Analysis of Leisure Workers and Earnings Data

The provided assignment involves analyzing data on leisure workers and their earnings per hour in London and Manchester. The first part presents a chart comparing the number of leisure workers and hourly workings, while the second part discusses economic order quantity and reorder level for inventory management. Statistical measurement is used to analyze various business data and compare it with set standards, helping managers effectively evaluate performance and take decisions accordingly. Growth rates for both male and female workers are increasing in the private sector, and earnings in Manchester are higher than in London.

STATISTIC FOR
MANAGEMENT

Table of Contents
INTRODUCTION...................................................................................................1
LO 1..........................................................................................................................1
a) Determine if earning of men in public sector is different from women..................................1
b) Determine if earning of men in private sector is different from women.................................2
c) Earning time chart for each group for period 2009-2016........................................................3
d) Determine annual growth rate in earning of four groups........................................................6
LO 2..........................................................................................................................6
LO 3..........................................................................................................................6
LO 4..........................................................................................................................7
CONCLUSION........................................................................................................7
REFERENCES........................................................................................................8

INTRODUCTION
Statistic of management can also be termed as the business statistic. It refers to a process
of science that deals with scrutinising of various data so that it could be used by the managers in
the financial analysis of the overall business (Anderson and et.al., 2017). The study provides
information about the earnings of males and female employees in the private business sector
along with articulation of earnings of all the leisure employees through ogive charts and other
statistical methods. Further, the study also provides a brief comparison of the earnings of London
and of Manchester region.
LO 1
a) Determine if earning of men in public sector is different from women
Null hypothesis: H0 : There is no difference in income of men and women in public sector
Alternative hypothesis: H1 : There is difference in income of men and women in public sector.
Interpretation: From above table it can be analyzed that average income of men in public sector
is 32276 and women is 26929. Also, the variance is income of male is 1449962 and in women is
977868. Besides this, it can be stated that significant value is less than 0.05 which means there is
no relationship between income of men and women in public sector.
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b) Determine if earning of men in private sector is different from women
Null hypothesis: H0 : There is no difference in income of men and women in private sector.
Alternative hypothesis: H1 : There is difference in earnings in income of men and women in
private sector
Interpretation: From above table it can be analyzed that average income of men in public sector
is 28062 and women is 20541. Also, the variance is income of male is 840242 and in women is
988729. Besides this, it can be stated that significant value is less than 0.05 which means there is
no relationship between income of men and women in private sector.
c) Earning time chart for each group for period 2009-2016
Gross Annual earnings of men in Public and private sector
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Gross Annual earnings of women in Public and private sector
d) Determine annual growth rate in earning of four groups
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Interpretation:
Growth rate of women in private sector: It can be observed that growth rate was lowest in 2010
with decline of -0.1%. Then, it got increased constantly in every year. In 2016 there was high
increase with 4%.
Growth rate of women in public sector: From table it can be stated that in 2010 growth rate was
3.5% which was highest. But then it got decreased with proportion of 0.5 every year. So, in 2016
it was least with 0.5 %.
Growth rate of men in private sector: In private sector growth rate was constantly fluctuating. It
was negative in 2010 and then increased in every year. In year 2016 it was highest with 2.8%.
Growth rate of men in public sector: It can be analyzed that growth rate was 2% in 2010 and it
declined to a great extent in 2011. Then, there was improvement in 2012 to 1.4%. So, in each
alternative year growth rate increases and decreases.
LO 2
A) Estimation of median hourly earnings and quartiles
Median
For the purpose of estimating median hours, ogives can be used. These are the graphs that
can be used for the purpose of analysing the values that lies under or above a specific set of data
(Ogives, 2018). With the help of ogive, a company can help the managers in quickly estimating
and observing various data of the company and analyse its actual situation for taking their
decisions accordingly.
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With the help of ogive the median of leisure workers can be determined as under:
Per hour
working (CI)
Number of
Leisure
workers (R) frequency Cumulative frequency CRF
0 to 10 4 4% 4 4%
10 to 20 23 23% 27 27%
20 to 30 13 13% 40 40%
30 to 40 7 7% 47 47%
40 to 50 3 3% 50 50%
Per hour earnings
Number of Leisure workers
(F) Cumulative Frequency (Cf)
0 to 10 4 4
10 to 20 23 27
20 to 30 13 40
30 to 40 7 47
40 to 50 3 50
Median: L+ Cf-n/ f* I
Median: L+ Cf-n/ f* I
= 10+(20-10)/ 23 * (25 - 4)
= 10 + ((10*21)/23)
= 10 + (210/23)
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= 10+ 9.13
= 19.13
= 27
Interpretation
From the analysis of above calculations and the ogive chart, it can be interpret that till the
working of 10 to 20 hours, the leisure workers get increment. But they after it the increment
starts declining. Further, the cumulative of the data is rising. On the other hand, the frequency of
the same data is declining. Therefore, it can be evaluated that the frequency 50 would be most
appropriate for the leisure workers.
Quartile
Quartiles are the statistical concept that provides an appropriate division of all the
observed and collected data (Quartile, 2019). In this concept the data is categorised into 4 parts
on the basis of which the whole values are being observed and results are being determined.
Quartiles of the following data can be determined as under:
Range of per hour earnings (CI) Leisure workers (F)
0 to 10 4
10 to 20 23
20 to 30 13
30 to 40 7
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40 to 50 3
Quartile Results
1 (25%) 4
2 (50%) 7
3 (75%) 13
Q1= 10 + ((20-10)/23)*(12.5 – 4)
= 10 + (10/23) * 8.5
= 13.70
Q3= 20 + ((30-20)/23)*(37.5 – 27)
= 20 + (10/13) * 10.5
= 28.08
Inter quartile range= Q3 – Q1
= 28.08 – 13.7
= 14.38
Interpretation
From, the analysis of above quartile table and its results, it can be interpret that the first
quartile provides 4 which is not closer to the median. On the other hand, another quartile i.e. 3
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provides 13 which is near to the median. In this regard, it can be evaluated that the first quartile
is smaller than the values of data and the 3rd quartile is higher than the data. Further, it can also
be analyzed that a part of 2nd quartile is higher than the median and another part is lower than the
median.
Standard deviation and mean for hourly working
Standard deviation
It is a statistical method in which the dispersion of the data is being measured (Gupta and
Gupta, 2017). This method is used by the managers for the purpose of determining the variations
in the business.
Hourly Earnings CI
No. of
leisure
workers
1: (F)
Mid value
2: (X)
FX
3: (1*2)
DX= X-A
4
FDX
1*4
FDX^2
5^2
0 to 10 4 5 20 -20 -80 6400
10 to 20 23 15 345 -10 -230 52900
20 to 30 13 25 325 0 0 0
30 to 40 7 35 245 10 70 4900
40 to 50 3 45 135 20 60 3600
Total 50 125 1070 0 -180 32400
Standard deviation = √ƸFdx^2/N - (ƸFdx/ N)^2
Therefore,
Standard deviation = = √32400/ 50 -(-180/50)^2
= 12.96
= 25.45
=10.15
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Interpretation
From the above calculations it can be interpret that standard deviation of the leisure
workers is 10.15. Therefore, at this level the per hour earnings of the leisure workers would be
the highest at the range of 10 to 20.
Mean
In simple terms, the mean can be defined as the middle most value of the data (Geraci,
and et.al., 2018). As per the statistical method, the mean is calculated by averaging all the values
of data.
Per hour
Earnings
Leisure
workers (F)
Middle value
(X) FX FX – A (FX – A)^2
0 to 10 4 5 20 -16.4 268.96
10 to 20 23 15 345 -6.4 40.96
20 to 30 13 25 325 3.6 12.96
30 to 40 7 35 245 13.6 184.96
40 to 50 3 45 135 23.6 556.96
50 1070 1064.8
Mean: sum of FX/ sum of F
Therefore, mean = 1070/ 50
= 21.4
Interpretation
From the above calculations, it can be interpret that the mean of the above data is 21.4. In
this regard, the middle value of data of leisure worker will fall under the frequency of 20 to 30.
Comparison of earnings of London and of Manchester region
Basics Median
Interquartile
range (IQ) Mean
Standard
deviation
Manchester (£) 14 7.5 16.5 7
London (£) 13 3 13 12.5
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LO 3
a) Find economic order quantity ?
Particulars Amount
Demand per year 30*50
1500
Ordering cost of per order 5
Inventory holding cost 2
Economic order quantity √2 * 1500 * 5/ 2
7500
86.60
b) How often she needs to order tee- shirts?
Particulars Amount
Order tee shirts per year Annual demand / EOQ
Annual demand 1500
Economic order quantity 86.6
Order yearly basis 17.32
Ordering cost Number of orders per year * Cost per order
5 * 17.32
86.60
c) Calculate inventory policy cost?
Safety stock
Z score (95%) 1.65
Average weekly demand 30
Standard deviation 15
Safety stock Z* Standard deviation * Demand
742.5
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d) Current service level to customers?
The current service level of the customers is 95%.
and the Z has scored 1.65
e) determining re order level
Reorder level Minimum quantity + Safety stock
Minimum quantity 150
892.5
LO 4
RPI, CPI and CPIH for the year 2007 to 2017
Retail price index (RPI) : The retail price index is a method of statistic with the help of which
the inflation rate can be measured. The RPI is published by the office for National Statistics on
monthly basis.
Consumer price index (CPI): Consumer price index helps in determination of weighted
average value of the consumer's basket (Zhou and Dixon, 2018). This index is calculated by
taking into account change in price of various items like, foods, transportation, etc. and
averaging the changes.
Consumer price inflation with occupier's housing cost (CPIH): In this statistical measure, the
key element that is considered is housing cost. It is also a measure of determining the inflation
rate for the consumers.
Year
Retail price index
(RPI)
Consumer price index
(CPI)
Consumer price
inflation with
occupier's housing
cost (CPIH)
2007 4.3 2.3 2.4
2008 4 3.6 3.5
2009 -0.5 2.2 2
2010 4.6 3.3 2.5
2011 5.2 4.5 3.8
2012 3.2 2.8 2.6
2013 3 2.6 2.3
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2014 2.4 1.5 1.5
2015 1 0 0.4
2016 1.8 0.7 1
2017 3.6 2.7 2.6
Presenting orgive charts for leisure workers and their earnings per hour
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Interpretation
The present ogive chart is presenting the variations in the number of leisure workers and
hourly workings. In the above ogive chart, the frequency is taken as a specific data; on the other
hand, the value of the data is following above or below the frequency.
CONCLUSION
From the analysis of above assignments, it can be concluded that statistical measurement
is useful for the managers as to analyse various data of the business and compare it with the set
standards. It helps them in effectively evaluating the actual performance of the company and
taking decisions accordingly. Further, the study has also concluded that growth rate for both
male and female is increasing in the private sector. It has also concluded that as per the data of
earnings of London and Manchester, the earnings of Manchester is higher than the earnings of
London. At the end, the assignment has also provided information about the economic order
quantity and re order level of the inventory.
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