Statistics Solution Assignment

STATISTICS

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
a) Determining difference in earnings of men and women in public sector using hypothesis
tests .............................................................................................................................................1
b) Determining difference in earnings of men and women in private sector using hypothesis
tests..............................................................................................................................................2
c) Earning time charts for each group..........................................................................................3
d) Determining annual growth rate in earnings using chart.........................................................4
TASK 2............................................................................................................................................5
a) Evaluation and analysis of Hourly pay rates ..........................................................................5
b) Comparing earnings among two regions.................................................................................7
TASK 3............................................................................................................................................7
Section A .....................................................................................................................................7
Section B .....................................................................................................................................8
TASK 4............................................................................................................................................8
4.1 Representing data using charts and tables.............................................................................8
4.2 Evaluation of average prices in 2 and 3 bedrooms over three streets..................................13
CONCLUSION..............................................................................................................................17
REFERENCES..............................................................................................................................18

INTRODUCTION
Statistics is concerned with collecting, organizing, analysis, display presentation and
interpretation of data. Statistical analysis refers to data analysis that in business intelligence is
used for analysing and collecting data samples from which samples can be derived (Searle and
Khuri, 2017). Report will cover the analysis for evaluating data from different sources, and for
analysing the quantitative raw business data using statistical methods. The explanations would be
given using appropriate tables, charts and variable findings for better understandings.
TASK 1
a) Determining difference in earnings of men and women in public sector using hypothesis tests
Null Hypothesis : There is no significant difference between men and women income in public
sector.
Alternate Hypothesis : There is significant difference between men and women income in
public 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
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
1

2.1447866879
Interpretation
From the two tail test value of probability is more than 0.05 i.e. 1.35 which shows there is
no significant difference theretofore the null hypothesis is accepted.
b) Determining difference in earnings of men and women in private sector using hypothesis tests.
Null Hypothesis: There is no significant difference between men and women income in private
sector.
Alternate Hypothesis:There is significant difference between men and women income 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
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
2

Interpretation
Applying the two tail tests of probability over the private data it is identified that probability is
more than 0.05 i.e. 2.16 theretofore there is no significant difference between income of men and
women and null hypothesis is accepted.
c) Earning time charts for 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
2016 34011 28053
3
1 2 3 4 5 6 7 8
0
5000
10000
15000
20000
25000
30000
35000
40000
Year
Men public sector
Women public sector

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
d) Determining annual growth rate in earnings using chart.
PUBLIC SECTOR
ANNUAL GROWTH RATE
Year Men public
sector
YOY Growth
rate
Women public
sector
YOY Growth
rate
2009 30638 25224
2010 31264 2% 26113 4%
4
1 2 3 4 5 6 7 8
0
5000
10000
15000
20000
25000
30000
35000
Year
Men private sector
Women private sector

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 growth rate of men has shown a declining trend from year 2009 and to
2011, and after it is decreasing and increasing alternatively every year. Where the growth rate of
women has declined from 4% in 2011 to 1% which revived to 3% in year 2013 which again
remained constant at 1% for three years. The data signifies that growth rate of women in public
sector are not showing positive returns.
PRIVATE SECTOR
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 is seen that annual growth rate of men was negative in year 2010
which increased to 1% in year 2011 and remained constant at 2% till 2013. Growth showed an
upward trend after decline to 1% in year 2014. Growth rate of women was null till year 2011 but
increased to 4% in year 2012. Growth rate remained constant at 2% for three years and increased
to 4% in 2016. This shows that in private sector income growth rate are showing positive returns.
5

TASK 2
a) Evaluation and analysis of Hourly pay rates
i) Estimating median hourly earnings and quartiles
Median : Median refers to value in such manner that number equally likely falls below or above
it (Median. 2019).
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
1. Dividing the last CF by 2= N/2
2. Applying the formula = L/2 + H/F[N/2 – C]
QUARTILE
Quartile : These are values which are used for dividing the list of numbers in quarters. This is
done by putting number list in order and then dividing list into equal parts.
Calculation of quartile:
1 Quartile 4
3 Quartile 13
Interquartile 9
6

0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
0
0.2
0.4
0.6
0.8
1
1.2
ogive chart
ii) Calculating arithmetic mean and standard deviations for hourly earnings
Mean: Arithmetic mean refers to average in a clear context and sum of all numbers dividing
them with number counts in collection (Johnson and Bhattacharyya, 2019).
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
= Ƹfx / fm
=1070/50 = 21.4
Interpretation
Arithmetic mean is 21.4 that is falling between the class interval of 20-30 and among
7

leisure centre staff of 50 hourly earnings are get by only 21.4 members.
Standard Deviation: Standard deviation refers to measurement of variation and dispersion in
value set.
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
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
Standard deviation is 10.13 that shows it is not much deviated. The 10.13 is not very
much dispersed from average mean determined of complete leisure staff.
b) Comparing earnings among 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 analysis it could be interpreted that from Manchester earnings of London
are higher which is 14.13. Variation of income level is seen much higher in London as compared
8

with Manchester. Also the s.d. of London is more in London as compared to Manchester (Lee,
2019). Fluctuating trend is seen in staff of London where staff of Manchester is getting equal
pay.
TASK 3
Section A
Particulars Figures
X 200
Mean 202
STDEV 2.4
Z score
-
0.83333333
33
Probability 20.00%
Interpretation
It is seen that probability of filling the bottles more than it capacity is 20% where the
actual capacity of bottle is 200ml. Conclusions can be made that filling the bottles of olive oil
more than its capacity is breach of EU regulations (Standard Deviation. 2019).
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
Interpretation
It is calculated that economic order quantity is 2683.28 units which is most beneficial
level. It will be beneficial if it places order of 2683.28 with carrying cost of 0.5 and cost price of
2.
9

TASK 4
4.1 Representing data using charts and tables
1 .Bar Chart
Green street
Number of bedrooms Green street
1 8
2 28
3 37
4 17
5 10
Church lane
Number of bedrooms Church lane
1 6
2 18
3 24
4 9
10
1
2
3
4
5
0 5 10 15 20 25 30 35 40
Green street
Number of bedrooms

5 3
Eton avenue
Number of bedrooms Eton avenue
1 4
2 20
3 32
4 12
5 12
11
1
2
3
4
5
0 5 10 15 20 25 30
Number of bedrooms
Church lane

2. Pie Chart
Green street
Number of bedrooms Green street
1 8
2 28
3 37
4 17
5 10
12
1
2
3
4
5
0 5 10 15 20 25 30 35
Eton avenue
Number of bedrooms

Church lane
Number of bedrooms Church lane
1 6
2 18
3 24
4 9
5 3
13
1
2
3
4
5

Eton avenue
Number of bedrooms Eton avenue
1 4
2 20
3 32
4 12
5 12
14
1
2
3
4
5
6

4.2 Evaluation of average prices in 2 and 3 bedrooms over three streets
A ) Relationship between 2 number bedroom & house prices of different street
1.Green street
Number of
bedrooms Green street Church lane
2 600000 700000
Percentage change 16.67%
15
1
2
3
4
5

2.Church lane
Number of
bedrooms Church lane Eton avenue
2 700000 750000
Percentage change 7.14%
16
1.5 2 2.5 3 3.5 4
540000
560000
580000
600000
620000
640000
660000
680000
700000
720000
Green street
Church lane
1.5 2 2.5 3 3.5 4
670000
680000
690000
700000
710000
720000
730000
740000
750000
760000
Church lane
Eton avenue

3.Eton avenue
Number of
bedrooms Green street Eton avenue
2 600000 750000
Percentage change 25.00%
Interpretation
In Green and Eton streets percentage change is higher that shows the relation between the
two is varying. Price are high and varying as compared to other streets.
B) Relationship between 2 number bedroom & house prices of different street
1.Green street
Number of
bedrooms Green street Church lane
3 700000 850000
Percentage change 21.43%
17
1.5 2 2.5 3 3.5 4
0
100000
200000
300000
400000
500000
600000
700000
800000
Green street
Eton avenue

2.Church lane
Number of
bedrooms Church lane Eton avenue
3 850000 1000000
Percentage change 17.65%
18
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
2.5 3 3.5 4 4.5 5 5.5 6
750000
800000
850000
900000
950000
1000000
1050000
Church lane
Eton avenue

3.Eton avenue
Number of
bedrooms Green street Eton avenue
3 700000 1000000
Percentage change 42.86%
Interpretation
It is analysed from the above that percentage change in streets of Green and Eton is much
higher in comparison with other streets.
CONCLUSION
From the above studies it is concluded that statistics is an very important tool for the new
business environment. It enables the companies and analysts to figure out the trends using
different charts and tables. At the present time statistics is very useful for both companies and
individual for carrying out any research and coming at any decision.
19
2.5 3 3.5 4 4.5 5 5.5 6
0
200000
400000
600000
800000
1000000
1200000
Green street
Eton avenue