Statistics for Management: Earnings and Regional Analysis Report

This report presents a statistical analysis of earnings data, focusing on comparisons between men and women in the public and private sectors. It utilizes hypothesis testing, specifically t-tests, to determine significant differences in earnings. The report includes time charts illustrating earnings trends over several years and calculates annual growth rates for different groups. Furthermore, the analysis extends to hourly pay rates across various UK regions, employing median calculations, quartile analysis, and standard deviation to assess pay disparities. Data visualization techniques, such as bar and pie charts, are used to present the findings and provide a clear understanding of the relationships between variables, such as the number of bedrooms and house prices in different streets. The report concludes by summarizing the key findings and their implications.

Statistics for Management

Table of Contents
INTRODUCTION...........................................................................................................................2
MAIN BODY...................................................................................................................................2
TASK 1............................................................................................................................................2
A. Determine how earnings of men in public sector is different from earnings of women in
public sector by using hypothesis................................................................................................2
B. Determine how earnings of men in private sector is different from earnings of women in
private sector by using hypothesis...............................................................................................3
C. Earning time chart of each group............................................................................................4
D. Evaluating the annual growth rate in the context of earnings of given four group.................6
TASK 2............................................................................................................................................8
A) Analysis and evaluation of hourly pay rates in different UK regions....................................8
B) Earnings comparison in between two regions......................................................................12
TASK 3 .........................................................................................................................................12
Section A....................................................................................................................................12
Section B....................................................................................................................................13
TASK 4 .........................................................................................................................................13
4.1...............................................................................................................................................13
1. Bar chart.................................................................................................................................13
2. Pie chart.................................................................................................................................16
....................................................................................................................................................18
4.2 Relationship between the number of bedrooms and the house price of bedrooms in all of
the three streets..........................................................................................................................19
CONCLUSION..............................................................................................................................25
REFERENCES..............................................................................................................................26
1

INTRODUCTION
Statistics is a term which is related with the process of data collection, analysis as well as
interpretation so as to ascertain some meaningful information from it. With the help of
mathematical as well as statistical tools, data gathered can be evaluated in effective manner.
Also, by making use of different types of graphs, charts presentation of numerical data provides
better understanding to end users and assists in their decision making process. The present report
will define about economic data with the help of time chart. Furthermore, with the help of
comparison among hourly earnings of two different regions, statistical meaning will be derive.
Also, by applying statistical methods such as Economic order quantity, normal distribution
curves etc. explanation related to different section will be done. At last, the report will made
emphasis on making presentation of given data set in both the bar as well as pie chart form.
MAIN BODY
TASK 1
A. Determine how earnings of men in public sector is different from earnings of women in
public sector by using hypothesis
Null hypothesis H0: There is no significant difference between earnings of men and
women in public sector.
Alternative hypothesis H1: There is a significant difference between earnings of men
and women in private sector.
t-Test: Two-Sample Assuming Equal
Variances
Men earnings in
public sector
Women earnings in
public sector
Mean 32276.625 26933.25
Variance 1449962.26785714 975692.5
Observations 8 8
Pooled Variance 1212827.38392857
Hypothesized Mean Difference 0
2

df 14
t Stat 9.7038964331
P(T<=t) one-tail
6.76878422104249E-
008
t Critical one-tail 1.7613101358
P(T<=t) two-tail 1.3537568442085E-007
t Critical two-tail 2.1447866879
Interpretation - From the above table it can be interpreted that null hypothesis will be
accepted as 1.35 is greater than 0.05 depicting about no significant difference in between the
earnings of men and women working in the public sector. No discrimination has been made on
gender basis in the context of income payment. Equal pay and status has been provided to both
the genders as per the Government norms and regulations as well (Berman and Wang, 2016).
Thus it can be said that because of no significant difference among earnings of men and women
working in the public sector, it has assisted in improving standard of living.
B. Determine how earnings of men in private sector is different from earnings of women in
private sector by using hypothesis
Null hypothesis H0: There is no significant difference between earnings of men and
women in private sector.
Alternative hypothesis H1: There is a significant difference between earnings of men
and women in private sector.
t-Test: Two-Sample Assuming Equal
Variances
Men earnings in
private sector
Women earnings in
private sector
Mean 28096.625 20541.25
Variance 795287.696428572 988729.928571429
3

Observations 8 8
Pooled Variance 892008.8125
Hypothesized Mean Difference 0
df 14
t Stat 15.9993171714
P(T<=t) one-tail
1.08089238375977E-
010
t Critical one-tail 1.7613101358
P(T<=t) two-tail
2.16178476751954E-
010
t Critical two-tail 2.1447866879
Interpretation - From the above table it can be assessed that null hypothesis will be
accepted as there is no significant difference in between the earnings of men and women
employed in the private sector. Also, 2.16 is greater than 0.05 which defines that equal pay and
benefits has been provided to both men and women (Bhattacharyya, 2018). By imparting equal
payment, it helps the company in motivating its employees which directly increases productivity
as well as profitability level.
C. Earning time chart of each group
Public sector
Year Men public sector Women public sector
2009 30638 25224
2010 31264 26113
2011 31380 26470
2012 31816 26663
2013 32541 27338
2014 32878 27705
2015 33685 27900
4

2016 34011 28053
Interpretation: From the above table it can be interpreted that income of men in the
public sector has increased within a time frame of 8 years whereas income of women is also
increasing but with very small percent in past 8 years.
Private sector
Year Men private sector Women private sector
2009 27632 19551
2010 27000 19532
2011 27233 19565
2012 27705 20313
2013 28201 20698
2014 28442 21017
2015 28881 21403
2016 29679 22251
5
1
2
3
4
5
6
7
8
0500010000150002000025000300003500040000
Men and women income in public sector

1
2
3
4
5
6
7
8
0
5000
10000
15000
20000
25000
30000
35000
Men and women in private sector
Men private sector Women private sector
Interpretation: From the above table it can be evaluated that income of men in case of
the private sector is facing mix trend of increasing as well as decreasing till 2012. After 2012, it
has been observed that the level of income has arises with increasing rate (Cornett and
Sarangam, Intel Corp, 2019). In case of women working in the private sector, the level of their
earnings has been increasing from the last 8 years which helps in improving the standard of
living as well as in fulfilment of desired needs and wants.
D. Evaluating the annual growth rate in the context of earnings of given four group.
PUBLIC SECTOR
Year Men public sector Women public sector
2009 30638 25224
2010 31264 26113
2011 31380 26470
2012 31816 26663
2013 32541 27338
6

2014 32878 27705
2015 33685 27900
2016 34011 28053
ANNUAL GROWTH RATE
Year Men public
sector
YOY Growth
rate
Women public
sector
YOY Growth
rate
2009 30638 25224
2010 31264 2% 26113 4%
2011 31380 0% 26470 1%
2012 31816 1% 26663 1%
2013 32541 2% 27338 3%
2014 32878 1% 27705 1%
2015 33685 2% 27900 1%
2016 34011 1% 28053 1%
Interpretation – As per the given table, it can be assessed that the YOY growth rate of
Men is showing declining trend when compared among year 2015 to the year 2016. The growth
rate of earnings of men as employed in the public sector has declined from 2% in 2010 to 1% in
the year 2016 (De Vries and Hitomi, Numecent Holdings Inc, 2016). On the other hand, the
YOY annual growth rate of women was 4% in the year 2010 which has declined to 1% in the
year 2011. It signifies that the financial progress of women working in the public sector firms are
not showing positive returns.
PRIVATE SECTOR
Year Men private sector Women private sector
2009 27632 19551
2010 27000 19532
2011 27233 19565
2012 27705 20313
7

2013 28201 20698
2014 28442 21017
2015 28881 21403
2016 29679 22251
ANNUAL GROWTH RATE
Year Men private
sector
YOY Growth
rate
Women private
sector
YOY Growth
rate
2009 27632 19551
2010 27000 -2% 19532 0%
2011 27233 1% 19565 0%
2012 27705 2% 20313 4%
2013 28201 2% 20698 2%
2014 28442 1% 21017 2%
2015 28881 2% 21403 2%
2016 29679 3% 22251 4%
Interpretation – From the above table it can be interpreted that the year over year growth
rate of men was -2% in the year 2010 which was improved in the year 2011 to 1%. Later on, it
has been assessed that the financial progress level of men private sector is increasing and
performing in much better manner from the year 2014 to the year 2016. In case of women private
sector YOY growth rate for the very first year there has been no growth (Fischer and et.al.,
2017). In year 2012, it has increased to 4% from 0% which later on declines to 2% till the year
2015. From 2013 to 2015, the YOY growth rate among women private sector was constant i.e.
2% which has increased to 4% in the year 2016 depicting about growth level of earnings of
women.
TASK 2
A) Analysis and evaluation of hourly pay rates in different UK regions
1. Estimation of median hourly earnings and quartiles with the help of ogive chart:
8

Median: A statistical method which helps in measuring the central tendency or central
value of the given data set. It determines median value by arranging all the values ranging from
the smallest to the largest value (Gardener, 2017). If the value obtained is of odd nature than
median will be the middle most value present in the data set arranged. In case of even
observation, then median will be calculated by taking average of middle values.
Hourly
earning
No. of leisure
centre staff
Relative
frequency
Cumulative
frequency
Cumulative relative
frequency
0 – 10 4 0.08 4 0.08
10 – 20 23 0.46 27 0.54
20 – 30 13 0.26 40 0.8
30 – 40 7 0.14 47 0.94
40 – 50 3 0.06 50 1
Total 50
Median can be calculated as follows:
1. Divide last CF by 2.
= N/2
2. Apply the formula
= L / 2 + H / f [N / 2 – C]
Here,
F = corresponding frequency
N = summation of all frequency
L = lower limit of middle class
H = size of class
C = cumulative frequency
According to the given table median is 50/2 = 25.
Quartile: It is a method which describe division of data into four intervals having its
basis on values present in the data set. Also, it helps in identifying as well as comparing different
set of observations. It determines a set of data by breaking them into different quarters. The value
9

of second quartile is called as the median (Keller, 2015). Interquartile range on the other hand
helps in measuring the variability of data thereby dividing values of data into several quarters.
Calculation of quartile:
1 Quartile 4
3 Quartile 13
Interquartile 9
0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
0
0.2
0.4
0.6
0.8
1
1.2
ogive chart
2. Calculation of mean and standards deviation for hourly earnings:
Mean: Is defined as an average value as calculated from among the given set of data. It
helps in determining the central tendency value of data among given number of values. It is
calculated by summing up all the numbers and dividing the value obtained by the total number of
count actually present. The value obtained is known as mean value which is also called as the
arithmetic mean or average mean.
Standard deviation: It is a method which can be used for determining variation or
dispersion of a data value from among the given data (Keller, 2017). If value determined is
10

having low standard deviation, then it will be close to average number of data set. In case of high
standard deviation value, it signifies that values in the given data set are highly spread out.
Arithmetic mean
Hourly
earning
Number of leisure
centre staff (f) Mid value (x) fm
0 – 10 4 5 20
10 – 20 23 15 345
20 – 30 13 25 325
30 – 40 7 35 245
40 – 50 3 45 135
50 1070
Arithmetic mean = Σfx/fm
= 1070/ 50
Arithmetic mean = 21.4
Interpretation – It can be analysed from the above table that the average value
determined from the given data set with the help of statistical formula is 21.4. This value of
mean is falling in the class interval ranging from 20 – 30. The number of leisure centre staff (i.e.
frequency) requisite to the class interval ranging from 20 – 30 is 13. With the help of Arithmetic
mean method, it has been evaluated that among 50 number of leisure centre staff, only 21.4 or 21
staff members are getting the hourly earnings in between 20 – 30 range.
Calculation of Standard deviation
Hourly
earning
Number of
leisure
centre staff
(f)
Mid
value
(x)
fm X- average (X-
average^2) (X- average)^2*f
0 – 10 4 5 20 -16.4 268.96 1075.84
10 – 20 23 15 345 -6.4 40.96 942.08
11

20 – 30 13 25 325 3.6 12.96 168.48
30 – 40 7 35 245 13.6 184.96 1294.72
40 – 50 3 45 135 23.6 556.96 1670.88
50 1070 5152
Standard deviation = √( X- x̄)^2*f /n
= √(5152 / 50)
Standard deviation = 10.13
Interpretation – The value of standard deviation determined is 10.13 which indicates that
the earnings of leisure centre staff is very low deviated in relation with the average value
determined. Furthermore, it can be said that the value of 10.13 is not much dispersed from the
average value determined of the total number of leisure centre staff and their hourly earnings.
B) Earnings comparison in between two regions.
Particular Manchester London
Median 14 14.13
Interquartile 7.5 9
mean 16.5 21.4
Standard deviation 7 10.13
Interpretation: From the above table it can be interpreted that the average earning of
London is much higher as compared to the earnings of Manchester Leisure centre staff i.e. the
mean value of London Leisure centre staff is 21.4 and of Manchester Staff is 16.5. Furthermore,
the dispersion level or variation among the income level is more in case of London than
Manchester (Lindström, Madsen and Nielsen, 2015). It can be said that standard deviation of
Manchester i.e. 7 is much better in respect of London which is 10.13. Fluctuating trend has been
observed among the earning levels of London Leisure centre staff whereas Manchester staff is
getting equal pay.
12

TASK 3
Section A
Particulars Figures
X 200
Mean 202
STDEV 2.4
Z score
-
0.83333333
33
Probability 20.00%
Interpretation – From the above table it can interpreted that there is a probability of 20%
that the firm is filling in more olive oil than the capacity of the bottle. The actual capacity of the
bottle is 200 ml whereas the mean content of the firm calculated is 202 ml with the standard
deviation of 2.4 ml. It can be concluded that the firm has made breach of the EU regulations by
filling in more olive oil in the bottle as per the prescribed limit of the bottle. It is required on the
part of the firm to make compliance of prescribed standards while filling in the olive oil in the
packaging bottle, thus non compliance has been done by the firm resulting in breaching of the
EU regulations.
Section B
Particulars Amount ( in £ )
Demand for year 450000
Cost of delivery 20
Value 9000000
Ordering cost per order 2
Total ordering cost 900000
Inventory holding cost 112500
Economic order quantity 2683.28
13

Interpretation – As per the calculation done in above table it can be said that the supplier
should make order of 2683.28 units for making the order more economical. It will be beneficial
on the part of the supplier to place order of 2683.28 units with the storage cost of £0.5 and cost
price of £2.
TASK 4
4.1
1. Bar chart
Green street
Number of bedrooms Green street
1 8
2 28
3 37
4 17
5 10
14
1
2
3
4
5
0 5 10 15 20 25 30 35 40
Green street
Number of bedrooms

Church lane
Number of bedrooms Church lane
1 6
2 18
3 24
4 9
5 3
Eton avenue
Number of bedrooms Eton avenue
1 4
2 20
3 32
4 12
5 12
15
1
2
3
4
5
0 5 10 15 20 25 30
Church lane
Number of bedrooms

2. Pie chart
Green street
Number of bedrooms Green street
1 8
2 28
3 37
4 17
5 10
16
1
2
3
4
5
0 5 10 15 20 25 30 35
Eton avenue
Number of bedrooms

8
28
37
17
10
1
2
3
4
5
Church lane
Number of bedrooms Church lane
1 6
2 18
3 24
4 9
5 3
17

6
18
24
9
3
1
2
3
4
5
Eton avenue
Number of bedrooms Eton avenue
1 4
2 20
3 32
4 12
5 12
18

4
20
32
12
12
1
2
3
4
5
19

4.2 Relationship between the number of bedrooms and the house price of bedrooms in all of the
three streets.
A. Relationship between 2 Number of bedrooms and house price in different streets.
1. Relationship between Price of 2 bedroom in the Green street and Church Lane
Number of
bedrooms Green street Church lane
2 600000 700000
Percentage change 16.67%
20
1.5 2 2.5 3 3.5 4
540000
560000
580000
600000
620000
640000
660000
680000
700000
720000
Green street
Church lane

2. Relationship between Price of 2 bedroom in the Church Lane and Eton Avenue
Number of
bedrooms Church lane Eton avenue
2 700000 750000
Percentage change 7.14%
21
1.5 2 2.5 3 3.5 4
670000
680000
690000
700000
710000
720000
730000
740000
750000
760000
Church lane
Eton avenue

3. Relationship between Price of 2 bedroom in the Green street and Eton Avenue
Number of
bedrooms Green street Eton avenue
2 600000 750000
Percentage change 25.00%
22

Interpretation -In case of Green street and Eton avenue, the percentage change is very
high which depicts that the relationship in between both streets varies a lot. The prices is very
high and use to vary as per the street area and number of bedroom as well.
B. Relationship between 3 Number of bedrooms and house price in different streets.
1. Relationship between Price of 3 bedroom in the Green street and Church Lane
Number of
bedrooms Green street Church lane
3 700000 850000
Percentage change 21.43%
23
1.5 2 2.5 3 3.5 4
0
100000
200000
300000
400000
500000
600000
700000
800000
Green street
Eton avenue

2. Relationship between Price of 3 bedroom in the Church Lane and Eton Avenue
Number of
bedrooms Church lane Eton avenue
3 850000 1000000
Percentage change 17.65%
24
2.5 3 3.5 4 4.5 5 5.5 6
0
100000
200000
300000
400000
500000
600000
700000
800000
900000
Green street
Church lane

3. Relationship between Price of 3 bedroom in the Green street and Eton Avenue
Number of
bedrooms Green street Eton avenue
3 700000 1000000
Percentage change 42.86%
25
2.5 3 3.5 4 4.5 5 5.5 6
750000
800000
850000
900000
950000
1000000
1050000
Church lane
Eton avenue

Interpretation – It can be said that in case of 3 number of bedroom, the percentage
change is high in the streets of Green street and Eton Avenue as compared to other street lane.
26
2.5 3 3.5 4 4.5 5 5.5 6
0
200000
400000
600000
800000
1000000
1200000
Green street
Eton avenue