Statistics for Management: Comprehensive Data Analysis Report

This report provides a comprehensive analysis of statistical data relevant to management. It begins with hypothesis testing, comparing male and female income levels in both public and private sectors using t-tests. The report includes earning time charts and determines annual growth rates across different sectors and genders. Further analysis involves graphical presentations of data, including student marks trends, and calculations of mean, mode, and standard deviation. The report also explores economic order quantity and evaluates housing data based on the number of bedrooms. Various charts and tables are used to visualize and interpret the data, leading to a conclusion summarizing the findings. The report demonstrates a strong understanding of statistical methods and their application in management contexts.

STATISTICS FOR MANAGEMENT

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
(a)Testing of hypothesis..............................................................................................................1
(b)Identification of difference between male and female income level in private sector............2
© Earning time chart for year 2009 to 2016................................................................................3
d) Determining annual growth rate..............................................................................................3
.....................................................................................................................................................4
TASK 2............................................................................................................................................5
Section A.........................................................................................................................................5
2.1 Graphical presentation of data...............................................................................................5
2.2 Analysis of data.....................................................................................................................5
2.3 Report on analysis of students performance in the exam......................................................8
Section B..........................................................................................................................................9
2.4 Line of best fit........................................................................................................................9
TASK 3..........................................................................................................................................11
(a)Number of delieveries made in a years.................................................................................11
(b) Deliveries made on each round............................................................................................11
©Economic order quantity.........................................................................................................11
(d) Comparison of EOQ and cost..............................................................................................12
TASK 4..........................................................................................................................................14
4.1 Evaluation of figures by using different charts for number of houses with different
bedrooms....................................................................................................................................14
4.2 Relationship between number of bedrooms and their prices in varied streets....................16
CONCLUSION..............................................................................................................................17

REFERENCES..............................................................................................................................18
Figure 1Earning time chart from year 2009 to 2016.......................................................................3
Figure 2Graphical representation of percentage change in variable................................................4
Figure 3Student marks trends..........................................................................................................5
Figure 4Number of bedrooms in varied areas...............................................................................14
Figure 5Number of homes having specific number of bedrooms in Church Lane.......................14
Figure 6Number of homes having specific number of bedrooms in Church Lane.......................15
Figure 7Number of homes having specific number of bedrooms in Church Lane.......................15
Figure 8Number of bedrooms and house prices............................................................................16
Table 1T table..................................................................................................................................1
Table 2T test for male and female income in private sector............................................................2
Table 3Percentage change in income level in public and private sector across male and female...3
Table 4Calculation of mean and standard deviation........................................................................5
Table 5Number of bottles transported...........................................................................................11
Table6 Calculation of economic order quantity............................................................................11
Table 7 Cost at different level of EOQ..........................................................................................12

INTRODUCTION
Analytics is the one of the growing domain in the most of nations of the world. In
current time period descriptive statistics tools are applied on dataset. By analyzing facts and
figures lots of facts are identified. Apart from this, charts in respect to different variables are
prepared in the report and same are analyzed in proper manner. In middle part of the report
varied calculations like economic order quantity are performed and on that basis varied facts are
identified. Apart from this, different areas houses data in terms of bedrooms are analyzed by
preparing pie and bar charts. Trends that prevailed in these areas are identified through charts. It
can be said that extensive analysis is done in the present research study. At end of the research
report, coorelation analysis is done and by doing so relationship is identified between multiple
variables. Along with this, conclusion section is also prepared and in this way research work is
carried out.
TASK 1
(a)Testing of hypothesis
H0: There is no significent difference betweeen male income level in public sector and female
income level in public sector.
H1: There is significent difference betweeen male income level in public sector and female
income level in public sector.
Table 1T table
Male Public
sector
Female Public
sector
Mean 32276.625 26929.875
Variance 1449962.268 977868.4107
Observations 8 8
Hypothesized Mean Difference 0
df 13
t Stat 9.705673424
P(T<=t) one-tail 1.2709E-07
t Critical one-tail 1.770933396
P(T<=t) two-tail 2.54179E-07
t Critical two-tail 2.160368656
Interpretation
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T test is the one of the important method that is used to identify whether there is
significent difference between multiple variables. It can be observed that value of level of
significence is 2.16>0.05 and this is indicating that there is no significent mean difference
between variables. It can be said that almost same salary is issued to male and female at the
workplace. Mean value of salary in case of male is 32276.62 and same for female is 26929.87. It
can be said that higher amount of salary is paid to male relative to female. However, in temrs of
variation at 95% confidence interval there is similarity in income level of individuals. It can be
said that there is no big difference in income level of male and female. On basis of facts it can be
said that there is significent importance of t test for the individuals.
(b)Identification of difference between male and female income level in private sector
Table 2T test for male and female income in private sector
Male Private sector
Female Private
sector
Mean 28062.875 20541.25
Variance 840242.6964 988729.9286
Observations 8 8
Hypothesized Mean 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
t Critical two-tail 2.144786688
Interpretation
It can be observed from the table that value of level of significence is 2.144>0.05 and this
is again reflecting that there is no significent difference between male and female in the private
sector in terms of income level. On average basis male are earning amount of 28062.87 in private
sector and female are earning 20541.25. It can be said that again in th private sector higher
amount of salary is offered to male then female. Thus, overall it can be said that in private sector
and public sector both male earning level is higher then same of female. So, it can be said that to
some extent there is difference between income level of both and in both sectors difference is
made in respect to gender. It can be said that there is great significence of the t test for the
analysis purpose. In T test basically t distribution is taken in to account for calculation purpose.
T distribution is similar to z distribution and there is small difference between both. Hence, it
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can be said that t distribution technique have wide application and due to this reaosn t test is
quite popular among the analysts.
© Earning time chart for year 2009 to 2016
2009 2010 2011 2012 2013 2014 2015 2016
0
5000
10000
15000
20000
25000
30000
35000
40000
30638 31264 31380 31816 32541 32878 33685 34011
25224 26113 26470 26636 27338 27705 27900 28053
19551 19532 19565 20313 20698 21017 21403 22251
Chart Title
Public sector male Private sector male Public sector female Private sector female
Figure 1Earning time chart from year 2009 to 2016
Interpretation
It can be observed that public sector male income increased from 30368 to 34011 and this
means that at fast rate salary level get increased in the mentioned sector. On other hand, in case
private sector male income level increased from 25224 to 28053. It can be said that increase in
salary is high in public sector for male then female. Similalry, in case of public sector income
level in case of female increased from 19551 to 22251. In same way, in private sector for female
income level increased from 19551 to some more points. It can be said that females are
observing high salary growth in public sector then private sector. Thus, overall in nutshell it can
be said that in public sector there is high salary growth then private sector in case of both male
and female. However, in case of females thee is slow growth rate of salary then males.
d) Determining annual growth rate
Table 3Percentage change in income level in public and private sector across male and female
2010 2011 2012 2013 2014 2015 2016
Public sector male 2.0% 0.4% 1.4% 2.3% 1.0% 2.5% 1.0%
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Private sector male -1.3% 0.9% 1.7% 1.8% 0.9% 1.5% 2.8%
Public sector female 3.5% 1.4% 0.6% 2.6% 1.3% 0.7% 0.5%
Private sector female -0.1% 0.2% 3.8% 1.9% 1.5% 1.8% 4.0%
2010 2011 2012 2013 2014 2015 2016
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
2.0%
0.4%
1.4%
2.3%
1.0%
2.5%
1.0%
-1.3%
0.9%
1.7% 1.8%
0.9%
1.5%
2.8%
3.5%
1.4%
0.6%
2.6%
1.3%
0.7% 0.5%
-0.1%
0.2%
3.8%
1.9% 1.5% 1.8%
4.0%
Chart Title
Public sector male Private sector male Public sector female Private sector female
Figure 2Graphical representation of percentage change in variable
Interpretation
It can be seen from chart that in case of pubic sector male income level is fluctuating at
fast rate. It can be observed that growth rate keeps on changing consistently and there is no
specific level where stability can be observed in same. Apart from this, in case of public sector
female it can be seen that growth rate in salary decline most of times and less amount is paid to
them most of times. On taking a look at private sector it can be seen that in case of female salary
growth rate keeps on changing consistently and its growth rate decline one or two times but by
high percentage. It can be said that growth rate remain at specific level most of times. In case of
public sector female it can be seen that growth rate remain up most of times. Thus, overall
picture is that there is uptrend in growth rate of females. By preparing such kind of charts it can
be identified that at what rate changes comes in the variable and what sort of trends comes in
different situatuions. Thus, it can be said that there is huge importance of data visualization for
the firms. Many advanced softwares like Tableau ae available to the firms which can be used for
making decisions.
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TASK 2
Section A
2.1 Graphical presentation of data
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
0
10
20
30
40
50
60
70
80
20
72
60
41
37
32
43
4645
6264
30
39
58
75
45
5856
3940
21
29
68
59
54
42
37
30
70
4546
36
43
33
48
3941
48
44
57
52
55
32
46
40
48
68
40
48
56
Student marks
Figure 3Student marks trends
Interpretation
Chart that is given above is reflecting that student marks are changing consistently and
same are not in specific direction. It can be said that there is not a specific level where students
are gaining marks specifically. Overall range can be prepared where most of observations comes
in terms of trends. It can be seen from chart that most of students gain marks in range of 40 to
70. There are number of individuals that comes in this range.
2.2 Analysis of data
Table 4Calculation of mean and standard deviation
S.no Student marks
1 20
2 72
3 60
4 41
5 37
6 32
7 43
8 46
9 45
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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
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
Mean 46.74
Mode 48
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STDE
V 12.82187226
Interpretation
Mean, mode and standard deviation are the one of the most important tools that are used
to analyze dataset. It can be observed that mean value of the variable is 46.74 which reflect that
on an average students score 46.74 marks. Mode value is 48 and this indicate that it is the value
of mark that is observed in case of many students apart from mean value. Standard deviation
value which is 12.82 and it is reflecting that variable values are deviating at very slow rate.
Hence, it can be said that most of students score marks in very specific range. There is
importance of all these tools as they are if collectively used then reflect that what is point that is
observed most of times and rate at which same get changed. This is the reason due to which
these statistical tools are used at wide level by the business firms. These methods can be used to
make decisions which are given below along with strength and wekaness.
Average
Strength Weakness
Major strength of this method is that it reflect
the performance that is usually given by the
variable (Bendat and Piersol, 2011). By using
this approach it can be identified that in which
direction variable value move most of times.
Major weakness of this approach is that it
does not indicate that range of values within
which most of observation comes.
Mode
Strength Weakness
It is the tool that indicate value that is
commonly observed in case of most of
observations. Thus, it can be said that this tool
give extension to the results obtained on
mean.
In case of mode major weakness is that it does
not reflect how many observations are there in
relevance to which mode value is observed.
Standard deviation
Strength Weakness
In cast of standard deviation major strength is Major weakness of this method is that
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that it reflect how far data points are moving
away from mean value (Cressie, 2015). It can
be said that it give overview of the
performance of the variable.
calculation process is complex and for non
technical person it is diffiult to understand
calculation process and meaning of
calculation.
2.3 Report on analysis of students performance in the exam
To
The Director of Company Date: 31-1-2018
Subject: Evaluation of dataset to meausre students performance.
Deriving meaning of output of descriptive statistics
Tables given above reflect that on average basis students score marks 46.74 and their mode
value is 48 which means that most of entities are making score of 46.74 but there are few one
that make score of 48. It can be said that presumable in range of 46.74 to 48 most of
observations comes. Standard deviatuon value is equal to 12.82 which is indicating that
variables values are not deviating at fast rate. Hence, it can be concluded that most of students
are making score within mentioned range.
Technique use for comparing subjects
ANOVA or analysis of variance is the one of the most important method that can be used to
make comparison between subjects. At specific significence level testing of values can be
done. It is the tool that is used to evaluate categorical variable by using specific variable in the
dataset (DeGroot and Schervish, 2012). Thus, ANOVA reflect that on certain parameter
whether there is similarity or difference among varied groups. Thus, there is huge significence
of the mentioed tool for data analysts and business firms. This is the reason due to which in
current time period more and more firms are making use of relevant method at workplace.
Ways to measure association between subjects
There are number of ways in which association is identified between varied subjects or
variables by using coorelation analysis. It is the one of the method that is used to identify
relationship that exist between variables. Apart from coorelation analysis chi square test
method can also be used under which relation between expected and actual facts is identified.
Hence, it can be said that there are multiple ways in which statistical analysis can be done.
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Section B
2.4 Line of best fit
Regression Statistics
Multiple R 0.979385884
R Square 0.95919671
Adjusted R Square 0.952396162
Standard Error 0.769048233
Observations 8
ANOVA
df SS MS F Significance F
Regression 1
83.4201
4
83.4201
4
141.04
7 2.15623E-05
Residual 6
3.54861
1
0.59143
5
Total 7
86.9687
5
Coefficie
nts
Standard
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Interc
ept
7.652777
778 0.690242
11.08
71
3.21E
-05
5.963816
659
9.34173
9 5.963817
9.341738
896
Age
2.152777
778 0.181266
11.87
632
2.16E
-05
1.709234
858
2.59632
1 1.709235
2.596320
697
PROBABILITY
OUTPUT
Percentile Weight
6.25 9
18.75 11.5
31.25 14.5
43.75 15
56.25 16.5
68.75 17
81.25 18.5
93.75 19.5
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0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
Normal Probability Plot
Sample Percentile
Weight
Interpretation
Regression analysis is the one of the most important technique that is used to measure
relationship between different variables. There are number of elements of the regression analysis
that help one in identifying relationship between multiple variables (Regression Analysis: Step
by Step Articles, Videos, Simple Definitions, 2017). These elements are alpha values, R square
and beta values as well as intercept. All these elements show relationship between variables in
different manner. It can be observed from the table given above that value of R square in model
is 0.95 which means that with change in independent variable 95% change comes in dependent
variable. On other hand, value of multiple R is 0.97 which means that both independent and
dependent variables are associated with each other. It can be said that variables age and weight
are associated with each other (Huber, 2011). Means that with change in age weight changed by
95%. Apart from this degree of relationship is also high between both variables and they are
perfectly coorelated to each other. Hence, with change in one variable high percentage change
will comes in other variable. Value of level of significence is 2.15>0.05 and it can be said that
both variables are no significently different. It can be said that in terms of rate of change or
variation there is similarity among these variables. Beta value for the variable is 778 which
means that with change in age weight changed by 778 points. Intercept value is 7.65 and it is
reflecting that mean value of weight remain 7.65 in case no change is observed in dependent
variable. It can be said that both variables age and body weight are coorelated to each other and
independent variable is coorelated to dependent variable (Regression Analysis: Step by Step
Articles, Videos, Simple Definitions, 2017). There are some of the asumptions of regression
analysis like data must be normally distributed and there must be homogenity in independent
predicted data points. After fulfillment of all assumptions regression give acurate prediction of
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results. There is huge importance of regression analysis metthod for the firms and it is widely
used by the companies to make decisions. Hence, there is wide application of regression analysis
method for the firms.
TASK 3
(a)Number of delieveries made in a years
Facts revealed that within specific duration total number of goods delievered are 450000.
There are some of the assumptions that are made in the calculation process like it is assumed that
figure is completely in context of the company. Thus, full amount of value is considered for
calculation purpose. Apart from this, same value is taken for performing other calculations in
respect to project.
(b) Deliveries made on each round
Table 5Number of bottles transported
Annual demand 450000
Number of trips 30
Number of bottles in each delivery 15000
Interpretation
Facts are reflecting that number of bottles in each delievery are 15000. In amid of this
yearly consumption and number of times vehicles transport done is taken in to acount. Just by
dividing yearly demand by nmber of times vehicle transport it is identified that how many bottles
are transported in each delievery. Facts are revealing that truck can deliever 15000 units.
©Economic order quantity
Table6 Calculation of economic order quantity
Quantity 450000
Cost per order 2
Carrying cost per order 0.5
EOQ 6000
Interpretation
It is the one of the approach that is used to identify quantity that need to be sold in the
market in order to cover inventory cost in the business. It can be seen from table that value of
economic order quantity is 6000. Thus, company require to sold these 6000 units in the market
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so that both fixed and variable expenses can be covered in the business. After selling these 6000
units firm will start earning profit in the business. This approach is usually used by most of
business firms because they have to set target for the employees at workplace. By using this
approach they identify that how much units to be sold in the market. Apart from this, according
to target profit number of units that employees need to sold is ascertained. In this way, economic
order quantity help business firms in making decisions. There are number of techniques that can
also be used to make decisions in respect to determination of target quantity but economic order
quantity is one that gain a wide popularity in comparison to other approach (Lee, 2012). Some of
merits of EOQ approach are given below.
Minimizing storage and holding cost: It is the technique that assist business firms in mimizing
storage and holding cost in the business. As it is well known fact that by using economic order
quantity approach it is identified that how much products need to be sold in the market and
accordingly target are divided on monthly basis. Accordingly, raw materials are purchased from
the market. Thus, this lead to reduction in the storage cost in the business. Less space is covered
by inventory at workplace and all these lead to sharp control on expenss. Thus, it can be said that
by using economic order quantity method storage cost can be minmized in the business.
Specific to business: Economic order quantity is the method that assist firms in making core
business decisions. Timing by which raw material need to be purchase is easily determined from
the suppliers by using mentioned approach. Hence, it can be said that this approach help firms in
making accurate decisions at workplace in respect to inventory control. Thus, it can be said that
there is huge importance of economic order quantity for the business firms. In upcoming time
period more and more firms that are of small size will increase use of this approach at workplace.
In order to make acccurate decisions (Roger and et.al., 2012). On basis of merits it can be said
that these methods help firms in making prudent decisions. This is the reason due to which large
number of business firms are actively using mentioned approach to make business decisions.
(d) Comparison of EOQ and cost
Table 7 Cost at different level of EOQ
Quantity 450000 450000 450000 450000 450000
Cost per order 2 2 2 2 2
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Carrying cost per
order 0.5 0.52 0.54 0.56 0.58
EOQ 1897.367 1860.521
1825.74
2 1792.842914 1761.661
Interpretation
In above chart easy comparison can be made between economic order quantity and cost
per order which is carrying cost. It can be observed that with decrease in economic order
quantity level carrying cost get increased. Further, when economic order quantity value declined
from 1860.52 to 1825.74 carrying cost per order will increase. Hence, it can be said that with
decline in economic order quantity carrying cost is increasing. There is inverse relationship
between both. It can be seen that when economic order quantity declined from 1825.74 to
1792.84 carrying cost per order increased to 0.56. Further, economic order quantity declined to
1761.66 economic order quantity value increased to 0.58. It can be said that in case of all
observations it is identified that with decrease in economic order quantity carrying cost get
increased.
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
On basis of calculation given above it can be observed that total variable cost value is high in
first calculation then second calculation. Figures reflect that second option is better to select
because cost is low in that case.
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TASK 4
4.1 Evaluation of figures by using different charts for number of houses with different bedrooms
1 2 3 4 5
0
5
10
15
20
25
30
35
40
1 2 3 4 5
8
28
37
17
10
6
18
24
9
34
20
32
12 12
Chart Title
Number of bedrooms Green street
Church Lane Eton Avenue
Figure 4Number of bedrooms in varied areas
6
18
24
9
3
Church Lane
1 2 3 4 5
Figure 5Number of homes having specific number of bedrooms in Church Lane
Interpretation
It can be observed that number of homes having 1 bedroom are 6 and there are 18 homes
that have 2 bedrooms. Apart from this, there are 24 homes that have 3 bedrooms followed by 9
homes that have four bedrooms. There are only 3 homes that have 5 bedrooms. Thus, it can be
said that most of homes have 2 bedrooms.
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8
28
37
17
10
Green street
1 2 3 4 5
Figure 6Number of homes having specific number of bedrooms in Church Lane
Interpretation
In Green street there are 8 homes that have 1 bedroom and 28 homes that have 2
bedrooms. Apart from this, there are 37 houses with thrree bedrooms. 17 houses have four
bedrooms and 10 homes have 5 bedrooms. It can be said that there are large number of homes
that have three bedrooms in Church Lane.
4
20
32
12
12
Eton Avenue
1 2 3 4 5
Figure 7Number of homes having specific number of bedrooms in Church Lane
Interpretation
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It can be seen from chart that in case of Eton Avenue there are 4 homes that have 1 room
followed by 20 houses that have 2 bedrooms. Apart from this, there are 32 houses with three
bedrooms followed by 12 homes with 4 bedrooms. Apart from this, there are 5 homes that have
12 rooms. Thus, it can be said that there majority of houses that have 3 bedrooms.
4.2 Relationship between number of bedrooms and their prices in varied streets
Coorelation table
Number of
bedrooms
Green
street
Church
Lane
Eton
Avenue
Number of
bedrooms 1
Green street 1 1
Church Lane 1 1 1
Eton Avenue 1 1 1 1
Graphical representation
Number of bedrooms Green street Church Lane Eton Avenue2
600000
700000 750000
3
700000
850000
1000000
Chart Title
Series1 Series2
Figure 8Number of bedrooms and house prices
Interpretation
It can be seen from table that coorleation value is one which is reflecting that there is
perfect coorelation between variables which means that with change in number of rooms change
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also comes in house prices. It can be said that if number of rooms get increased then in that case
house price will also improved (Siegel and et.al., 2014). Thus, one must while taking any home
must identify number of rooms that are in it. By considering number of rooms it can easily
identified that what may be home price. Apart from this, one need to identify that how much
rooms it require in home and whether for same there will be availability of sufficient amount of
fund in the business. By considering these factors one will be able to make prudent purchase
related decisions.
CONCLUSION
On basis of above discussion it is concluded that there is significent importance of data
analysis method for the business firms. There are number of techniques like mean, median and
mode as well as standard deviation which are used to evaluate specific variable. By using these
tools facts are analyzed in proper manner. It is also concluded that techniques like economic
order quantity help managers in making lots of business decisions. Data visualization tools are
other techniques that can also be used to analyze facts and figures. By doing visual
representation of data it can be identified that what are the trends that were in picture in previous
year time period. Thus, it can be said that there is significent importance of data visualization
tool and analysis techniques. On basis of received output better decisions can be made by the
managers.
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REFERENCES
Books and Journals
Bendat, J.S. and Piersol, A.G., 2011. Random data: analysis and measurement procedures (Vol.
729). John Wiley & Sons.
Cressie, N., 2015. Statistics for spatial data. John Wiley & Sons.
DeGroot, M.H. and Schervish, M.J., 2012. Probability and statistics. Pearson Education.
Huber, P.J., 2011. Robust statistics. In International Encyclopedia of Statistical Science (pp.
1248-1251). Springer Berlin Heidelberg.
Lee, P.M., 2012. Bayesian statistics: an introduction. John Wiley & Sons.
Roger, V.L. and et.al., 2012. Executive summary: heart disease and stroke statistics—2012
update: a report from the American Heart Association. Circulation. 125(1). pp.188-197.
Siegel, R. and et.al., 2014. Cancer statistics, 2014. CA: a cancer journal for clinicians, 64(1),
pp.9-29.
Online
Regression Analysis: Step by Step Articles, Videos, Simple Definitions, 2017. [Online]. Available
throug:< http://www.statisticshowto.com/probability-and-statistics/regression-analysis/>.
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