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# Statistics Assignments 090427

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### Statistics Assignments 090427

1. 1. SAS DIPLOMA IN BUSINESS MANAGEMENT Statistics (Individual Assignment) Date of report submission: 27th April 2009 Name of student : Kua Siong Zhuang NRIC : S8237534D Synopsis Statistics are used by all industries and businesses as a standardized unit of measurement for presenting data in a useful and meaningful format. For managers and leaders, statistics provide insight into how business units are performing relative to an organizations goals and objectives Explain and illustrate with examples how statistics is used in organizations and analyse how it has been able to contribute to Organizational Decision-making. You may select any organization (public / private sector) or business domain and use it as a basis for your discussion and reference.
2. 2. Contents Introduction of Statistics Page 3 Common Statistical Terminology with Applications Page 4 – 6 Overview of American Express Page 7 American Express Total Returns to Shareholder Page 8 Pie Chart on American Express cards members Page 9 Bar Chart on American Express card holder spending VS Age Group Page 10 Key Charateristics of Resident Labour Force, 1997 – 2007 Page 11 Most Favorable Spending of Retailer Merchant Categories Page 12 American Express Road Show Statistic for Year 2008 Page 13 American Express Out-door sales team performance for Year 2008 Page 14 American Express Market review during bad economies Page 15 List of references Page 16 2
3. 3. Introduction of Statistics Statistics is the scientific application of mathematical principles to the collection, analysis, and presentation of numerical data It is the study of data that includes descriptive statistics the study of methods and tools for collecting data. Mathematical models to describe and interpret data and inferential statistics the systems and techniques for making probability-based decisions and accurate predictions based on incomplete sample ot data. Statistics is a discipline which is concerned with: • Use data to solve a wide variety of fields • Designing experiments and other data collection, • Summarizing information to aid understanding, • Drawing conclusions from data, and • Estimating the present or predicting the future. In making predictions, Statistics uses the companion subject of Probability, which models chance mathematically and enables calculations of chance in complicated cases. Data are not just numbers, but numbers that carry information about a specific setting and need to be interpreted in that setting. With the growth in the use of data comes a growing demand for the services of statisticians, who are experts in the following: • Producing trustworthy data • Analyzing data to make their meaning clear • Drawing practical conclusions from data The main objective of Business Statistics is to make inferences (e.g., prediction, making decisions) about certain characteristics of a population based on information contained in a random sample from the entire population. The condition for randomness is essential to make sure the sample is representative of the population. Business Statistics is the science of good decision making in the face of uncertainty and is used in many disciplines, such as financial analysis, econometrics, auditing, production and operations, and marketing research. It provides knowledge and skills to interpret and use statistical techniques in a variety of business applications. Just like weather, if you cannot control something, you should learn how to measure and analyze it, in order to predict it, effectively. 3
4. 4. Common Statistical Terminology with Applications Like all profession, also statisticians have their own keywords and phrases to ease a precise communication. However, one must interpret the results of any decision making in a language that is easy for the decision-maker to understand. Otherwise, he/she does not believe in what you recommend, and therefore does not go into the implementation phase. This lack of communication between statisticians and the managers is the major roadblock for using statistics. Population: A population is any entire collection of people, animals, plants or things on which we may collect data. It is the entire group of interest, which we wish to describe or about which we wish to draw conclusions. In the above figure the life of the light bulbs manufactured say by GE, is the concerned population. Qualitative and Quantitative Variables: Any object or event, which can vary in successive observations either in quantity or quality is called a"variable." Variables are classified accordingly as quantitative or qualitative. A qualitative variable, unlike a quantitative variable does not vary in magnitude in successive observations. The values of quantitative and qualitative variables are called"Variates" and"Attributes", respectively. Variable: A characteristic or phenomenon, which may take different values, such as weight, gender since they are different from individual to individual. Randomness: Randomness means unpredictability. The fascinating fact about inferential statistics is that, although each random observation may not be predictable when taken alone, collectively they follow a predictable pattern called its distribution function. For example, it is a fact that the distribution of a sample average follows a normal distribution for sample size over 30. In other words, an extreme value of the sample mean is less likely than an extreme value of a few raw data. Sample: A subset of a population or universe. An Experiment: An experiment is a process whose outcome is not known in advance with certainty. Statistical Experiment: An experiment in general is an operation in which one chooses the values of some variables and measures the values of other variables, as in physics. A statistical experiment, in contrast is an operation in which one take a random sample from a population and infers the values of some variables. In order to make any generalization about a population, a random sample from the entire population; that is meant to be representative of the population, is often studied. For each population, there are many possible samples. A sample statistic gives information about a corresponding population parameter. For example, the sample mean for a set of data would give information about the overall population mean m . It is important that the investigator carefully and completely defines the population before collecting the sample, including a description of the members to be included. 4
5. 5. An experiment is any process or study which results in the collection of data, the outcome of which is unknown. In statistics, the term is usually restricted to situations in which the researcher has control over some of the conditions under which the experiment takes place. Design of experiments is a key tool for increasing the rate of acquiring new knowledge. Knowledge in turn can be used to gain competitive advantage, shorten the product development cycle, and produce new products and processes which will meet and exceed your customer's expectations. Primary data and Secondary data sets: If the data are from a planned experiment relevant to the objective(s) of the statistical investigation, collected by the analyst, it is called a Primary Data set. However, if some condensed records are given to the analyst, it is called a Secondary Data set. Random Variable: A random variable is a function that assigns a numerical value to each simple event. For example, in sampling for quality control an item could be defective or non-defective, therefore, one may assign X=1, and X = 0 for a defective and non-defective item, respectively. You may assign any other two distinct real numbers, as you wish; however, non-negative integer random variables are easy to work with. Random variables are needed since one cannot do arithmetic operations on words; the random variable enables us to compute statistics, such as average and variance. Any random variable has a distribution of probabilities associated with it. Probability: Probability (i.e., probing for the unknown) is the tool used for anticipating what the distribution of data should look like under a given model. Random phenomena are not haphazard: they display an order that emerges only in the long run and is described by a distribution. The mathematical description of variation is central to statistics. The probability required for statistical inference is not primarily axiomatic or combinatorial, but is oriented toward describing data distributions. Sampling Unit: A unit is a person, animal, plant or thing which is actually studied by a researcher; the basic objects upon which the study or experiment is executed. For example, a person; a sample of soil; a zip code area Parameter: A parameter is an unknown value, and therefore it has to be estimated. Parameters are used to represent a certain population characteristic. For example, the population mean m is a parameter that is often used to indicate the average value of a quantity. Within a population, a parameter is a fixed value that does not vary. Each sample drawn from the population has its own value of any statistic that is used to estimate this parameter. For example, the mean of the data in a sample is used to give information about the overall mean min the population from which that sample was drawn. Statistic: A statistic is a quantity that is calculated from a sample of data. It is used to give information about unknown values in the corresponding population. For example, the average of the data in a sample is used to give information about the overall average in the population from which that sample was drawn. A statistic is a function of an observable random sample. It is therefore an observable random variable. Notice that, while a statistic is a"function" of observations, unfortunately, it is commonly called a random"variable" not a function. 5
6. 6. It is possible to draw more than one sample from the same population, and the value of a statistic will in general vary from sample to sample. For example, the average value in a sample is a statistic. The average values in more than one sample, drawn from the same population, will not necessarily be equal. Statistics are often assigned Roman letters (e.g. and s), whereas the equivalent unknown values in the population (parameters ) are assigned Greek letters (e.g., µ, s). The word estimate means to esteem, that is giving a value to something. A statistical estimate is an indication of the value of an unknown quantity based on observed data. More formally, an estimate is the particular value of an estimator that is obtained from a particular sample of data and used to indicate the value of a parameter. 6
7. 7. Overview of American Express American Express is a world class prestige brand and well recognizes Multi-National Corporation. She was established since year 1850 in United States and evolved from a successful express delivery business into a company that created and sold money orders and travler’s cheques. American Express is the largest global card issuer by spend volume. One of the to its success has been offering card members a choice of products designed to meet their spending In addition to the many cards AMEX issued, they had partnered with more than 100 banks and other institutions in more than 120 countries to issue cards accepted on the American Express network. At year end 2008, American Express had 92.4 million cards-in-force (including cards issuing by partners), issued in more than 40 currencies with a total billed business of \$683 billion. References: www.americanexpress.com Top 10 Customer satisfaction (J.D. Power and Associates 2008 Credit Card Satisfaction Study Rankings) (Based on a 1,000-point scale) 1. American Express -- 783 2. Discover Card -- 751 3. National City -- 721 4. Chase -- 719 5. U.S. Bank -- 716 6. Washington Mutual -- 712 7. Citi -- 710 8. Wells Fargo -- 709 9. Bank of America -- 692 10. GE Money -- 683 (Source: J.D. Power and Associates, September 2008) – references: www.creditcards.com.sg 7
8. 8. American Express Total Returns to Shareholder This chart compare the cumulative total shareholder return on American Express common shares with the total return on the S&P 500 Financial index for the last five years. It shoes the growth of a \$100 investment on December 21,2003, including the reinvestment of all diviends. References: http://www.americanexpress.com 8
9. 9. Pie Chart on American Express cards members Credit cards are personal credit card that gives all segmentation of consumer to enjoy the benefits discounts and promotions when they pay the bill with American Express merchant. The following surveys, statistics and analyst reports will show the data of different segments to help the management and marketing team to identify their most groups of consumer and which campaign will best reach out to the targeted group. Sample Data of active American Express card holders in year 2008 Year 2008 American Express Active Card Holders 40 yrs old & above , 24,000 21 to 25 yrs old, 3,000 25 to 30 yrs old , 8,000 3% 24% 8% 18% 31 to 35 yrs old , 18,000 25% 21 to 25 yrs old 40 to 45 yrs old, 25,000 25 to 30 yrs old 21% 31 to 35 yrs old 36 to 40 yrs old , 21,000 36 to 40 yrs old 40 to 45 yrs old 40 yrs old & above Age group Percentage Total no of active card holder 21 to 25 years old 3% 3,000 members 26 to 30 years old 9% 9,000 members 31 to 25 years old 18% 18,000 members 36 to 40 years old 21% 21,000 members 40 to 45 years old 25% 25,000 members 45 & above years old 24% 24,000 members Total No. of active card holders 100,000 members 9
10. 10. Bar Chart on American Express card holder spending VS Age Group In this chart, it’s clearly shown that the higher the age group, the spending is higher. Therefore, the management shall focus their target market more on mature age group from 30 years old has got more spending power or willing to spend more than the younger age group. Year 2008 Spending VS Age Group \$1,400,000.00 \$1,200,000.00 21 to 25 yrs old \$1,000,000.00 26 to 30 yrs old \$800,000.00 31 to 35 yrs old \$600,000.00 36 to 40 yrs old \$400,000.00 40 to 45 yrs old 45 yrs old & above \$200,000.00 \$- Age Group Age group Spending Total no of active card holder 21 to 25 years old \$ 450,000.00 3,000 members 26 to 30 years old \$ 800,000.00 9,000 members 31 to 25 years old \$ 1,192,000.00 18,000 members 36 to 40 years old \$ 1,238,000.00 21,000 members 40 to 45 years old \$ 1,380,000.00 25,000 members 45 & above years old \$ 1,180,000.00 24,000 members Total Spending & \$ 6,240,000.00 100,000 members members 10
11. 11. Key Charateristics of Resident Labour Force, 1997 – 2007 In this tables, we’ll be able to view the analyst between year 1997 to 2007 on the key characteristics of resident labour force on employment aged between 35 to 64 against the median monthly income. The median monthly income shown on recent year 2007 was \$ 2,330 on the total. Males median income was \$ 2,500 & Females was \$ 2,170. Based on this report, the conclusions of more males monthly incomes is greater than the females for a decade. Literally, this report could not conclude the spending of males are higher than females even though the earnings are greating References: http://www.mom.gov.sg Singapore Yearbook of manpower Statistics in Singapore 11
12. 12. Most Favorable Spending of Retailer Merchant Categories The credit cards spending with the retailer merchant is predominately the most revenue based on records from the number of cards swiped each month. These data however will need more survey given by card holders as there might be probability of exploring new or potential merchant categories (e.g. internet purchases) that would be more favorable & most willingly spend by new and card holders. It can also maximize the spending of new & existing card holders. In this questionnaire survey, out of 100,000 new and existing card holders, American Express took a sample of 60,000 members to give their survey by getting a free pair of movie tickets. Apparently, only 50,000 samples participated in this survey. The survey data as follows: Age Group & Sex 21 to 30 yrs 31 to 40 yrs 41 to 50 yrs 50 & above yrs Flavorite Merchant old old old old Restaurant / Dining 7312 8421 7120 4260 Holiday 850 690 961 795 Beauty / Spa / fitness centre 902 833 740 425 Electronics / IT gadget 1002 910 502 382 Automotive 563 390 295 55 Fashion 800 463 200 104 Super Market 984 3284 2063 1252 Entertainment / Movie / Concert 490 392 300 153 Internet Purchases 192 185 120 78 Others 462 230 340 500 This survey shows that America Express should focus its promotions on restaurant/dining category & rewards the existing / new clients. American Express can also reach out to more dining restaurant to add on the group of their rewarding merchant. Secondary will be for electronics / IT Gadget segments. PC show & road shows on IT mall will be more advantages to bring the awareness that purchases with American Express gives the benefits & freedom to decide for a wide range of merchant. Shopping will be much fun for AMEX card holders. 12