Statistics for Management Assignment (Doc)
Added on 2020-10-05
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Data Science and Big Data
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STATISTICS FORMANAGEMENT
Table of ContentsINTRODUCTION...........................................................................................................................1TASK 1............................................................................................................................................1(a) Investigating Hypothesis under Public Sector.......................................................................1(b) Investigating Hypothesis under Private Sector......................................................................3(c) Using excel to generate Earnings-Time Chart for each group..............................................4(d) Calculation of Annual Growth Rate......................................................................................6.........................................................................................................................................................7TASK 2............................................................................................................................................9(i) Employing Cumulative Histogram in estimation of Median and Quartiles for LeisureCentre..........................................................................................................................................9Computation of Additive Frequency...........................................................................................9Ogive.........................................................................................................................................10(ii) Computation of Central Tendency and Dispersion:............................................................13(a) Comparison between the statistical measurements of two leisure centre............................14TASK 3..........................................................................................................................................15(a) Computing optimal level of stock .......................................................................................15(b) Number of Orders to be placed for tee-shirts......................................................................16(c) Computing Inventory Policy Cost.......................................................................................16(d) Current Service Level to Customers....................................................................................17(e) Ascertaining re-ordering levels to fulfil desired service levels...........................................17TASK 4..........................................................................................................................................17CONCLUSION..............................................................................................................................20REFERENCES..............................................................................................................................21
INTRODUCTIONStatistics relates to the tools and techniques used in the process of decision-making in anorganisation. It takes into account important information derived in the form of qualitative andquantitative data to draw conclusions and take strategic actions by the business. Utilization ofstatistics in a business scenario helps in increasing productivity, reducing costs and measuringuncertainty in a scientific manner (Baglin and Da Costa, 2012). This report aims at depicting detailed account in regards to the measures of centraltendency, dispersion and variability. Moreover, the report is divided into four tasks which relateto hypothesis testing, ogive, inventory management model and production of charts through datacollected. TASK 1The term 'hypothesis' refers to a statement or explanation proposed in relation to thehappening or non-happening of a particular event. A hypothesis is usually formed on the basis ofpast experiences, observations and data collected to infer judgements regarding the givenstatement. In the context of Business Statistics, this methodology is adopted in order toexperiment with various assumptions and plans undertaken by the organisation to ascertain howsuccessful they would be in implementation of such scenarios in the real world (Borio, 2013).When forming a hypothesis, a researcher usually takes two scenarios for the proposedexplanation. One that is true (H0) and one that is not (H1). Hereafter, the researcher employsappropriate statistical techniques in order to spot patterns and connect information to ascertainwhether the formed hypothesis is true or not. In case, the hypothesis proves to be true, it is saidthat H0 is accepted and H1 is rejected. This process of experimentation is known as 'Investigationof Hypothesis' (BOUKACEM‐ZEGHMOURI and Schöpfel, 2012). For the given case scenario, the data has been extracted for public as well as privatesector and has been construed on the basis of sex. The following hypothesis have beenformulated in each scenario to ascertain the truth in such assertions:(a) Investigating Hypothesis under Public SectorUnder this scenario, the following hypothesis has been formulated:H0: Earnings of men is not substantially higher to that of women in Public Sector.H1: Earnings of men is substantially higher to that of women in Public Sector.1
The above calculations indicate that there has been a difference in pay for men and womenconstantly for the time-period of 2009 to 2016. The fourth column of the table depicts thedifference between the mean annual gross earnings. The fifth or last column shows thepercentage in gap on a yearly basis. In all the years taken into account, the minimum pay forMen have been £30,638 in 2009 and for women it has been £25,224 in 2009. This gives a pay-gap of £5,414 between the two genders. However, this gap has reduced over the years to as lowas £5,173. One can observe that the highest percentage change in the earnings is recorded in 2010where the difference reduced by 4.86% rendering a value of £5,151. Another subsequentdecrease in the gap lead to a further decrease resulting in the gap to be as low as £4,910. If the2009 to 2011 period is evaluated, there has been a total decrease in pay gap by 9.31%. However,these reductions were recovered with an increase in gap by 4.95% in 2012. After this point,almost similar difference has been maintained until 2014, which again reduced by 0.58% in2014. In 2015, the sector has experienced one of the biggest pay-gaps between men and womenmean annual gross earnings with an increment of 11.83%.If analysed closely, it is determined that while the earnings for men changed by 2.45%,the earnings for women in this industry rose by 0.70%. This inequivalent increase in the earningsresulted in broadening of the gap and hence the percentage. Furthermore, 2016 has been a year ofrecovery for the Public Sector as they were able to reduce the gap by 8.84% which is remarkable(Box and Woodall, 2012). Again, the contribution for this recovery goes to increase in incomefor men to £34,011 from £33,685 rendering a 0.97% whereas women's earnings from £27,900 to£28,053 attributing to 0.55% growth from previous year. Between 2009 and 2016, the totalincrease in Men's earnings is that of 11% whereas for Women it comes to 11.22%.2
One the basis of these findings, it can be concluded that the earnings of men are notsubstantially higher than that of women employed in the Public Sector. This means that H0 isaccepted and H1 is rejected.(b) Investigating Hypothesis under Private SectorUnder this scenario, the following hypothesis has been formulated:H0: Earnings of men is not substantially higher to that of women in Private Sector.H1: Earnings of men is substantially higher to that of women in Private Sector.The above figure, similar to the previous table, showcases the bifurcation of mean annualgross earnings in the Private Sector for males and females employed in the industry. Again, theabove table includes a column that depicts the difference of pay between the two genders alongwith a year-on-year percentage change in this difference regarding the same. For 2009 to 2016,the total increment in the earnings of Men has been by £2,047 and that of women has beenobserved by £2,700. Hence, the growth in pay to both the sex has been by 7.41% and 13.81%respectively. This indicates that the income earned by women is growing rapidly in comparisonto men in the given time-period.Unlike the Public Sector, this sector has experienced lesser frequency of change in gapsfor the period of 2009 to 2016. Again, the highest change in gap was felt in 2010 where the gapreduced by 7.59%. The main cause for this can be attributed to the decrease in income earned bymen and women which went from £27,632 in 2009 to £27,000 in 2010 accounting for a 2.29%decline in pay for this demographic. For women the pay declined from £19,551 in 2009 to£19,532 in 2010. This reported a total decline of 0.10% for the concerned segment. Hereafter,there has been an increase for both Men and Women till 2016. Both segments have been able tominimize the pay-gap by £7,425 in 2014 and then to £7,428 in 2016 indicating that proper3
measures have been taken by industry players to control the gap and encourage recognition aswell as equality in the work environment for both genders (George, Haas and Pentland, 2014). On the basis of such observations, the hypothesis holds true for the data extractedresulting in acceptance of H0 while H1 is rejected.(c) Using excel to generate Earnings-Time Chart for each groupEarnings in Public Sector for Men:Earnings in Public Sector for Women:4
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