This report examines the role of statistics in management decision-making. It analyzes inflation trends using CPI, CPIH, and RPI, and explores inventory management techniques like EOQ and reorder level. The report provides practical examples and calculations to illustrate the concepts.
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Statistics for Management
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INTRODUCTION Statistics for management is used by managers in order to formulate strategic decisions that may help organisation to attain long term sustainability. It is very important for the mangers top make appropriate decision so that their company can achieve all its predetermined goals. It is essential for the businesses to formulate effective strategies so that all the problems that may occur in future can be dealt appropriately (Groumpos, 2015). Success of business entities depends upon the management of operations and other activities that are performed by its employees. Statistics for management help to identify market conditions so that improvements can be made in the products or services that are offered to the customers. It helps to forecast the material requirements that are needed for the production process. This report covers various topics like evaluation of business and its strategies, economic information and data, raw data of business by using different statistical methods, application of all those methods in planning etc. communication of the findings by using appropriate charts and tables have also been discussed under this report. Activity: 1 (a): Use of office national statistics CONSUMER PRICE INDEX (CPI)is a term which measures inflation of consumer prices which means calculation of change in price for consumer goods and services in market basket it is also calledHARMONISED INDEX OF CONSUMER PRICES(HICP). (I) CPIis a statistical form of measuring changes that are continuously going on in market in relation to market price of consumer goods by taking different samples of various products on periodically basis and this also shows share of a product in total consumer expenditure and also which products leads to highest inflation. Use of CPI is done to calculate real value of wages, salary, pension as there is inflation in goods and services then income needs to be changed accordingly by taking this index as a base for such changes (Asante and Armstrong, 2012). CPIHrefers to βconsumer Price Inflation including ownerβs occupiers' Housing Costβ. It is same as Consumer Price Inflation but this also includes changes in housing rent. It does not include changes in value of house property as by its name it seems to be. Ownership of home is
widespread which a large part of population still leaves in rental apartments and that cost on an average to them at 10% of their earnings which makes it necessary to include housing rent to calculate inflation rate which helps in calculation of real pay. (ii): RETAIL PRICE INDEX(RPI)measures change in cost of represented sample of consumer goods and services. It is first calculated in 1947 and in year 1975 highest annual inflation was recorded according to RPI as 26.9%. In 2009 it was first time when RPI was recorded as negative as in that year reduction in cost of goods and services. RPI already consider housing rent inflation which gives more correct information regarding inflation (Inflation and price indices,2018). b) Indices from 2007 to 2017 CPI YearJanFebMarAprilMayJunJuly 2007103.2103.7104.2104.5104.8105104.4 2008105.5106.3106.7107.6108.3109109 2009108.7109.6109.8110.1110.7111110.9 2010112.4112.9113.5114.2114.4114.6114.3 2011116.9117.8118.1119.3119.5119.4119.4 2012121.1121.8122.2122.8122.3122.5123.1 2013124.4125.2125.6125.9126.1125.9125.8 2014126.7127.4127.7128.1128128.3127.8 2015127.1127.4127.6128128.2128.2128 2016127.4127.7128.3128.3128.5128.8129.2 2017129.8130.7131.2131.7132.2132.2132.1 AugSepOctNovDecTotal 104.7104.8105.3105.6106.21256.4 109.7110.3110109.9109.51301.8 111.4111.5111.7112112.61330 114.9114.9115.2115.6116.81373.7 120.1120.9121121.2121.71435.3
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2478.6 2577.92564.2 2682.7 2822.22912.72999.53072.43102.53156.6 3269.7 RPI (c): Difference between CPI and RPI CPIandRPIboth measures inflation for changes in price for consumer goods on a market base but there is a little difference between both is that RPI also includes cost of housing which CPI do not consider and this makes RPI a better base to make further calculation as it will provide more accurateresultsregarding inflation. When it comesto calculations RPI is calculated by arithmetic i.e., price of each product is added and they are simply divided by number of products whereas CPI is calculated geometric mean. It is calculated by multiplying price of each product then taking nth root of them, value of 'n' is number of products considered. It can be seen that geometric mean shows better reflection of change in consumers spending pattern in relation to change in price of products (Lin and et. al., 2011). When CPI and RPI will be calculated then difference of approximately 1 % will always be seen as CPI would be higher than RPI by 1% and this is called Formula Effect. (d): Calculation of annual inflation rate Measuring inflation is a very difficult task as it requires huge amount of data CPI measures price change form respective of purchaser. For calculation of CPI various samples are
taken from consumer goods that shows change in price in a year and inflation of that period is calculated. Inflation is always calculating between two periods like month, quarter, years. Amount of current years calculated data will be reduced by its base year then result of this is divided by base year information then multiplied by 100. EXAMPLE-INDEX OF PREVIOUS YEAR 100 INDEX OF CURRENT YEAR 145 INFLATION = (145-100/100) *100 =45% (e): Reason regarding importance of inflation INFLATIONcan mean either increase in price or increase in money supply. Inflation means increase in price is higher then set benchmarks which puts a economy in a very uncertain situation as this will increase price of some necessary goods high and capacity to afford them will reduce then demand for more pay as salary and wages by employees will be done. Inflation is increasing day by day and main reason to know rate of inflation is calculating amount that must be increased in pay so, when price of a product got up then affordable capacity can also be increased. Higher inflation leads to reduction in value of money and investors will find no real return on their money. Inflation has a great impact on economic development as higher inflation discourage investment because of uncertainty in returns as low inflation provides stability and encourage investments. Also higher inflation rate makes economy less competitive as higher priced goods loses their sale in international market which reduces exports and leads financial loss to country by less foreign exchange. In case inflation is higher than its benchmark then real wages are low and this leads low standard of living because income is low as compare to expenses. Significance of inflation is that it makes value of currency less as same amount of money will give you less purchase (Ichinose and Yamamoto, 2011). Activity 2 Hourly Earning No. of leisure centre staff Cumulative Frequency (x)Class
Boundaries 0-90-9.544 10-199.5-19.52327 20-2919.5-29.51340 30-3929.5-39.5747 40-4939.5-49.5350 N =50 N50 22 =25 Hence median class is 10-19i.e. 9.5-19.5 Theupper quartilecorresponds to the75th percentilei.e. 75% of the total frequency. 75% of the total frequency 75%*50 =37.5 Thelower quartilecorresponds to the25th percentilei.e. 25% of the total frequency 25% of the total frequency 25%*50 =12.5 The interquartile range = upper quartile β lower quartile 37.5-12.5 =25 Hourly Earning No. of leisure centre staffMid-point fxfx 0-944.518 10-192314.5333.5 20-291324.5318.5
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30-39734.5241.5 40-49344.5133.5 501045 mean(x)=sum(fx)/total(f)=1045/50=20.9 fxX-x(X-x)2f*(X-x)2 0-944.5-16.4268.961075.84 10-192314.5-6.440.96942.08 20-291324.53.612.96168.48 30-39734.513.6184.961294.72 40-49344.523.6556.961670.88 505152 Standard . d103.0410.15 Median1419.5 Interquartil e7.525 Mean16.520.9 Standard deviation710.15 (B) . Mean βIn the case of statistics, arithmetic mean is a tool which helps in ascertaining the average of various variables having different vales. This tool is based on quantitative data which has numbers. This tool enables to calculate average by dividing the total of all values by the number of values. This tool is the most common and best technique of analysing statistical data in order to calculate further deviations such as standard deviation. Mode βThis is a statistical term which helps in ascertaining frequency of repeating the numbers which can help in organising data to determine results from the huge data. It is a
measure of central tendency of counting the frequency of each result. The basic aim of this tool is to ascertain the highest number of occurrences.mean is the average value of the data. Median βThis is a technique of ascertaining mod point of a data of numbers. In order to determine mid value all, the numbers of a sequence must be arranged first from lowest to highest. In order to calculate the median, middle pair is determined first and then added together so that it can be divided by two. This tool is often used to skew the average of the values.median describes that if it is higher than the mean value then most of the data in the series will be above the average. STANDARDDEVIATION: -itdefinesthe variability or flexibility in given data series. INTERQUARTILERANGE: -By considering the value of medianthe dataspreadismeasured with the help of interquartile range (Gollier, 2011). On the basis of aboveexplanation,the statistical data of two given areas can be compared and interpretation asfollows: Onthe basis of mean it can be measured that the hourly earnings of the staffs in London area are higher than the staffs in Manchester area.onthe basis of standarddeviation,the uncertainty and variability was high in London area's staff earning than the Manchester area. on the basis of median,the most of staffs in London area earned hourly income above the average income. Apart from that, in another one the staffswerenot getting above the average (Boehm and Thomas, 2013). On the basis of interquartilerange,the hourlyincomes speared to more close to the average in London are but much far away in Manchester areas. And for quantitative significance level the various tests can be applied like, t-test, anova test, etc. Activity 3 (a) Economic Order Quantity (EOQ):It is that order quantity which a company is required to maintain as its stock so that the inventory cost can be minimized. It has elements such as annual consumption, ordering cost and carrying cost. The aim of using this method is to reduce the cost associated with placing an order. ο·EOQ =β2AO/C Where, A= Annual consumption; O = Ordering Cost; C = Carrying Cost ο·EOQ = β2*2000*5/2
= 100 Units (b) Re-order Level:It is a level at which company should replenish its order as soon as the re- order period arrives. It takes into accounts the time of replenishment and time of receipt at the store. A company also likes to keep safety stock so that it can carry out its activities without any difficulty. ο·Re-order level (ROQ) = (Lead time*daily average usage) +safety stock = (28*2) +150 = 206 units ο·Frequency of Re-order = Annual consumption/ ROQ = 2000/206 = 9.7 or 10 days (c) Inventory Policy Cost:A company is requiring to maintain the minimum level of stock and many costs are incurred for maintaining that stock, so the cost associated with ordering, receiving and maintaining the stock (Kyriakarakos and et. al., 2013). ο·Inventory Policy Cost = Purchase cost + Ordering cost + Carrying cost = 10 + 5 + 2 = Β£17 ο·The inventory cost is Β£17 because inventory includes all the cost of maintaining stock. (d) Current Level of service =Weekly Demand * Availability of t-shirt =40*95% =38 units (e) Re-order level to achieve desired service level: Re-order level (ROQ) = (Lead time*daily average usage) +safety stock = (28*2) +150 = 206 units The current level of service provided is 95% and the desired level is 100%. The company will be able to reach the desired level by ordering 206 units (Wheeler, Shaw and Barr, 2013). Activity 4 (a):
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CONSUMER PRICE INDEX:It is a remedy to estimate the inflation changes in the consumer prices of a particular country. Another name of Consumer Price Index (CPI) is Harmonised Index of Consumer Prices (HICP). YearAnnualChange 20172.70%2.00% 20160.70%0.70% 20150.00%-1.50% 20141.50%-1.10% 20132.60%-0.20% 20122.80%-1.70% 20114.50%1.20% 20103.30%1.10% 20092.20%-1.40% 20083.60%1.30% 20072.30%0.00% 29/06/1905 30/06/1905 01/07/1905 02/07/1905 03/07/1905 04/07/1905 05/07/1905 06/07/1905 07/07/1905 08/07/1905 09/07/1905 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 2.00% 0.70% -1.50%-1.10%-0.20%-1.70% 1.20% 1.10% -1.40% 1.30% 0.00%Change Table 1. Consumer Price Index Source: Self-generated
INTERPRETAION:The graph indicates the changes in the CPI from 2007 to 2017. From the year 2007 to 2011 the fluctuations were very high. In that span of time the inflation rate was negative for a year i.e. 2009. After 2009, the rate was going upward steadily till 2011. From the year 2012 to 2015 the inflation was downward. After maintaining a pace going downward the inflation was again on the rise in the year 2016 and 2017 due to air fares, fall in prices of goods like toys and games (Jiang and Pang, 2011). CPIH:It is a measure of CPI by which the owner occupiers' housing costs are calculated. Such costs attribute to oneβs costs of owning, maintaining and living in the own house. There are many other cost associated with owing a house such as repayment of housing loan, commission to a housing agent, insurance etc. For ascertaining the total cost of all the house owners this method of calculation is used (Murphy, Myors and Wolach, 2014). Year% change 20072.40% 20083.50% 20092.00% 20102.50% 20113.80% 20122.60% 20132.30% 20141.50% 20150.40% 20161.00% 20172.60% Table 2. CPIH indices Source: Self-generated
1234567891011 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Change Interpretation:The CPIH graph indicates that the movement of prices of owning and maintaining the houses by owners is steady from the year 2007 to 2010. In the year 2011, it reached at the highest of the CPIH for 10 years whereas the year 2015 recorded the lowest in CPIH index indicating downward movement and fall in the standard of living (BrozoviΔ and Schlenker, 2011). RPI:This measure is used to calculate the changes in the cost of the products and services sold and provided respectively in the UK market. The cost includes cost of living of the families consuming the products and services. The basis of calculation is the consumption by the family and the RPI increases with increase in the overall consumption. YearChange 20173.60% 20161.80% 20151.00% 20142.40% 20133.00% 20123.20% 20115.20%
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20104.60% 2009-0.50% 20084.00% 20074.30% 1234567891011 -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% Table 2. Retail Price Index Source: Self-generated Interpretation:RPI indicates an upward movement in the retail prices from the year 2007 to 2014. The upward movement states that the consumption was increasing every year till 2014. The consumption of the overall household goods and services declined in the year 2015 causing the RPI fall downward. The decline in the retail prices were negative in the year 2015. In the 2016 and 2017 the trend was steady and upward resulting in stability in retail prices (Beyer and Dye, 2012). (b) Hourly earningsClass Boundaries Number of leisure staffCumulative Frequency 0 β 090 β 9.544 10 β 199.5 β 19.52327 20 β 2919.5 β 29.51340 30 β 3929.5 β 39.5747