Statistical Analysis of Earnings Data

This assignment involves a statistical analysis of annual earnings data for male and female employees working in both public and private sectors. The report utilizes line, column, and scatter diagrams to visualize trends and compare performance across different categories. Specific recommendations are provided based on the analyzed data to enhance earnings within specific ranges.

Statistics of management

Table of Contents
INTRODUCTION...........................................................................................................................1
TASK1.............................................................................................................................................1
A) I:Observation changes in gross annual earnings of both male and female............................1
ii): Differentiate between earnings of female and male.............................................................3
TASK 2............................................................................................................................................5
PART A.......................................................................................................................................5
I: Use of Ogive to estimate the median of earning......................................................................5
ii): Calculation of mean and standard deviation.........................................................................7
b: .................................................................................................................................................9
PART B.......................................................................................................................................9
TASK 3..........................................................................................................................................12
a) Total number of deliveries in year........................................................................................13
b) Calculation of Number of bottles involved in each delivery................................................13
c) Economic order quantity.......................................................................................................13
d) Changes and suggestions......................................................................................................13
TASK 4..........................................................................................................................................14
a) Communication of findings with the use of line chart..........................................................14
b) Representation with the use of ogives..................................................................................15
CONCLUSION..............................................................................................................................16
REFERENCES..............................................................................................................................18

INTRODUCTION
Statistic is the study of statistical decision making in the face of uncertainty, it is used to
in many ways such as financial analysis, auditing, manufacturing process and other operational
activities which are performed by the company (Dey, MüIler and Sinha, 2012). Under this
project report, various process which are to be performed which includes data collection,
analysis and evaluation by using various charts and graphs. All the information collected under
this are used in order to take effective decision to attain it business objectives. However, certain
techniques are adopted by the company to analyse the results so that positive outcomes can be
drawn. At last, necessary recommendation is provided by taking the help of collected data charts.
TASK1
A) I:Observation changes in gross annual earnings of both male and female
Total gross earning of male:
Year
Public
sector Private sectors Changes
2009 30638 27362 3276
2010 31264 27000 4264
2011 31380 27233 4147
2012 31816 27705 4111
2013 32541 28201 4340
2014 32878 28442 4436
2015 33685 28881 4804
2016 34011 29679 4332
1

1 2 3 4 5 6 7 8
0
1000
2000
3000
4000
5000
6000
3276
4264 4147 4111 4340 4436 4804
4332
Column chart
Changes in Male annual earnings
Changes
2009,2010,2011,2012,2013,2014,2015,2016
Total earning of Female:
Year
Public
sector Private sectors Changes
2009 25224 19551 5673
2010 26113 19532 6581
2011 26470 19565 6905
2012 26636 20313 6323
2013 27338 20698 6640
2014 27705 21017 6688
2015 27900 21403 6497
2016 28053 22251 5802
2

1 2 3 4 5 6 7 8
0
1000
2000
3000
4000
5000
6000
7000
8000
5673
6581 6905 6323 6640 6688 6497
5802
Column chart
Total annual earning of female
Changes
2009,2010,2011,2012,2013,2014,2015,2016
According to the above present column charts, it has been found that total earning of both
male and female are fluctuating in different years. The results are calculated by taking both the
information from private or public sectors. In the 2001, the total earning is maximum as compare
to male. While in 2015, the highest earning in male is more as compare to female. It is difficult
to determine which one of them are getting maximum earning but on an assumption females are
more dominating as compare to males.
ii): Differentiate between earnings of female and male
Earning for male and female from public sectors only
Year male female Difference Gap
2009 30638 25224 55862
2010 31264 26113 57377
2011 31380 26470 57850
2012 31816 26636 58452
2013 32541 27338 59879
2014 32878 27705 60583
2015 33685 27900 61585
2016 34011 28053 62064
3

1 2 3 4 5 6 7 8
52000
54000
56000
58000
60000
62000
64000
55862
57377 57850 58452
59879 60583
61585 62064
Line chart
Earning for male and female from public sectors
Difference Gap
2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
Earning of male and female from private sector:
Year male female Difference Gap
2009 27362 19551 46913
2010 27000 19532 46532
2011 27233 19565 46798
2012 27705 20313 48018
2013 28201 20698 48899
2014 28442 21017 49459
2015 28881 21403 50284
2016 29679 22251 51930
4

1 2 3 4 5 6 7 8
43000
44000
45000
46000
47000
48000
49000
50000
51000
52000
53000
46913 46532 46798
48018
48899 49459
50284
51930
Line chart
Earning of male and female from private sector
Difference Gap
2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
From the above drawn line chart, under which earnings of both male and female are
represented that are collected from both public as well as private sectors individually. If we looks
into the male situation the line is very much straight and increasing at a constant rate. While, in
case of female the line is little curve in initial phase and then after starts increasing with a
positive rate. By closely looking into it at the 2015-2016 the earning in male are getting down
while in case of female they are increase in those two year. It means that the position of female
are more perfect as they are getting sufficient among as compare to males.
TASK 2
PART A
I: Use of Ogive to estimate the median of earning
Ogive chart: It is known as cumulative histogram or graphs that is used to analyse data
values which are above and below the data sets (Neave, 2013). It represent the cumulative
frequency function of the given number of observation.
Table showing calculation of Cumulative frequency
Hourly Earning C.I
% of
emplo
yees CF Relative CF
5

Less than 10 8 8 8.00%
10 to 15 22 30 30.00%
15 to 20 24 54 54.00%
20 to 25 14 68 68.00%
25 to 30 12 80 80.00%
30 to 40 14 94 94.00%
40 to 50 6 100 100.00%
Total 100
< 10 10 to 15 15 to 20 20 to 25 25 to 30 30 to 40 40 to 50
0
0.2
0.4
0.6
0.8
1
1.2
8.00%
30.00%
54.00%
68.00%
80.00%
94.00% 100.00%
Ogive chart (CF)
Relative CF
Hourly Earning rates
Commulative Frequency
Median: It help to divided the values in two equal parts such as half of the distribution is
below the mid value and half is above the mid-values (Menglu, 2013). If such kind of situation
arises in a data series then to calculate median :
Q1= N/4, Q2= 3* N/4
In case of UN-grouped data, median is calculated by using Q3= N+1/2
Median = L1 + (N/2) – c/F*i
L1 = It represent lower limit in the observations
N= Total number of frequency
C= CF of last class interval
I: Class interval
So, the calculation for above data series:
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M= N/2= 100/2
= 50. It lies in data range of 15 -20, whose cf is 54.
Median: 10 + [(50 – 8)/46*10]
: 10 + (42/46*10)
: 10+ 9.13 = £19.13
Quartile: It is known as one of the three set points that divide a range of data or
observation into four equal parts (Huber, 2011). The first quartile is fall under the 25th percent of
the below data. The second quartile divided the data into middle which have 50 percent of data
below it.
Quartile calculation:
Q1: N/4
: 100 /4 = 25. It lies in the data range of 10 -15 with the CF of 30.
Q1= 10 + (25- 8)/22*10
= 10+ 17 /22 *10
= 10+7.7 = £17.7
Q3 = 3(N+1)/4 = 3(110/4)= 75.7
The75.7 falls in class interval of 25 -30 with the CF of 80
Q3= 25 + (75 – 68)/12 *10
= 25 + (7/12*10)
= 25+ 5.8 = £ 30.8
According to the above computation, it has been observed that total hourly earning can be
determine by using values of median and quartile. Under this median value of £19.13 is incurred
from the available set of observations. It means that total wage earning is 19.13 per hours. It
means 50% of the employees are getting less than £19. If we talk about quartile values, 25th
percentile of the labour are getting wage rate of £17.7. While, 50 percentile is receiving at the
rate of £30 per hours. The overall analyse present a perfect image of the company's
performance. Only 6 people are getting less wage as compare to other those are related with 40-
50.
ii): Calculation of mean and standard deviation
Table for mean calculation
Hourly Frequency Mid value F * X
7

Earning
Less than 10 8 5 40
10 but under
15 22 12.5 275
15 to 20 24 17.5 420
20 to 25 14 22.5 315
25 to 30 12 27.5 330
30 to 40 14 35 490
40 to 50 6 45 270
Total 2140
Mean 21.4
Mean: It is known as numerical values which is collected by taking total average from
the available observations (Linoff and Berry, 2011). It is linked with the values that are incur
after dividing by the total number of frequencies.
Formula:
Mean: = ∑F*x /∑F
= 2140 /10
= 21.40
Standard deviation: The total value of dispersion available in the observation are said to
be SD (Anderson and et. al., 2014). It that quantity which is express by the total number of
observation of a group are different from the mean value for that particular group. It mostly
measure the dispersion of a set of value out of its total mean.
Table: Calculation of standard deviation:
Hourly Earning Frequency Mid value F* M Dx = X-A Fdx Fdx2
Below 10 8 5 40 -17.5 -140 19600
10 but under 15 22 12.5 275 -10 -220 48400
15 to 20 24 17.5 420 -5 -120 14400
20 to 25 14 22.5 315 0 0 0
25 to 30 12 27.5 330 5 60 3600
30 to 40 14 35 490 12.5 175 30625
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40to 50 6 45 270 22.5 135 18225
100 2140 -110 134850
Assume mean 22.5
Formula for SD:
: √ ∑Fdx2/N – (∑F d*x/N)2
= √ 134850 / 100 - (- 110/100)^2
= √ 1348.5- 12100 / 10000
= √ 1348.5-1.21 =√1347.29= 36.7
b:
Comparison of data analysis
Statistical measuring South East North East
Mean £21.4 £16.75
Median £19.13 £14.55
Standard deviation £36.7 £7.40
According to the above information, it has been found that the total average collected
from hourly earning from south east area is around £21.4. it is much higher as compare to that of
north east which is £16.75. While, median from data at south east is also more with £19.13 and
in north east it is only £14.55. If risk factors analysis the standard deviation is playing an
important role. Under this interpretation it has been seen that in south east the there is £36.7
deviation in value that indicated value are more closer to total mean. Likewise, in north east the
values are more spread from total mean. The risk factor in north east department is about £7.4.
PART B
a) Scatter Diagram: In any business there are several variables that are to be taken into
consideration and it is needed that proper relation shall be established between them (Venables
and Ripley, 2013). It is identified with the help of this chart which shows the modifications
which are occurring. So it is needed that the correlation which exist shall be determined and then
its representation shall be made on the graph by covering both axis.
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Outlet size(S) Turnover(T)
A 22 3.3
B 12 2
C 15 2.5
D 20 3.8
E 25 4.1
F 24 3.5
G 10 1.8
H 26 5
I 12 2.5
J 18 2.5
The above diagram shows the relation between the size or area used and turnover that is
made. It can be seen that company is using large area but there is not much turnover in respect of
it. It means that effective utilisation is not taking place. So for proper understanding the above
diagram is made which is able to show all the variations in most appropriate manner.
b) Scatter line equation
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In relation to total turnover:
Y= 0.133x+3.0267
In relation to Floor size:
Y= 0.0727x+18.8
c) Determination of Turnover:
Y= 0.133x + 3.0267
= (0.133 * 30) + 3.0267
= 3.99 + 3.0267
= 7.0167 per Sq m
d) Correlation Coefficient among them
Outlet size(S) Turnover(T)
A 22 3.3
B 12 2
C 15 2.5
D 20 3.8
E 25 4.1
F 24 3.5
11

G 10 1.8
H 26 5
I 12 2.5
J 18 2.5
Coefficient
correlation 0.91
Minimum range 1.8
Maximum range 5
e) In all the transaction there is some cause and then its has certain effect and due to this it si
required that relation that exist among them shall be identified. Fro this proper representation
shall be made by which statistical validity is ensured (Goodwin and Wright, 2014). This helps in
knowing the impact that is to be borne in case some change takes place in any of the factor.
Errors may arise because of some mistakes which can arise while performing measurements. In
respect of them there are several factors which are to be noted and they are presented below:
Selection effect: Under this such process is taken which helps in selection and that affects the
turnover made by business. This enhances the profitability and also other benefits are
received which are in overall interest of all. For this purpose all the reliable techniques shall
be taken into use by organization.
Testing effect: Under this the data which is present is to be tested so that required values can
be determined. By the use of this such results are achieved which are accurate and are
beneficial (Factor Analysis, 2017).
TASK 3
In an organisation, the main motive of effective planning is based on the techniques used
by the company in order to get more accurate results (Siegel, 2016). The outcomes can be more
effective when the tools which are used in this process are working according to the set
objectives. The numerical analysis of data can be done on continuous basis so that less chance of
mistake can arises. statistical methods are more effective to get more reliable and positive results
from the available resources. There are various methods which are available with the company to
take appropriate decision form the betterment of the company.
In those situation where the data is incline accountant are getting more difficulties to
handle statistical values. The major output is collected by using mean and standard deviation
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values. In accordance to get necessary results F-test and chi-square, regression analysis and other
methods are more effectively used. Some of them are explained underneath:
Chi-square test: It is refers as those sampling distribution which are measured by taking
hypothetical values in the data series. It is used at those situations under which null hypothesis is
positive or true.
F-Test: It is considered as any statistical test in which the observation are tested on the
basis of f-distribution in the case of null hypothesis (Horton, Baumer and Wickham, 2015).
Correlation: There is a mutual relationship among two variables which can be determine
by taking values from the provided data.
Factor analysis: It refers as statistical techniques which is used to identify variance
among various observation. It is done in terms of lower values of unseen data which is known as
factor.
a) Total number of deliveries in year
Total number of working days = 365 - 5 = 360
Time taken by one delivery: 12 days
Total number of deliveries in year = 360/12 = 30 deliveries
b) Calculation of Number of bottles involved in each delivery
Total demand of bottles = 450000
Total number of deliveries = 30
Bottles per delivery = 450000/30 = 15000 bottles
c) Economic order quantity
This is that quantity at which best advantage is received by organisation (Hamilton,
2012). As at this least cost will be incurred. This is such level at which less storage and other
expenses are incurred.
EOQ=√2RO/C
=√2*450000*20/0.50
=6000 bottles
d) Changes and suggestions
In the production of any product various cost are to be incurred which can be defined as
variable and fixed. Variable is that which deviates with the change in productivity and so it affect
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the profits on direct basis. Some of them are material, labor and all other expenses. In order to
control them there relation shall be properly understood so that decisions can be taken for them.
Inventory is to be carried at economic level as that is most advantageous position for company.
Also such policies shall be formulated which will help in attaining best results.
TASK 4
a) Communication of findings with the use of line chart
a) Total Gross annual earnings
For Male
Year Public sector Private sectors Changes
2009 30638 27362 3276
2010 31264 27000 4264
2011 31380 27233 4147
2012 31816 27705 4111
2013 32541 28201 4340
2014 32878 28442 4436
2015 33685 28881 4804
2016 34011 29679 4332
14

Total Gross Annual earnings
For Female
Year Public sector Private sectors Changes
2009 25224 19551 5673
2010 26113 19532 6581
2011 26470 19565 6905
2012 26636 20313 6323
2013 27338 20698 6640
2014 27705 21017 6688
2015 27900 21403 6497
2016 28053 22251 5802
The total earnings which are made by males and females are analyzed with the help of
above presented charts. It can be noted the earnings are fluctuating as they are changing. Returns
of females is rising and then it starts to decline and after reaching a certain downfall again
increase is there which then continuous with constant speed. Although the pattern followed in
case of males is same but if total earnings are compared then they are more for females than
males.
15

b) Representation with the use of ogives.
Hourly Earning % of employees CF
Less than 10 8 8
10 but under 15 22 30
15 to 20 24 54
20 to 25 14 68
25 to 30 12 80
30 to 40 14 94
40 to 50 6 100
< 10 10 to 15 15 to 20 20 to 25 25 to 30 30 to 40 40 to 50
0
0.2
0.4
0.6
0.8
1
1.2
8.00%
30.00%
54.00%
68.00%
80.00%
94.00% 100.00%
Ogive chart (CF)
Relative CF
Hourly Earning rates
Commulative Frequency
The hourly earnings which are made by all the employees has been represented with the
help of ogive in the cited organization. The increase can be noted in case of cumulative
frequency which has reached to 54 from starting of 8. after reaching at this point decline is noted
and then a rise is there which is made on constant basis. So for enhancement it is suggested that
earnings shall be increased in category of 20 to 25 range and reduction shall be done for those
who lies in below 10 category.
16

CONCLUSION
From the above project report, it has been articulated that statistic of management is an
effective tool used by the company in order to compare there financial position. This project
report summarised with various information related with annual earning of males and females
those are working in private as well as public sectors. Certain data is analysed by using line,
column chart and scatter diagram to know the reaction and position of performances of an
organisation. Few methods are used in order to compare the statistical values which are derived
from collected information. Overall, report is delivering positive outcome for the company by
providing necessary recommendation.
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REFERENCES
Books and Journals:
Anderson, D.R and et. al., 2014. Statistics for business & economics, revised. Cengage Learning.
Dey, D.D., MüIler, P. and Sinha, D. eds., 2012. Practical nonparametric and semiparametric
Bayesian statistics (Vol. 133). Springer Science & Business Media.
Goodwin, P. and Wright, G., 2014. Decision Analysis for Management Judgment 5th ed. John
Wiley and sons.
Hamilton, L.C., 2012. Statistics with Stata: version 12. Cengage Learning.
Horton, N.J., Baumer, B.S. and Wickham, H., 2015. Setting the stage for data science:
integration of data management skills in introductory and second courses in statistics.
arXiv preprint arXiv:1502.00318.
Huber, P.J., 2011. Robust statistics. In International Encyclopedia of Statistical Science (pp.
1248-1251). Springer Berlin Heidelberg.
Linoff, G.S. and Berry, M.J., 2011. Data mining techniques: for marketing, sales, and customer
relationship management. John Wiley & Sons.
Menglu, C., 2013. The factors of influencing the job type of informal employee. Statistics and
Management. 3. pp.24-26.
Neave, H.R., 2013. Statistics tables: for mathematicians, engineers, economists and the
behavioural and management sciences. Routledge.
Siegel, A., 2016. Practical business statistics. Academic Press.
Venables, W.N. and Ripley, B.D., 2013. Modern applied statistics with S-PLUS. Springer
Science & Business Media.
Online
Factor Analysis. 2017.[Online] Available through: <http://www.statisticssolutions.com/factor-
analysis-sem-factor-analysis/>.[Accessed on 24th October 2017].
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