Statistical Analysis for Business Decisions

This assignment delves into the significance of statistical tools for businesses by analyzing various datasets. It examines the relationship between store size and turnover, compares male and female income levels in public and private sectors, and utilizes an ogive chart to analyze the cumulative percentage of employees based on hourly earnings. The analysis demonstrates the impact of size on turnover and highlights discrepancies in pay between genders.

STATISTICS

TABLE OF CONTENTS
INTRODUCTION.......................................................................................................................................3
TASK 1.......................................................................................................................................................3
(a)Change in gross annual earning in public and private sector and pay gap across gender....................3
TASK 2.......................................................................................................................................................6
(A)Analysis of hourly earnings data........................................................................................................6
(B) Calculation of descriptive statistics...................................................................................................7
(b) Comparison of obtained figures of varied geographic area................................................................8
(A)Relationship between variables floor area and weekly turnover.........................................................9
(b) Equation of line of best fit for regression model..............................................................................10
©Calculation of turnover when outlet size is given...............................................................................10
(d) Correlation coefficient R..................................................................................................................10
(e) Measuring statistical validity of model.............................................................................................13
TASK 3.....................................................................................................................................................14
(a)Number of delivery made on annual basis.........................................................................................14
(b) Deliveries made on each round........................................................................................................14
©Economic order quantity.....................................................................................................................14
(d) Comparison of EOQ and cost...........................................................................................................15
TASK 4.....................................................................................................................................................15
(a)Scatter diagram of size and turnover.................................................................................................15
(b)Male income level line chart.............................................................................................................17
©Ogive chart for computing cumulative percentage of employees for hourly earnings data.................18
CONCLUSION.........................................................................................................................................19
REFERENCES..........................................................................................................................................20

INTRODUCTION
Statistics is the one of the most important branch that assist managers in making business
decisions and identifying factors due to which business performance is affected. In present
research study male and female earning data is analyzed deeply and charting of same is done.
Apart from this, regression analysis method is applied on size and turnover data set and
prediction is made about given value of independent variable. At end of the report charting of
variables is done and conclusion is formed.
TASK 1
(a)Change in gross annual earning in public and private sector and pay gap across gender
Figure 1Change in annual earning in public and private sector
Interpretation
Changes happened in public and private sector earning at same rate every year.
Fluctuation is observed consistently in the earning in both sectors as it change from 1% to 3%
every year. This reflects that every year 1% up and down usually happened in growth rate of
annual earning but in specific range these rates are changing.

2009 2010 2011 2012 2013 2014 2015
0
5000
10000
15000
20000
25000
30000
35000
40000
30638 31264 31380 31816 32541 32878 33685
27362 27000 27233 27705 28201 28442 28881
25224 26113 26470 26636 27338 27705 27900
19551 19532 19565 20313 20698 21017 21403
Chart Title
Public sector male Private sector male
Public sector female Private sector female
Figure2Public and private sector male and female
2009 2010 2011 2012 2013 2014 2015
0
5000
10000
15000
20000
25000
30000
35000
40000
Chart Title
Public sector male Private sector male
Public sector female Private sector female
Figure3Public and private sector male and female

Figure 4Gender pay gap
Interpretation
Gender pay gap increase consistently between male and female with passage of time period. In
starting years this rate decline but from 2014 this gap again start rising which is not good for the
nation. Thus, government need to promote business firm to ensure that there is no gender pay gap at
workplace.

TASK 2
(A)Analysis of hourly earnings data
Table 1Raw facts
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
Figure5 Variable ogive chart
Interpretation
Median value of the variable is 10 to 15 and its frequency is 22. It is the tool that divides
entire set of figures in two parts. Similar to median there is another tool which is known as

quartile as it classify entire set of figures in to three parts (Chen, Benjaafar and Elomri, 2013).
Q1 for variable is 0 to 10 and Q2 value is 10 to 15 as well as Q3 value may be 30 to 40. It can be
said that quartile are extended version of median.
(B) Calculation of descriptive statistics
Table 2Mean value of variable
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
Average reflects the variable value or feature that is most of times observed during
specific time period (Spillane and Hunt, 2010). In present case value of average is 21.42 and this
means that average hourly earnings in respect to respondents or sample units is in range of 20 to
25 during specific time period.

Table 3Standard 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
1715
0
40 but under 50 6
10
0 45 270
1215
0
100 2142
5659
8
432 Mean
21.4
2
107.163
6
STDEV
10.3519
9
Interpretation
Standard deviation reflects ups and downs that happened in data point from mean value
of variable (Leong and et.al., 2012). Standard deviation value is only 10.35 which is very low

and on this basis it can be said that there are majority of respondents that are earning amount for
hours in range of 20 to 25.
(b) Comparison of obtained figures of varied geographic area
Mean, median and standard deviation in case of North East geographic area is 16.75,
14.55 and 7.40. Whereas, same in case of other area which is South East is 21.42, 21 to 25 and
10.35. On this basis, it can be said that earning in case of North East area is low and deviating at
very low rate. Hence, it can be said that more amount is paid in South East then North East area.
(A)Relationship between variables 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
Figure6Size and turnover scatter diagram
Interpretation
There is relationship between both variables size and turnover as it can be observed that
both size and turnover are moving at same rate across most of observations. If one variable is
increasing then other one also increase or vice verse. On this basis it can be said that both
variables are interrelated to each other and if one will change then other one will move in same
direction.

(b) Equation of line of best fit for regression model
0 2 4 6 8 10 12
0
2
4
6
8
10
12
f(x) = NaN x + NaN
R² = 0 Size (S)
Figure 7 Scatter plot of floor size and turnover
Interpretation
In chart data points are above or below regression line and this means that there is
difference between actual and predicted value. It can be said that few variables need to be add
more to make reliable and accurate prediction by using regression model for dependent variable.
©Calculation of turnover when outlet size is given
Regression equation for variable is Y=0.20+0.15*30= 4.92 and this reflect that if size of
floor is 30 then in that case turnover will be 4.92. Regression equation is commonly used to
make prediction by business managers. In the equation beta coefficient and intercept are given
where beta reflect change that may come in dependent variable which is turnover due to change
in size of floor. Intercept reflect mean value of dependent variable when values of independent
variable remain unchanged. Values of both are used to make prediction.
(d) Correlation coefficient R
SUMMARY
OUTPUT
Regression Statistics

Multiple R 0.913767
R Square 0.834971
Adjusted
R Square 0.814342
Standard
Error 0.437532
Observatio
ns 10
ANOVA
df SS MS F
Significan
ce F
Regressio
n 1
7.7485
28
7.7485
28
40.476
22 0.000218
Residual 8
1.5314
72
0.1914
34
Total 9 9.28
Coefficie
nts
Standar
d Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 0.202177
0.4760
34
0.4247
11
0.6822
39 -0.89556
1.2999
12
-
0.8955
6
1.2999
12
Size (S) 0.15749
0.0247
54
6.3620
93
0.0002
18 0.100406
0.2145
74
0.1004
06
0.2145
74
RESIDUAL OUTPUT
Observati
on
Predicted
Turnover
Residua
ls
Standar
d
Residua

ls
1 3.666965
-
0.3669
7
-
0.8895
9
2 2.092061
-
0.0920
6
-
0.2231
7
3 2.564533
-
0.0645
3
-
0.1564
4
4 3.351985
0.4480
15
1.0860
74
5 4.139437
-
0.0394
4 -0.0956
6 3.981946
-
0.4819
5
-
1.1683
3
7 1.777081
0.0229
19
0.0555
61
8 4.296927
0.7030
73
1.7043
83
9 2.092061
0.4079
39
0.9889
21
10 3.037004 -0.537 -1.3018

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
Interpretation
Value of correlation coefficient R is 0.91 which reflect that there is strong relationship
between dependent and independent variable (Descriptive and inferential statistics, 2017).
Higher value reflects that with change in size equal changes may comes in turnover. Analysis of
facts reveal that with increase in size turnover increase which means that if size will increase by
15% turnover will also increase by 15%.
(e) Measuring statistical validity of model
In order to measure statistical validity of model there are few of factors that need to be
considered like error terms. It can be observed that there is no difference between actual and
predicted value and due to this reason it can be said that model is valid. Second assumption is
that there must by independence in predicted values which means that any predicted value must
not have impact on any other predicted value (Draper. and Smith, 2014). In chart it can be clearly
seen that there is independence in predicted values and on this basis it can be said that model is
valid. There is no multicollinearity in regression model as there is single variable in the model.
Due to this reason there is no chance of model invalidity. In other words it can be said that model
is valid and reliable prediction can be made from it.

TASK 3
(a)Number of delivery made on annual basis
On annual basis number of deliveries made by the business firm are 45000. In order to
compute this value assumption made is that firm only have market share of 10% in entire market.
Systematic approach is followed for computing number of deliverables on annual basis.
(b) Deliveries made on each round
Table 4Number of bottles transported
Annual demand 45000
Number of trips 30
Number of bottles in each delivery 1500
Interpretation
Number of bottles sold on each delivery is 1500 as it can be noted that number of trips
made is 30 and annual demand is 45000. Due to this reason number of bottles deleievred in each
delivery are 1500 as 45000n divided by 30.
©Economic order quantity
Table5Computation of EOQ
Quantity 45000
Cost per order 2
Carrying cost per order 0.5
EOQ 600
Interpretation
Value of EOQ is 600 which mean that purchase of 600 units of raw material must be
made so that storage cost remains minimum in business. EOQ approach proves highly effective
for business firms.

(d) Comparison of EOQ and cost
Table 6 Cost at different level of EOQ
Quantity 45000 45000 45000 45000 45000
Cost per order 2 2 2 2 2
Carrying cost per order 0.5 0.52 0.54 0.56 0.58
EOQ 600 588.3484
577.350
3 566.9467 557.086
Interpretation
From the table given above it can be seen that value of economic order quantity is
reducing consistently from 600 to 557 and at same time carrying cost per order is increasing.
Thus, there is direct relationship between carrying cost and EOQ as EOQ increase carrying cost
decline.
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 6Scatter diagram of size vs turnover

8 10 12 14 16 18 20 22 24 26 28
0
1
2
3
4
5
6
Turnover
Figure 8Chart of turnover
Interpretation
Chart that is given above is clearly reflecting that size and turnover both are interrelated
variables. Both size and turnover are changing at same rate as mentioned above if size is
increasing then turnover is also increasing or vice verse. Hence, it can be said that if firm will
increase its retails stores flour size then definitely turnover will increase.

(b)Male income level line chart
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
Figure 9Annual income gender wise
Interpretation
There is huge difference between gross annual income level of male in public and private
sector. It can be observed that annual income for male is greater than same of female and on this
basis it can be said that male are earning more money in public then private sector.

©Ogive chart for computing cumulative percentage of employees for hourly earnings data
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
Figure5Ogive chart
1 2 3 4 5 6 7
0
20
40
60
80
100
120
8
30
54
68
80
94 100
CF
Figure 10Cumulative frequency chart
Interpretation
Chart is indicating that 50% employees are covered up to 15 to 20 ranges and on this
basis it can be said that half of respondents are earning moderate amount on hourly basis. 80%
respondents fall in class of 25 to 30 and this means that above level of 30 there are few people
that are earning money more then 30. Means that majority of sample units are earning amount
below 25.

CONCLUSION
On the basis of above discussion it is concluded that there is significant importance
statistical tools for the business firms because it help them in making prudent business decisions.
In current time period analysis tools are used by most of business firms to solve their problems.
It is also concluded that that there is difference in pay that is given to male and female. Apart
from this, it is also deduced that size have impact on turnover as size will increase traction will
be observed in turnover.