms
houses. It can be further understood that most of the houses with 2 and 3 bedrooms are in Green
Street and Church Lane. There are 100 houses in Green Street, 60 houses in Church Lane and 80
Houses in Eton Avenue.
4.2 Relationship between number of bedrooms and their prices in varied streets
Number of
bedrooms
Green street Church Lane Eton Avenue
Number of Bedrooms 1
Green street 1 1
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Illustration 7: Number of homes having specific number of bedrooms in
Eton Avenue

Church Lane 1 1 1
Eton avenue 1 1 1 1
Graphical presentation
Figure 8 number of bedrooms and house prices
From the above analysis, we have discussed about to relationship between number of
bedrooms and their prices in varied street such as number of bedrooms, green street, church lane
Eton avenue these are the current location of the bedrooms in which availability of number of
bedrooms. From the above data analysis, it could be concluded that on the above correlation
table is formulated and graphic interpretation is completed. There are two ways of Graphics
representation and correlation table in which are formulated to let the peoples know about to the
pricing and several bedrooms' relationship. On the above graph interpretation, it could be stated
that there is value of green street between 600000-700000 and moreover, Church lane houses
prices are between 700000 to 85000 and likewise Eton avenue house values are between 750000
to 1000000. From the above chart and analysis of various prices of their bedroom and houses
value, It could be seen that correlation value is 1 which means that there is equivalent
relationship between house prices and number of bedrooms. It could be said that if number of
bedrooms raises then in that situation prices of property house raises as well. In this case, there
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are two bedrooms then in that situation Green street home's value would be 600000, church
house's value would be 700000 and at Eton Avenue houses value would be 750000. Another side
of this, if there would be 3 bedrooms house then it that situation Green street house's prices
would be 700000. At Church Lane house would be valued at 85000 and at Eton Avenue house
would be valued at 1000000.
CONCLUSION
From the above discussion, we have concluded that there are vital necessity of data
analysis in the business because with the help of data analysis a lot of facts and figures are
recognised that could be utilized to make decision in very efficient way. In this investigation, it
is also concluded that there are several advantages of using these techniques such as economic
order quantity while using same lots of decision are taken by managers such as measurement in
which product and services must be brought and a timer period in which the buying process must
be completed etc. Decision are made in the basis of economic order quantity are major faithful
and demonstrate the advantages for the business. It is also concluded that there is direct
concerning between numbers of bedrooms and house prices. If there are number of bedrooms
raised then there are house prices would also be raised. Thus, it could be said those individual
persons that intend to increase purchase at low prices should purchase house with two quantity
of bedrooms.
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Wiley and sons.
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Online
Measures of Dispersion, 2018 [Online] Available Through:
<https://www.emathzone.com/tutorials/basic-statistics/measures-of-dispersion.html>
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