Income Analysis: Gender, Sector & Size Correlation

This assignment involves analyzing income data across different factors: gender (male/female), sector (public/private), and business size. It includes creating visualizations like scatter plots, ogive charts, and cumulative frequency charts to illustrate trends. Key findings indicate a difference in income levels between genders and sectors, with public sector earnings higher than private sector ones. Additionally, there's a linear relationship between business size and turnover. The assignment concludes by discussing the importance of regression analysis for making informed business decisions.

STATISTICS FOR MANAGEMENT

TABLE OF CONTENTS
INTRODUCTION.......................................................................................................................................3
TASK 1.......................................................................................................................................................3
1Introduction of change in gross annual income across private and public sector...................................3
2 Gap between male and female income.................................................................................................5
TASK 2.......................................................................................................................................................5
(A)Analysis of hourly earnings data........................................................................................................5
(2) Calculation of descriptive statistics....................................................................................................6
(b)Comparison of results.........................................................................................................................8
(A)Floor area and weekly turnover..........................................................................................................8
© Calculation of turnover when value of size given..............................................................................11
(d) Calculation of correlation coefficient...............................................................................................12
(e) Statistical validity of model..............................................................................................................12
TASK 3.....................................................................................................................................................13
(a)Number of delivery made on annual basis.........................................................................................13
(b) Deliveries made on each round........................................................................................................13
©Economic order quantity.....................................................................................................................14
(d) Comparison of EOQ and cost...........................................................................................................14
TASK 4.....................................................................................................................................................15
(a)Scatter diagram of size and turnover.................................................................................................15
(b) Income level of gender in public and private sector.........................................................................17
(c)Male gross annual earning for public................................................................................................18
CONCLUSION.........................................................................................................................................19
...............................................................................................................................................................19
REFERENCES..........................................................................................................................................20
Figure 4Public and private sector male income level...................................................................................5
Figure 5Public and private sector female income level...............................................................................5
Figure6 Ogive chart.....................................................................................................................................7
Figure8 Relationship between size and turnover.........................................................................................9
Figure 9Turnover chart..............................................................................................................................17
Figure10 Trend in gross income across gender and public as well as private sector..................................18

Table 1Change in public and private sector income....................................................................................4
Table 2Gap between male and female income............................................................................................6
Table 2Data for Ogive.................................................................................................................................6
Table 3Calculation of mean.........................................................................................................................7
Table 4Input for computing standard deviation...........................................................................................8
Table 6Number of bottles transported.......................................................................................................14
Table7 Calculation of economic order quantity.........................................................................................15
Table 8 Cost at different level of EOQ......................................................................................................15

INTRODUCTION
Statistics is one of the most important area that is proving very helpful to managers for making
business decisions. In current report income related trends are analyzed in respect to public and private
sector and charting of same is done to identify trends that remain in existence. Regression analysis
technique is also applied on dataset in order to identify relationship that exists between dependent and
independent variables. On the basis of correlation coefficient relationship between variables is find out
validity of model is evaluated. In this way it is determined that reliable results are obtained from model.
TASK 1
1Introduction of change in gross annual income across private and public sector
Table 1Change in public and private sector income
Public sector 55862 57377 57850 58452 59879 60583 61585 62054
Private sector 46913 46532 46798 48018 48899 49459 50284 51930
% Change in public sector 3% 1% 1% 2% 1% 2% 1%
% Change in private
sector -1% 1% 3% 2% 1% 2% 3%
Interpretation
Facts revealed that at same rate income level in public and private sector is changing on
yearly basis. However, if growth rate will be compared across varied years then it can be
observed that rate keeps on fluctuating. Thus, it can be said that wages on yearly basis is
changing at same rate. Second fact that can be observed from table is that earning in public
sector is much higher than private sector. Hence, scope of earning is high in public then private
sector.

2009 2010 2011 2012 2013 2014 2015 2016
0
5000
10000
15000
20000
25000
30000
35000
40000
30638 31264313803181632541 328783368534011
27362 27000272332770528201 284422888129679
Public sector male
Private sector male
Figure 1Public and private sector male income level
2009 2010 2011 2012 2013 2014 2015 2016
0
10000
20000
30000
40000
50000
60000
70000
2522426113264702663627338277052790028053
19551195321956520313206982101721403
63690
Public sector female
Private sector female
Figure 2Public and private sector female income level
Fact is also indicating that for male there is high level of income in public sector then private sector.
Similarly, in case of female also earning is more from public then private sector. However, it can be said
that in case of female trend get changed slightly and women are now earning more money in private
sector then public sector

2 Gap between male and female income
Table 2Gap between male and female income
Male 58000 58264 58613 59521 60742 61320 62566 63680
Female 44775 45645 46035 46949 48036 48722 49303 50304
Difference 13225 12619 12578 12572 12706 12598 13263 13376
Interpretation
Gap between male and female income level is fluctuating consistently. It can be observed that
income level for male is much higher then females which reflect that there is gender pay gap inequality.
There is needed to take step to control such kind of discrimination across gender.
TASK 2
(A)Analysis of hourly earnings data
Table 3Data for Ogive
F CF
Below 10 8 8
10 but under 15 22 30
15 but under 20 24 54
20 but under 25 14 68
25 but under 30 12 80
30 but under 40 14 94
40 but under 50 6 100

Below 10 10 but under
15 15 but under
20 20 but under
25 25 but under
30 30 but under
40 40 but under
50
0
20
40
60
80
100
120
8
30
54
68
80
94 100
Chart Title
Figure3 Ogive chart
Interpretation
Value of median for hourly earnings lie in range of 15 to 20. This range is determined as median
value because it comes in middle of data set. Quartile is the one of the important tool of statistics as it
classified data set in to three equal parts. Value of Q1 in data set is below 10 and same of Q2 is 15 to 20
and Q3 may value is 30 to 40.
(2) Calculation of descriptive statistics
Table 4Calculation of mean
F CF
Mid
point FX
Below 10 8 8 5 40
10 but under 15 22 30 12 264
15 but under 20 24 54 18 432
20 but under 25 14 68 23 322
25 but under 30 12 80 27 324
30 but under 40 14 94 35 490
40 but under 50 6 100 45 270
100 2142

432 Mean 21.42
Interpretation
Mean value is 21.42 and it reflect average value of the variable. On the basis of obtained results it
can be said that majority of respondents are earning amount of 21.42 in specific duration. Above 25
income level there are large number of respondents that comes in above class. This means that number of
respondents may almost equally distribute across different income levels. This is evident from fact that in
range of 25 to 30 there are 12 respondents and in class of 30 to 40 there are 14 employees. Apart from
this, in range of 40 to 50 there are only 6 employees. Hence, it can be said that almost in all categories of
income equally respondents are distributed.
Table 5Input for computing standard deviation
F CF Mid point FX fxx
Below 10 8 8 5 40 200
10 but under 15 22 30 12 264 3168
15 but under 20 24 54 18 432 7776
20 but under 25 14 68 23 322 7406
25 but under 30 12 80 27 324 8748
30 but under 40 14 94 35 490 17150
40 but under 50 6 100 45 270 12150
100 2142 56598
432 Mean 21.42
107.1636
STDEV 10.35199
Interpretation

Standard deviation is the one of the most important tool because it reflects extent to which values
of variable are deviating from their mean value (Descriptive and inferential statistics, 2017). It can be
observed that value of standard deviation is only 10.35 which mean that values are deviating at very slow
rate and due to this reason there is less variance in data set. It can be said that salary of employees is
deviating at very slow rate.
(b)Comparison of results
Results on comparison are indicating that in case of South portion of England there is higher
amount of annual earning then North portion of England. It can also be seen that values are deviating at
very slow rate 7.40 in case of Noth eastern part which is very low and along with this salary is high. This
means that in case of South Eastern part heavy amount is earned then North Eastern area of England.
(A)Floor area and weekly turnover
0 2 4 6 8 10 12
0
5
10
15
20
25
30
3.3 2 2.5 3.8 4.1 3.5 1.8
5
2.5 2.5
22
12
15
20
25 24
10
26
12
18
Chart Title
Size (S) Turnover
Figure4 Relationship between size and turnover

0 2 4 6 8 10 12
0
2
4
6
8
10
12
f(x) = NaN x + NaN
R² = 0 Size (S)
Size and turnover are two variables that are analyzed using above image as it can be seen that both these
variables are interlinked to each other with change in one variable change comes in other variable.
However, coefficient value is less and this reflect that with change in independent variable big change
does not comes in dependent variable.
(b) Coorelation cofficient r
SUMMARY
OUTPUT
Regression Statistics
Multiple
R 0.913767
R Square 0.834971
Adjusted
R Square 0.814342
Standard
Error 0.437532
Observati
ons 10
ANOVA

df SS MS F
Significa
nce F
Regressio
n 1
7.7485
28 7.748528
40.476
22 0.000218
Residual 8
1.5314
72 0.191434
Total 9 9.28
Coefficie
nts
Standa
rd
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.202177
0.4760
34 0.424711
0.6822
39 -0.89556
1.2999
12
-
0.8955
6
1.2999
12
Size (S) 0.15749
0.0247
54 6.362093
0.0002
18 0.100406
0.2145
74
0.1004
06
0.2145
74
RESIDUAL
OUTPUT
Observati
on
Predicte
d
Turnover
Residu
als
Standard
Residual
s
1 3.666965
-
0.3669
7 -0.88959
2 2.092061
-
0.0920
6 -0.22317
3 2.564533 -
0.0645
-0.15644

3
4 3.351985
0.4480
15 1.086074
5 4.139437
-
0.0394
4 -0.0956
6 3.981946
-
0.4819
5 -1.16833
7 1.777081
0.0229
19 0.055561
8 4.296927
0.7030
73 1.704383
9 2.092061
0.4079
39 0.988921
10 3.037004 -0.537 -1.3018
Regression is the one of the most important analytical tool that is used for analysis purpose and
making prediction. Regression reflects that with change in independent variable what change will come in
dependent variable (Gnanadesikan, 2011). Beta coefficient reflects points by which change may be
observed in independent variable with change in dependent variable which is turnover in present case.
Intercept is another one of the most important tool because it reflects value of dependent variable that can
be observed if none of value independent variable does not changed. Alpha value in regression model
reflect whether there is significant mean difference between dependent and independent variable in terms
of rate of change. Thus, it can be said that it is one of the important tool for making prediction.
© Calculation of turnover when value of size given
Regression equation is Y=0.20+0.15*30= 4.92 and it can be said that in case value of SQM is 30
then in that case turnover earned will be equal to 4.92. Regression equation is common approach that is
used to make prediction because in it there are coefficients and value of intercept which is one that can be
observed if all other independent variable values remain unchanged. If data will be analyzed then it can
be observed that with increase in size turnover also increased. In this way prediction made proved correct.
There are number of assumptions that are associated with regression analysis and if same are satisfied
then it is assumed that prediction that is made on the basis of regression is reliable in nature. On the basis

of results obtained in prediction it can be said that firm must consistently make an efforts to increase size
of floor of its premises because by doing so operations can be increased at rapid pace and this will lead to
elevation in turnover.
(d) Calculation of correlation coefficient
Correlation coefficient R reflects the relationship that exist between two variables. In present case it can
be seen from table that value of correlation coefficient is 0.91 which means that there is high degree of
relationship between dependent and independent variable. This clearly indicate that with change in size
turnover will definitely change to great extent. Correlation value always remain in range of 0 to 1 or 0 to -
1. In case correlation value is zero then it means that there is no relationship between independent and
dependent variable. On other hand, if it is identified that correlation value is positive then it means that
both variables are positively related to each other. More value is positive it is assumed that there is heavy
correlation between variables. In case correlation value is more then 0.5 it is assumed that there is high
degree of relationship between dependent and independent variable. Opposite to this if correlation value
is less than 0.5 but value is positive it is assumed that there is less relationship between dependent and
independent variable. Similarly, correlation value may be negative. In case it is identified that correlation
value is negative it is assumed that there is no relationship between dependent and independent variable.
In case negative value of correlation is more than -0.5 it is considered that there is highly negative or
inverse relationship between dependent and independent variable. On other hand, in case there is less
correlation value it is assumed that there is less correlation between dependent and independent variable.
(e) Statistical validity of model
Statistical validity of model is measured to identify whether model is giving accurate results for
making prediction. In order to measure statistical validity of model regression analysis has some
assumptions. On fulfillment of these assumptions it is assumed that model is making accurate prediction.
One of these assumptions is that there must be less errors between predicted and actual values. In this
regard line of best fit plot is used. If actual and predicted values are accurate then it is assumed that model
is valid and making accurate prediction.

8 10 12 14 16 18 20 22 24 26 28
0
1
2
3
4
5
6
3.3
2 2.5
3.8 4.1
3.5
1.8
5
2.5 2.5
Size (S) Line Fit Plot
Turnover
Predicted Turnover
Size (S)
Turnover
From chart given above it can be observed that most of times accurate and predicted values are same and
due to this reason it can be said that model is making accurate prediction. Other common assumption is
that there must be independent relationship among residuals. Means that residuals that are obtained in
chart must not interrelate to each other. Sometimes due to presence of outliers errors of high amount
comes in existence. If residuals will be high then in that case same will affect other residuals and this may
affect model results. Third assumption in respect to linear regression is that there is no presence of
outliers in data set. If there will be absence of outliers from data set then in that case accurate prediction
can be made in the business. In data set there is no presence of outliers and due to this reason it can be
said that assumption is satisfied and model that is prepared is valid.
TASK 3
(a)Number of delivery made on annual basis
Total number of deliverables made during year is 450000 and it is assumed that demand given is
entirely related to company. Thus, same value is taken in to account for doing entire calculation. It can be
said that total number of deliverables are large in quantity.
(b) Deliveries made on each round
Table 6Number of bottles transported
Annual demand 450000
Number of trips 30
Number of bottles in each delivery 15000

Interpretation
Number of bottles on each delivery is 15000 as it is well known fact that number of trips made is
30 and annual demand is 450000. On this basis these inputs it is identified that number of bottles sold or
transported by firm on each delivery is 15000.
©Economic order quantity
Table7 Calculation of economic order quantity
Quantity 450000
Cost per order 2
Carrying cost per order 0.5
EOQ 6000
Interpretation
EOQ refers to economic order quantity and it is that quantity by purchasing which cost of
inventory or stocking of goods can be minimized. It can be seen from table given above that value of
economic order quantity is 6000. This means that 6000 units must be purchased in order to ensure that
cost of inventory will remain in control.
(d) Comparison of EOQ and cost
Table 8 Cost at different level of EOQ
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
1825.74
2 1792.842914 1761.661
Interpretation

EOQ at different quantity carrying cost is different as it can be observed that with increase in
carrying cost per order EOQ declined while cost per order and quantity remain same. This means that
with increase in economic order quantity carrying cost declined and it can be said that more quantity must
be purchase to meet requirements.
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
It can be observed that total variable cost in case of first option is 4350 and in case of section
option same is 3000. On this basis it can be said that it will better to select second option which
is related to EOQ where cost is very low.
TASK 4
(a)Scatter diagram of size and turnover
0 2 4 6 8 10 12
0
5
10
15
20
25
30
3.3 2 2.5 3.8 4.1 3.5 1.8
5
2.5 2.5
22
12
15
20
25 24
10
26
12
18
Chart Title
Size (S) Turnover
Figure 6Relationship between size and turnover

8 10 12 14 16 18 20 22 24 26 28
0
1
2
3
4
5
6
Turnover
Figure 5Turnover chart
Interpretation
There is positive relationship between size and turnover as reflected by scatter plot. It can
be seen from chart that both size and turnover are moving in same direction in terms of data
points (Hayes and Preacher, 2014). Ups and downs are in same direction in case of both sizes a
turnover and on this basis it can be said that in case size of premises will increase turnover will
enhance. Similarly, if size of premises will decline then in that case turnover will decline. Thus,
there is linear relationship between both variables.

(b) Income level of gender in public and private sector
2009 2010 2011 2012 2013 2014 2015 2016
0
10000
20000
30000
40000
50000
60000
70000
Public sector male
Private sector male
Public sector female
Private sector female
Figure6 Trend in gross income across gender and public as well as private sector
From above chart it can be seen that in case of male and female former sort of gender is earning
good amount of money in its business. It can also be seen that in public sector people are earning
more amount of money then private sector (Kraemer and Blasey, 2015). This is because private
sector firms wants to obtain labor of best quality at low cost and due to this reason there is higher
amount of pay in case public sector then private sector.

(c)Male gross annual earning for public
Below 10 10 but under
15 15 but under
20 20 but under
25 25 but under
30 30 but under
40 40 but under
50
0
20
40
60
80
100
120
8
30
54
68
80
94 100
Chart Title
Figure11 Ogive chart
1 2 3 4 5 6 7
0
20
40
60
80
100
120
8
30
54
68
80
94 100
CF
Figure 12Cumulative frequency chart
Interpretation
Chart is reflecting that with increase in income range number of frequency is elevating.
Chart given above is reflecting that within range of below 30 numbers of people is 8 and in range
of 10 to 15 there are 30 respondents. Apart from this, 15 to 20 there are 54 respondents and in
range of 20 to 25 respondents there are 68 respondents. It can be said that with increase in
income range number of respondents in income slab is also elevating. Chart is clearly indicating
that with increase in income level number of respondents is increasing regularly but growth rate

of same declined with increase in income level. It can be said that there are majority of number
of people that fall in low income category but this number does not decline too much with
increase in income level. On this basis it can be said that there is approximately equal
distribution of income across all these categories of income range. Thus, it can be said that there
is no specific trend that is observed in terms of earning of salary by people on their job.
CONCLUSION
On the basis of above discussion it is concluded that there is difference in income level of
male and female. Means that male are earning higher amount of money then female. In case of
public and private sector it can be observed that public sector is generating higher amount of
income then private sector. It is also concluded that regression analysis is one of the most
important prediction technique that used in analytics domain to make business decision. There
are number of statistics in regression model that can be used to make accurate prediction and
making business decisions.