Statistics

2.0 INTRODUCTION Statistics is the study of the collection, organization, and interpretation of data.[1][2] It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.[1] A statistician is someone who is particularly well versed in the ways of thinking necessary for the successful application of statistical analysis. Such people have often gained this experience through working in any of a wide number of fields. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject. The word statistics, when referring to the scientific discipline, is singular, as in "Statistics is an art."[3] This should not be confused with the word statistic, referring to a quantity (such as mean or median) calculated from a set of data,[4] whose plural is statistics ("this statistic seems wrong" or "these statistics are misleading"). Statistics is a set of tools used to organize and analyze data. Data must either be numeric in origin or transformed by researchers into numbers. For instance, statistics could be used to analyze percentage scores English students receive on a grammar test: the percentage scores ranging from 0 to 100 are already in numeric form. Statistics could also be used to analyze grades on an essay by assigning numeric values to the letter grades, e.g., A=4, B=3, C=2, D=1, and F=0. Employing statistics serves two purposes, (1) description and (2) prediction. Statistics are used to describe the characteristics of groups. These characteristics are referred to as variables. Data is gathered and recorded for each variable. Descriptive statistics can then be used to reveal the distribution of the data in each variable. Statistics is also frequently used for purposes of prediction. Prediction is based on the concept of generalizability: if enough data is compiled about a particular context (e.g., students studying writing in a specific set of classrooms), the patterns revealed through analysis of the data collected about that context can be generalized (or predicted to occur in) similar contexts. The prediction of what will happen in a similar context is probabilistic. That is, the researcher is not certain that the same things will happen in other contexts; instead, the researcher can only reasonably expect that the same things will happen. Prediction is a method employed by individuals throughout daily life. For instance, if writing students begin class every day for the first half of the semester with a five-minute freewriting exercise, then they will likely come to class the first day of the second half of the semester prepared to again freewrite for the first five minutes of class. The students will have made a prediction about the class content based on their previous experiences in the class: Because they began all previous class sessions with freewriting, it would be probable that their next class session will begin the same way. Statistics is used to perform the same function; the difference is that precise probabilities are determined in terms of the percentage chance that an outcome will occur, complete with a range of error. Prediction is a primary goal of inferential statistics. 3.0 SOLUTION 1. A drug manufacturer is interested in the proportion of persons who have depression whose condition can be controlled by a new drug company has developed. A study was conducted involving 6000 individuals with depression and found that 80 % of the individuals are representative of the group who have depression, answer the following questions. a) What is the population' The population is 6000. b) What is the sample' The sample is 6000. c) Identify the statistic and give its value. Proportion of sample for which drug is effective is 80% of the 6000. d) Do we know the value of the parameter' Why' No. It’s not defined anything. 2. Draw a histogram and ogive to represent the following data. Lifespan (hours) | 10-14 | 15-19 | 20-24 | 25-29 | 30-34 | Frequency | 0 | 8 | 6 | 9 | 7 | 30 - 34 25 - 29 20 - 24 15 - 19 10 - 14 3. A survey on 50 workers at Kodak Company was taken last May. Each worker was asked: “How many minutes did you exercise per week outside work time'” The results were shown tabulated in the table below: 30 | 43 | 74 | 32 | 29 | 45 | 48 | 65 | 37 | 64 | 41 | 63 | 28 | 58 | 48 | 40 | 55 | 35 | 59 | 55 | 69 | 52 | 41 | 38 | 41 | 39 | 47 | 49 | 54 | 79 | 51 | 38 | 47 | 56 | 40 | 27 | 68 | 61 | 51 | 65 | 43 | 67 | 44 | 36 | 50 | 54 | 57 | 29 | 48 | 52 | Construct a stem-and-leaf diagram for this data. Leading digit ( Stem) | Trading digit (Leaf) | 2 | 7, 8, 9, 9 | 3 | 0, 2, 5, 6, 7, 8, 8, 9 | 4 | 0, 0, 1, 1, 1, 3, 3, 4, 5, 7, 7, 8, 8, 8, 9 | 5 | 0, 1, 1, 2, 2, 4, 4, 5, 5, 6, 7, 8, 9 | 6 | 1, 3, 4, 5, 5, 7, 8, 9 | 7 | 4, 9 | 4.0 REFERENCE 1. en.wikipedia.org/wiki/Statistics 2. www.statistics.com 3. www.malaysia.gov.my/EN/Pages/Statistic.aspx 4. Textbook of AIM 1001 5.0 Coursework Name: Lee Yoor Feng NRIC: 920727 – 08 – 6952 Student ID: 200520 H/P : +6017 - 6100905 1. Using a table to prepare a summary of strengths and weakness of basic sampling techniques. Non – probability sampling | Techniques | Strengths | Weaknesses | Convenience sampling | Less expensive, less time consuming, most convenient | Selection bias, sample not representative, not recommended for descriptive or causal research | Judgmental sampling | Low cost, convenient, not time consuming | Does not allow generalization, subjective | Quota sampling | Sample can be controlled for certain characteristics | Selection bias, no assurance of representativeness | Snowball sampling | Can estimate rare characteristics | Time consuming | Probability sampling | Simple random sampling | Easily applied. Result can be projected on population | Difficult to obtain sampling frame, expensive, sometimes no assurance of representativeness | Systematic sampling | Easier to implement than simple random sampling | Can decrease representativeness if certain patterns exist in sampling frame | Stratified sampling | Includes all important subpopulations, precision is improved | Difficult to select relevant stratification variables, not feasible to stratify on many variables, expensive | Cluster sampling | Easy to implement, cost- effective and work is reduced | Imprecise, difficult to compute and to interpret results | 2. Managers, decision – makers and researches use statistical problem – solving procedures to help them in making wise and effective decisions. List and describe al the steps in statistical problem – solving. Managers, decision – makers and researches use statistical problem – solving procedures to help them in making wise and effective decisions. The basic steps in statistical problem – solving are outlined below. Step one: Identifying the problem or opportunity A manager must understand clearly and define correctly the problem at hand. He must be careful not to confuse the actual problems that the management is trying to solve and the symptoms. However, sometimes one can use symptoms as clues to find the actual problem. For example, the monthly sales of Proton cars have been declining significantly for the past 24 months even though the overall auto industry has shown steady growth. The management is trying to identify the actual causes or factors that had contributed to the problem of declining local car sales so that corrective action can be taken immediately. Failing to find the actual causes might result in the local auto industry having to slow down, and hence, reduced sales and lower profits. The objective is to determine the factors that contributed to the decline in demand for Proton cars. The actual problem is unknown while the symptoms are a decline in sales, high cancellation of bookings and slow growth of new bookings. Step two: Gathering available facts Data and information that are related to the actual problem must be gathered. Internal data can be obtained from the departments within an organization. For example, accounting and financial data can be obtained from the financial and accounting departments, production figures are obtainable from the production department and sales data can be obtained the marketing and sales department. The customer service department and human resource department also provide useful data for analysis. External data can be obtained from other organizations such as the Ministry of domestic Trade and Consumer Affairs, Bank Negara, the Ministry of International Trade and other business organizations. Other sources include the Journal of Auto Industry, the Journal of Malaysian Business, Newspapers and magazines. Step three: Gathering new data If the available data are inadequate to get a clear picture of the problem, the management may decide to collect new data. Sometimes, data on important variables are not available from secondary sources or the data obtained from those sources are already outdated or not suitable for use. As such, the management must obtain data from primary sources. Appropriate data collection methods must be applied so that the data are gathered accurately. For example, the management may want to collect data on customers’ expectations on certain characteristics of passenger cars such as the safety standard, design, performance, price, after-sales service, resale value and rate of financing. At the same time, the management may also require information regarding the marketing strategy of competitors such as advertisement and promotional strategies, package offer, incentive for trade-in, or switching incentive. Several data collection methods can be applied. They are direct observation, personal interview, telephone interview (especially for long distance respondents), direct questionnaires, mailed questionnaires and focus group study. Before primary data is obtained, the manager must determine the representative sample to be used for the research. In choosing the sample, the researcher must apply appropriate sampling techniques so that the sample selected represents the target population. Selecting a wrong sample will produce data that will not accurately represent the population and results in inaccurate information for decision-making. Any analysis on the biased data is not valid. The sampling technique used depends on the nature of the target population, the budget available and also the objectives of the study. Among the sampling techniques available are simple random sampling, systematic sampling, stratified sampling, duster sampling, quota sampling, judgmental sampling and ssnowball sampling. Step four: Classifying and organizing the data After the required data have been collected, the next task is to make the data more meaningful, readable and understandable in the context of the problem being investigated. Raw data are meaningless. They must be transformed into meaningful forms. Step five: Presenting and analyzing data Data must be represented in useful and meaningful ways so that they are useful for decision-makers, and the people reading the report. Some of the common methods of presenting data are through frequency tables, bar charts, graphs, histograms, frequency polygons, ogives and stem-and leaf plots. Frequency tables are used to summarize data based on variables of interest. For example, Proton customers can be grouped according to demographic variables such as income level, education level, ethnic group and type of job, so that useful information on demand can be obtained and analyzed. Data presentation through charts, graph, scatter plots and other visualized methods helps in identifying the relationship between variables of interest. For example, a manager of a local car company may want to determine the relationship between the demand for local cars and demographic variables such as gender, educational level, income level and social classes. At the same time, he may be interested to establish the relationship of these variables with the choice of models, price, quality of service and product performance. If we want to get more through information, the data need to be further analyzed. Among the methods of data analyses are cross tabulation, chi-square test, regression analysis and time series analysis. Step six: Making a decision After going through data representation, data analysis and interpretation of the results, the management should have a clear idea of the problem at hand. Certain variables may influence some other variables. The management can list down the possible alternative action to take under various economic conditions, and other influential conditions such as change in interest rates, change in consumers’ lifestyles and developments in technology. With appropriate statistical analyses techniques and models, the management can make the right decision. Among the models that can be applied are decision-making under certainty, decision-making under uncertainty and decision-making under risk. This is followed by the implementation of the plan. Appropriate corrective action should be carried out in cases where deviation from the plan occurs. 3. The table below shows the speeds of 100 vehicles that pass by a small town in a certain period of time. Speed (km hour-1) | Number of vehicles | 40-44 | 8 | 45-49 | 18 | 50-54 | 16 | 55-59 | 26 | 60-64 | 22 | 65-69 | 10 | Calculate a) The mean, b) The first quartile, median and third quartile using formula. Solution a) Mean = 42X8+47X18+52X16+57X26+62X22+(67X10)8+18+16+26+22+10 = 5530100 = 55.3 The mean is 55-59 km hour-1. Rearrange the numbers: 8, 10, 16, 18, 22, 26 b) Q1= L1+N4-F1-1f1c1 median = Lm+N2-Fm-1fmcm = 45+1004-8185 = 55+50-42265 = 49.72 = 56.54 Q3 = L3+3N4-F3-1f3c3 = 60+75-68225 = 61.59