Statistical Analysis of Earnings: Public, Private Sectors and Regions

This report presents a statistical analysis of earnings across various sectors and regions. It begins with an introduction to statistical concepts and then delves into a comparison of male and female earnings in both public and private sectors using hypothesis testing. The report includes time charts illustrating gross annual earnings for both genders in each sector, from 2010 to 2016, and discusses annual growth rates. Furthermore, it analyzes leisure staff earnings in the London area, utilizing ogive charts and descriptive statistics like quartiles, mean, and standard deviation. A comparative analysis of earnings between London and Manchester is also provided. The report concludes with the calculation of the Economic Order Quantity (EOQ) for a given scenario. The analysis provides valuable insights into earning trends, sectorial differences, and regional variations, using statistical tools to derive meaningful conclusions.

STATISTICS FOR
MANAGEMENT

INTRODUCTION
Statistics is replicated as branch of mathematics which directly deals with organising,
interpretation, collection, presentation and analysis. This term is used for summarising process
which one could use for developing interpretations related to population primarily on basis of
statistical outcome via sample (Bzdok, Altman and Krzywinski, 2018). This analysis involves
process of collecting and evaluating data and then data is summarised in mathematical form. It is
science for appropriate decision making with context to uncertainty and implied is many
disciplines like financial analysis, auditing, operations and production which considers
improvement in services along with marketing research. It allows undertaking smarter decision
and this helps for offering organization with appropriate information that one could rely for
reference. The present report will discuss about earnings of men and women employed in public
and private sector. In the same series, it will articulate about earnings of leisure staff with Ogive
and other descriptive statistics in London area. Furthermore, it will articulate comparison in
earnings of London and Manchester region.
ACTIVITY 1
1.a Determining earnings of male and female are different in public sector with reference to
hypothesis testing
H0 Null hypothesis There is no significant difference in male and female earnings
who are working in public sector.
H1 Alternative hypothesis There is significant difference in male and female earnings who
are working in public sector.
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Interpretation: TTabular presentation shows t test for extracting that male and female
earnings are different in public sector. In this scenario, p>0.05 which in turn indicates that null
hypothesis is appropriate. Hence, it can be mentioned that statistically no significant difference
take place in the earnings public sector workers including both male and female (Chevalier and
Kashyap, 2019). The average earnings of male and female in public sector accounts for £32276
and £26929 respectively.
1.b Determining earnings of male and female are different in private sector with reference to
hypothesis testing
H0 Null hypothesis There is no significant difference in male and female earnings
who are working in private sector.
H1 Alternative hypothesis There is significant difference in male and female earnings who
are working in private sector.
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Interpretation: in the above scenario, there is articulation of average income in private
sector of male and female as 28062 and 20541 respectively. On basis of statistical significance of
p value which is higher than 0.05 so in this context, alternative hypothesis is not accepted. In
simple terms, it could be justified that there is absence of significant difference in earnings of
male and female who are employed in private sector.
1.c. With application of excel spreadsheet, framing earning time chart of each group over year
2009 to 2016.
Gross annual earnings of male of public and private sector
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Interpretation: The above table and graph is articulating about time chart for earnings of
male category who are working in public and private sector as well over year 2010 to 2016. it
could be clearly observed about significant growth but will less proportion. On basis of private
sector as in every year it raised but in 2016, it had major change of 2.76%. In the similar aspect,
its lowest change was in year 2014 as 0.85%. While extracting change, it has been evaluated that
earnings of private sector is raising at rapid pace comparatively to public sector. Numerically, it
could be elaborated as public sector from 2007 to 2017 was 8.78% as smaller than private sector
of same duration by 9.92% (Lachowska and Myck, 2018). Thus, it shows presence of high
potential in private sector along with variation in earnings of male in public and private sector as
well.
Gross annual earnings of female of public and private sector
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Interpretation: The above table and graph is reflecting gross annual earnings of female
over year 2010 to 2016 of both public and private sector. It has been viewed that, it is increasing
on significant aspect as depicted graph had entailed about earnings of female in year 2010 as
26113 and in year 2016 it reached on 28053 respectively. On the contrary, by considering private
sector earnings of female had inclined as 19532 to 22251 on respective basis. As this graph is
clearly showing variation which undertakes in female earnings with context to private and public
sector (Puri and Sengupta, 2018). Furthermore, this time graph provides clear exhibit about
females employed in public sector are higher than compared to private sector.
1.d Identifying annual growth rate of earnings of each group
Female Male
Year Private Rate of Public Rate of Private Rate of Public Rate of
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sector
(Women)
growth
(in
percentag
e)
sector
(Women)
growth
(in
percentag
e)
sector
(Men)
growth
(in
percentag
e)
sector
(Men)
growth
(in
percentag
e)
2009 19551 25224 NA 27362 NA 30638 NA
2010 19532 -0.1 26113 3.5 27000 -1.3 31264 2
2011 19565 0.2 26470 1.4 27233 0.9 31380 0.4
2012 20313 3.8 26636 0.6 27705 1.7 31816 1.4
2013 20698 1.9 27338 2.6 28201 1.8 32541 2.3
2014 21017 1.5 27705 1.3 28442 0.9 32878 1
2015 21403 1.8 27900 0.7 28881 1.5 33685 2.5
2016 22251 4 28053 0.5 29679 2.8 34011 1
Growth rate of males and female in the context of both private & public sector is
enumerated below:
Females (Private sector): There is articulation of gross annual earnings which is raising
on annual aspect with reference to fluctuation outcome. On basis of this table, in 2016 it inclines
with high variation as it was about 4%. In simple words, it could be elaborated that women are
giving priority to private sector comparatively to public because of raise in involvements and
earnings as well.
Females (in public sector): With reference to gross annual earnings of women, there is
clear articulation about drastic impact in each year (Walker, Michailov and Trukhanov, 2019).
However, in year 2013, it faced raise with high proportion and this was leading change over
2010 to 2016. On the similar note, in year 2016 it has presence of little change of approx 0.53%.
Male (private sector): The above table is reflecting gross annual earnings of male with
context to private sector. It has been clearly viewed that, it raised in every year but in year 2016
it had alteration of huge proportion of 2.76%. Simultaneously, there was the least increase in
year 2014 was about 0.85%.
Male (public sector): The above scenario is depicting gross annual earnings of public
sector of male category over year 2010 to 2016. It is clearly viewed that in 2015 there was
alteration with high proportion as it was about 2.45% with this specified duration. In this aspect,
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it was followed by year 2013 as on the contrary, there was presence of increment but with small
proportion as of 0.37%. Furthermore, this tabular format is reflecting fluctuating trend in
earnings of males with duration of 7 years as in 2012 and 2013 there was high percentage change
in earnings was greater over past year. Conversely, in year 2013, its percentage change related to
earnings of male in public sector falls by 2.28% to 1.04% which is not replicated as good signal.
ACTIVITY 2- CLIENT B
2.A
2.A.a Using ogive for estimating median hourly earnings along with quartile
Ogive may be served as a statistical tool which is used to exhibit curve pertaining to
cumulative distribution function. In other words, ogive chart provides high level of assistance in
exhibiting CF distribution function of grouped data set. It is the most effectual way which helps
in understanding data set and deriving appropriate results from the same. By using such
statistical tool concerned authority can assess the extent to which many figures vary from
particular value in data set. In Ogive graph, cumulative percentage figures are presented from left
to right. In this aspect, mean, standard deviation and median are referred as basic tool which are
applicable for plotting outcome which appeared on direct basis. In the similar aspects, CF is
plotted on graph on y axis as every class boundary is on x axis. Usually, it is used for
determining number of data points which is equalised to specific value in specific data set.
Thus, it is unique by frequency polygon because of plotting of cumulative values rather
than plot of valuing themselves. There is presence of analysis of variation in hourly earnings of
London area with application of multiple statistical tools. With this consideration, there is
reflection of descriptive analysis of specific data base which consist of analysis of quartile,
standard deviation along with mean and median.
Discussion on Median:
This is replicated as value which categorise higher half with lower half of sample data as
value which is likely to fall above or below it. In simple terms, median is referred as middle
value in the list of numericals where it is replicated as simple measure of central tendency as for
extracting this, observations are arranged in increasing order and then formula is implicated. This
is not influenced through outliers at extreme of data set (Nisar, Prabhakar and Strakova, 2019).
Due to this reason, it is used with presence of extreme values which could greatly influence
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distort and mean which is typically considered. In the same series, it is replicated as primary
method to extract statistical data. With context to above statement, median could be calculated in
the easiest way comparatively to other descriptive statistics. Simultaneously, this could be
reflected as method for determining average of grouped number which is common mean as
middle value in specified number list is known as median.
Hourly
Earnings CI
Number of
Leisure
Employees 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%
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Interpretation: the above graph is showing ogive chart related to leisure employee's
hourly earnings of specific London region. In this aspect, it is clearly observed that there is
increment till 10 to 20 hours but after that till 40 to 50 is decreasing. On the contrary, cumulative
is raising from left to right as observation of trend has been viewed that hours are increasing
whereas frequency is falling. Thus, most important aspect is all about last plot of cumulative
frequency is at 50 which shows about appropriateness.
Discussion on quartile:
Quartile is replicated as statistical term which provides description of division of
observations into four categorised intervals on basis of data value which provides differences in
whole observations. Such tool helps in analysing and evaluating performance over the quarters.
Through this, business owner can assess trend and thereby develops strategic framework for the
upcoming time period. It must be noted that this is not limited to discrete variables but applies
on equal basis with context to continuous variables (Quartile, 2019). As this is measure of
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central tendency of data but does not reflect that how distributed data in two arms on either side
of median with context to quartile.
Quartile Outcome
Quartile 1 Value of 50 / 4 th item
Value of 12.5 th item
10 + (20 – 10) / 23 * (12.5 – 4)
= 13.69
Quartile 3 Value of (3 * 50) / 4 th item
Value of 37.5 th item
20 + (30 – 20) / 13 * (37.5 – 23)
= 31.15
Inter-quartile 31.5 – 13.69
= 18.46
Interpretation: The above outcome of quartile of leisure employees has been clearly
viewed first quartile is 13.69 which is far away from median whereas 3 quartile is 31.15 which is
closer to it. In simple words, 25th percentile of data is smaller than first quartile by 25% and 75%
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of data is higher than this. Simultaneously, with context to third quartile, 25% of data is greater
and 75% is smaller. On basis of second quartile, it is all about median as 50% or half of data is
smaller and half data is larger comparatively to value.
2.A.b Finding standard deviation and mean with context to hourly earnings
Discussion on mean:
The statistical mean is referred as mean or average which is used for purpose of deriving
data's central tendency. It is identified that by considering aggregate of data points in population
and then divided through sum of number of points. As, the outcome is considered as mean or
average. The mean might be not replicated as fair representation as it is directly influenced
through outliers as it is common measure of centre but prone through distortion through presence
of extreme values might be need of this specific distortion (Venkatesan, 2019). Furthermore,
mean is useful when data is skewed on worsen aspect but mean because of skewness. However,
sample mean has presence of less variable comparatively to median as huge amount of data is
summarized into single value and reflects variability around individual value by considering
original data.
Mean: FX/ F
= 1070/ 50
= 21.4
The above table is articulating mean step wise as on initial basis, leisure staff employees
are denotes as F i.e. frequency and mid value of each interval as X. X is calculated by dividing
sum of both interval by 2 and then FX is multiplication of F and X. In the continuation of this
series, total of FX is divided by total of F which helps in deriving final outcome as mean.
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Numerically, it is replicated as 1070 is divided by 50 whose mean is 21.4. Logically, it could be
elaborated that measure of mean distance in entire data set with context of mean.
Discussion on standard deviation
Standard deviation is replicated as dispersion measure where dataset is relative to mean
and articulated as square root of variance. There is determination of variance;'s square root and
each data point is directly associated to mean. This is very commonly used statistics but does not
attain high attention as it deserves. As median and mean are in common sight as it has rarely
been observed accompanied through measure about diverse data set. With absence of this
measure, one cannot handle that whether data are close to average or spread out with broad
range.
Standard deviation √Ƹf(X – A)^2 / N
√5152 / 50
= √103.04
= 10.15
Interpretation: In the above data, there is clear observation of standard deviation of
leisure staff as 10.15 as it is affected through outliers. This standard deviation is measuring about
concentrated earnings of leisure staff employees which is high as its outcome is farther away
from mean on average. In simple words, it could be elaborated that its particular data points are
spread with large range of specified values.
2.B Stating comparison on earnings of London and Manchester region
Interpretation: In the above scenario, earnings of London and Manchester are compared
with reference to vital elements of descriptive statistics. With reference to descriptive statistics,
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there is extraction of median of both whereas it has been articulated that Manchester's middle
value is higher comparatively to London. On basis of this, Manchester has higher earnings of its
leisure staff employees but there is difference of 1 basis point which is very minor for reaching
to final comparison. On basis of average of both data set Manchester's average earning is 16.5
and London has 10 as it is also measure of central tendency. It could be clearly viewed that,
Manchester's earning is higher on basis of average as well (Venkatesan, 2019). Furthermore,
there is articulation of Interquartile range as it is observed as better measure of spread as range is
not impacted through outliers. It is replicated as difference among upper and lower quartile and
provides description about middle 50% of values when ordered through lowest to highest. As
Manchester's IQ range is also higher 7.5 and London as 9 which shows positive aspect for
Manchester. In the same series, there is comparison on basis of standard deviation of earnings of
both region where earnings of London has high risk comparatively to Manchester. Henceforth, it
could be articulated that leisure staff employees has better earnings and low risk comparatively
to London.
ACTIVITY 3
a. Calculating Economic order quantity
Particulars Amount
Price (per unit) £20
Demand (weekly) 30
Holding cost
20 * £10
= £2
Fixed cost associated with each order £10
Economic order quantity
√2 * 30 * 10 / 2
= √300
= 17
b. How often order and cost
On the basis of cited case situation 117 t-shirts can be used till 2.3 weeks
Moreover = 117 / 55
= 2.3 weeks
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Annual demand for t-shirts = 50 * 55
= 2750
According time period for ordering t-shirts are: 2750 / 17
= 24 times
c. Calculating Inventory policy cost
d. Identifying Current service level
Current service level of customers = 150
Z (37.05 – 30) / 15
= 0.5
0.5 or 50% = 0.195 or 19.15%
50% + 19.15%
= 69.15%
The above depicted assessment shows that approximately 69.15% t-shirt should be in
stock. On the basis of this, it can be said that maintenance of t-shirt’s stock can be avoided by
business unit on an average 30.85% time.
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e. Finding re-order level
ACTIVITY 4
4.A Drafting chart for RPI, CPI and CPIH over year 2007 to 2017
Retail Price Index: On basis of this index there is track of changes in cost of fixed basket
of goods which is implied for indices of various prices with consideration of income like index
linked gilts, state benefits, pensions and tax allowance. This is replicated as official measure of
inflation at general level as shown in retail price of basket goods along with services like energy,
housing, household goods, food gasoline (petrol), travelling fare, food etc. usually, it is
computed on monthly aspect but its annual rate is directly published as they directly serves
yardstick for purpose of adjusting salaries which are inflation indexed, wages, pensions and tax
allowances. There is observance of price of item where one directly spends along with
consideration of housing cost such as council tax and mortgage interest payments as well.
In simplest form, this is considered as particular measure of inflation published through
Office of national statistics and reflects alteration in cost of representative sample on basis of
services and goods.
Consumer Price Index: this is replicated as measure of alterations in currency of
purchasing power along with inflation rate. Usually, this price index reflects recent prices of
basket of services and goods with context of prices of similar duration in past year. It reflects
inflation impact on purchasing power as it is referred as one of the best known lagging indicator
(Rachel Lacey, 2019). This is known as comprehensive measure with context of estimating
changes in price with basket of goods and services representation of consumption of expenditure
in the economy. Mostly inflation is measured by CPI and changes in indices with specified
duration as it reflects raise in price of consumed basket of goods.
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Simultaneously, this is replicated as measure of mean alteration over time through urban
consumers on basis of market which tracks decrease and increase in price. Majorly, it is used as
inflation measure with high effectiveness of numerous economic policies on basis of
government. In the same series, it offers businesses, government and citizens as idea with
context to price alteration in economy as guide to undertake informed decisions.
Consumer price inflation with occupier's housing cost [CPIH]: This is replicated as
measure which considers inclusions of housing cost of owner occupiers. Apart from this it is
referred as measure which considers alterations in house prices. Usually, this is conventional
along with familiar measure of CPI of UK generated each month through Office of national
statistics but there is presence of adjustments as reflects alterations in high residential rents. In
the same series, housing make significant contribution of monthly cost of people but CPI
measure of inflation is not accounted. It has been designed to help for fulfilling gap and reporting
inflation with high accuracy (CPIH Inflation, 2018). The headline inflation rate reflects that how
price of service and goods households directly spends money on increment and decrement on
monthly basis. This is referred as very important indicator to reflect that how economy of UK is
performing along with measure used through government and business for undertaking decisions
about things such as tax allowances, wages, state benefits, pensions, bills and other payments as
well.
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4.B Drafting Ogive chart of cumulative % of leisure staff employees vs earning on hourly
perspective
Interpretation: There is representation of Ogive chart which reflects about cumulative %
of staff vs hourly earning along with identification of variation in ogive as particular plot value
of the cumulative. In the same series, frequency polygon is considered as plot with specific value
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whereas its data value is above or below particular point which represents middle or quarter data
base.
CONCLUSION
From the above report it had been concluded that statistics are very important for purpose
of decision making in business along with measuring various parameters. It has shown
significant difference in earnings of men and women in both public and private sector as there is
reflection of growth rate which is higher in private sector especially, with context to male
category. This report has shown statistical significance about absence of earning are different of
male and female in both sector. Moreover, it has shown detailed information related to
descriptive statistics on basis of London and Manchester's earning. While evaluating comparison,
it has articulated that Manchester area has higher earnings comparatively to London in context of
each measure such as standard deviation, mean, inter quartile range and median as well. It has
shown about economic order quantity and shown trend over 2007 to 2017 of CPI, RPI and CPIH.
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REFERENCES
Books and Journals
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