Statistics for Management: Analysis of Income and Student Data

This report presents a comprehensive statistical analysis of various datasets relevant to management. It begins with an introduction outlining the scope, including hypothesis testing comparing male and female income levels in both public and private sectors, and the construction of an earning time chart. The report then delves into data analysis, employing graphical representations and descriptive statistics to analyze student marks. The report also includes the calculation and interpretation of mean, mode, and standard deviation, as well as an analysis of the strengths and weaknesses of these statistical tools. Furthermore, the report explores the relationship between economic order quantity and costs, and analyzes the relationship between the number of bedrooms and housing prices using pie and bar charts, before concluding with a summary of the key findings and references.

STATISTICS FOR MANAGEMENT

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................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.....................................................................................................................6
2.3 Preparation of report and interpretation of results.................................................................9
Section B........................................................................................................................................10
2.4 Line of best fit......................................................................................................................10
TASK 3..........................................................................................................................................11
(a)Number of delivery made relevant time period....................................................................11
(b) Deliveries made on each round............................................................................................12
©Economic order quantity.........................................................................................................12
(d) Comparison of EOQ and cost..............................................................................................13
TASK 4..........................................................................................................................................14
4.1 Data analysis by using pie and bar chart.............................................................................14
4.2 Relationship between number of bedrooms and their prices in varied streets....................16
CONCLUSION..............................................................................................................................17
REFERENCES..............................................................................................................................18

INTRODUCTION
Data analysis is emerging as one of the important tool that is used by the firms for
making business decisions. In the current report, varied tools and methods are used to analyze
data. In the present research study, data related public and private sector income that that is
earned by male and female is analyze and comments are made on same. In middle part of the
report, students related data is anlayzed through graphical representation and descriptive
statistics. Along with this, advantage and disadvantage of mean and mode are also explained.
Apart from this, standard deviation is computed and same is analyzed. At end of the report,
calculation related to economic order quantity is performed. Apart from this, relatioship between
price of home and number of bedrooms is also identified. In this way, entire research work is
carried out in the report.
(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
T test is the one of the most important tool that is used to identify whether there is
significent mean difference between variables. It can be observed that value of level of
significence is 1.27>0.05 and this reflects that there is no significent mean difference between
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male and female income level in the public sector. Means that both male and females are
receiving salary of almost same amount in the relevant time period. It can be said that most of
male and females are receiving salary of same amount. This means that government is not only
commited towards promoting gender equality but it is also make efforts to do women
empowerment. In this regard, almost by paying same amount of salary government is trying to
bring women in respect to male. It can be said that there is significent importance of the t test
because it help one in finding out facts and figures in respect to variable. It can be observed that
mean income level of male in public sector is 32,276 and same for females is 26929. This means
that income level in case of male is higher then females but there is no big difference between
both (Simonoff, 2012). Variance is also high in case of male then female and it can be said that
income level for male is deviating at fast rate in public sector then female.
(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
In case of private sector it can be observed that value of level of significence is 1.35>0.05
and on this basis it can be said that there is no significent mean difference between male and
female income level in private sector. Mean income level in private sector for male is 28062 and
same for female is 20541.25. Level of variance is 988729.92 for female in the private sector and
same is 840242.89 for make in private sector. On this basis it can be said that deviation is higher
in case of female then male. Hence, it can be assumed that like public sector in private setor also
big difference is not made in salary that is given to male and female (Lee, 2012). On this basis it
can be said that salary level if almost same for both genders and there is minor difference
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between the amount that is paid to them. There is significent importance of t test for the analysts
because by using same lots of facts and figures are identified and on that basis decisions are
taken by the relevant entities. Thus,it can be said that there is wide scale use of the relevant
statistical tool for experts and business people as well as government.
© 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
It can be seen from chart that public sector male income rise consistently from 30638 to 34011.
On other hand, private sector male income level increased from 25224 to 28053. It can be said
that in respect to male income level is quite different in both public and private sector. In case of
private sector female value increased from 19551 to 22251 which is again reflecting that their
salary increased with passage of time. In case of public sector female value of income increased
from 25224 to 28053. Thus, it can be said that with passage of time female income level in
public sector increased at rapid pace. It can be said that income level is high for both male and
femlae in case of public sector then private sector.
(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
On basis of chart it can be said that for male in public sector income increased by 1-2%
on yearly basis in all years analyzed. On other hand, in case of males in private sector most of
times growth rate remains in range of 1.5% to 2.5%. However, in most of years growth rate
remain low in private sector then public sector. In case of public sector female variable it can be
seen that growth rate of salary declined sharply from 3.5% to 0.5%. Thus, it can be seen that
trends in case of females is different then male in both public and private sector. In case of male
good percentage of hike is observed in public sector then private in respect to income level but in
case of female inverse thing happened and it is seen that women observe slow growth in their
income level in public sector then private. Thus, trends are inverse in respect to growth rate of
income for both male and female in public and private sector.
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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
From image given above it can be observed that student marks are fluctuating consistently and
there are specific peal and low level up to which marks are going. On viewing above chart it can
be observed that most of students score maximum marks in range of 72 to 75. Minimum level
touch by most of students in range of 30 to 35. Within these maximum and minimum limit most
of times observations comes. It can be said that students are not scoring marks in specific
direction. Teachers need to pay due attention on their students so that their marks can be atleast
brought nearby to 60. There are large number of respondents that are making a score between
range of 40 to 50. This means that most of respondents make a socre less then 60% which is
matter of concern. There is need to take lots of steps to improve condition. In this regard time to
time internals can be taken under which on weekly basis students will get their report cards and
they will be able to measure ther preparation level (Huber, 2011). It can be said that by doing so
students performance can be improved to maximum possible extent. Apart from this, teachers
can specially ask questions to students in middle of lecture and by doing so also attention of
students can be maintained and their performance can be improved to great extent. Apart from
this, on basis of performance reflected by chart it can also be said that parents must also make an
efforts to improve students marks. This is because they are the entities that are mostly concerned
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about students and can focus on them to maximum possible extent. Thus, if parents will pay due
attention of their childrens then in that case latter entity condition can be improved because after
school hours they are the entities that live most of time with students. Hence, parents can also
guide their childrens in better way.
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
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
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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
STDE
V 12.82187226
Interpretation
It can be seen from table given above that mean value of marks scored by students is
46.74 which means that on average basis students failed even to score half marks on the subjects.
This reflect that consdition is very critical and students are really not performing well in their
subjects. Mode value is 48 which is reflecting that most of students are making score equal to
average value which is 46.74 but there are number of students that are making score of 48. So
overall it can be deduced that most of students are making score in range of 45 to 50. Strength
and weakness of statistical tools is given below.
Average
Strength Weakness
 Major strength of the average method
is that it gives an overview of the
value that is observed most frequently
in the dataset.
 Major weak point of average method
is that it does not reflect range in
which specific variable values are
observed. If same thing would be in
average method then one can obtain
better overview of the variable in
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terms of range in which most of
observations of variable comes.
However, this weak point does not
undermine importance of the average
method for the analysts.
Mode
Strength Weakness
 Major strength of the mode formula is
that is help one in identifying data
points that mostly occurred in dataset.
Thus, it can be said that apart from
mean mode show another picture of
the variable (DeGroot and Schervish,
2012).
 Second major strength of the mode is
that it assist managers in identifying
specific group of customers in the
business. Thus, it can be said that
mode value attract attention of
managers in specific direction.
 Major weakness of mode is that it
does reveal range in which apart from
mean value observations most
frequently comes.
(b)Measure of dispersion
Measure of dispersion can also be considered as standard deviation as it is the statistical
tool which reflect deviation that happened in value of the specific variable. If deviation is high
then it is assumed that variable values are moving at fast rate (Siegel and et.al., 2014). On other
hand, if deviation value is low then it is assumed that deviation or fluctuation is very low in the
business. It depend on the situation whether standard deviation is assumed good or bad for the
variable. For example if sales is increasing regularly then high standard deviation can be
considered good by the business firm. On other hand, standard deviation is not increasing at fast
rate then in that case higher standard deviation can not be considered good because it means that
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sales is fluctuating on regular basis which reflect lack of stability in the business. It can be seen
from table that value of standard deviation is 12.82 which can be considered a moderate value
and this reflects that values of variable is deviating at moderate or high rate. Hence, values of the
variable is not remaining constant level. Due to this reason it is hard or almost impossible to
make prediction of marks for the students. It can be said that measure of dispersion is the one of
the most important tool that can be used to make decisions by the individuals.
2.3 Preparation of report and interpretation of results
To
The Director of Company Date: 9-1-2018
Subject: Performance measurement of students
Interpretation of mean and mode
As given above it can be observed that value of mean and mode is 46.74 and 48. This means
that majority of students are making score nearby to 46.74 but there are number of students
that are making score of 48 in exams.
Interpretation of standard deviation
Standard deviation value is 12.82 and its value is moderate which is indicating that variable or
marks are deviating at fast rate due to which it is difficult to make estimation of direction in
which students can make score in future time period.
Way that can be adopted to make comparison between subjects
In order to make comparison between subjects t test can be used by analyst. This is because by
using mentioned test it can be identified whether there is significent difference between two
independent variables at specific value of level of significence (Cressie, 2015). Apart from t
test ANOVA or analysis of variance can also be used by the firms. This is because under this
exams results can be compared with each other on basis of specific parameter. Thus, it can be
said that both ANOVA and t test have due importance for the firms because by using same it
can be easily identified that marks scored by students in both exams are same or different from
each other.
Way to measure association between two subjects
In order to measure association between two subjects coorelation analysis can be used because
by using mentioend tool it can be identified that to what extent these variables are related to
each other. Apart from this, chi square tool can also used for analysis purpose. This is because
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by using same coorelation can be identified categorical variables.
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