Topic 1 Week 1 Introduction to Statistics (PDF)

TOPIC 1: INTRODUCTION TO STATISTICS PN NOR AZIAN BINTI ABU ASAN @ ABU HASSAN Quantitative Science Department, KPMSI 1 STATISTIC FUN 34 percent of adults and 75 percent of FACTS children sleep...

TOPIC 1: INTRODUCTION TO STATISTICS PN NOR AZIAN BINTI ABU ASAN @ ABU HASSAN Quantitative Science Department, KPMSI 1 STATISTIC FUN 34 percent of adults and 75 percent of FACTS children sleep with a stuffed animal or a blanket, or other sentimental object as their comfort object. 2  Dragonflies have a 95% hunt STATISTIC success rate. Making them the most effective hunters in the world. FUN FACTS 20% of the mammal species on our planet are different types of bats. There’s about 5000 species of mammals, and about 1000 of them are varieties of our little winged buddies. 3  This makes my head hurt Why study Statistics? I’m never going to use this again! 4  1.0 Introduction Why study something you will never use Data don’t make Have you Have you any sense, ever been ever voted? Numerical wewill haveto Recognise Information To doctor? resort to statistics brands? Is everywhere Ever taken a Do you have test? insurance? Fill out Helps you to Have you understand ever watched a survey? Do you watch sport? the whether? Use to make Own stock or Do you use decision investment? facebook? 5 STATISTIC FUN FACTS 6  Learning Objectives: 1. Briefly explain statistics. 2. Differentiate between population and TOPIC 1: sample. INTRODUCTION 3. Distinguish between a parameter and TO STATISTICS a statistic. 4. Differentiate between type of statistics 5. Explain and give example of variable and its data 7 1.1 What is Statistics? Science of i. collecting, ii. organizing, iii. presenting, iv. analysing and v. interpreting data to assist in making more effective decision 8  1.1.1 Key Statistical Concepts Population vs Sample Group of ALL items of interest in a statistical problem Subset of data drawn The size is frequently from the population large Descriptive measure is Nor necessary refer to called STATISTICS. a group of people Descriptive measure is called PARAMETRIC 9 1.1.1 Key Statistical Concepts Discussion: Identify Key Statistical Concepts Online Shopping Preferences Survey You are a marketing analyst working for an e-commerce company. Your team is interested in understanding the preferences of online shoppers to improve the user experience and tailor marketing strategies. You decide to conduct a survey to gather insights. 10  1.1.1 Key Statistical Concepts Discussion: Identify Key Statistical Concepts Online Shopping Preferences Survey Population Sample All online shoppers who have made a A randomly selected group of 500 purchase on the e-commerce platform customers from the e-commerce (This includes every single customer who platform's database. (due to practical has bought something from your website) limitations, you cannot survey every single online shopper) Parameter Statistics The average amount spent per transaction The average amount spent per by all online shoppers who have made a transaction by the randomly selected purchase on the e-commerce platform. group of 500 customers in the sample. 11 Exercise: Identify Key Statistical Concepts On August, 2022 issues of national magazine reported that in a national public opinion survey conducted among the 1200 registered voters, 36% favored Candidate A, 34% favored Candidate B and 23% were in favor Candidate C for President chair. From above information, (a) What constitute the population, (b) What is the sample 12 Exercise: Identify Key Statistical Concepts In the shrimping industry, fisherman bring their boats to the packinghouse pier and unload their catch into larger holding tanks. The price that the packinghouse will pay the fisherman is based on the average size of the shrimp. To determine the average size, the shrimp are thoroughly mixed in the holding tank, and then a bucket of shrimp is taken out, and the shrimp in the bucket are sized. From the given information; (a) What is the population of the shrimp, (a) What is the sample 13 1.1.1 Key Statistical Concepts Identify whether each of the following involves a population or a sample: a) Yearly bonus of all employees in a company b) Number of holidays of six colleges in Pahang c) Sales record during mega sales at all supermarkets in Kuala Lumpur. d) Monthly wages of all employees in a company. e) Customers whose telephone numbers have been contacted during survey. 14 1.2 Type of Statistics 15 1.2 Type of Statistics Descriptive vs Inferential Average GPA if the data were taken from the sample of KPMSI students. e.g: GPA = 3.37 On average, the GPA of KPMSI students is 3.37 16 1.2 Type of Statistics Determine whether descriptive or inferential statistics is being used in the cases below: a) A product manager plotted his daily sales and observed that sales has increased. b) A quality control engineer detected 2% defective parts after inspecting a sample of 50 parts from one production run. From this finding, he would then decide if the production should continue. 17 1.3 Types of Data and Variable Data is a collection of observation, measurement, figures, fact obtained from study carried out. e.g: Marital status Weight Types of house Temperature 18 1.3 Types of Data and Variable Data is a collection of observation, measurement, figures, fact obtained from study carried out. e.g: 20kg, 63kg, Single, Married, 35kg, 106kg… Widowed, Divorced 37oF, 77oC, Hut, detached, 40oF bungalow 19 1.3 Types of Data and Variable e.g: VARIABLE DATA Weight 20kg, 63kg, 35kg, 106kg Marital Status Single, Married, Widowed, Divorced Temperature 37oF, 77oF, 40oF Types of house Hut, detached, bungalow Data must be collected to provide information 20 1.3.1 Quantitative and Qualitative VARIABLE / DATA Qualitative Quantitative (Categorical) (Numerical) Nominal Ordinal Discrete Continuous Unordered, Ordered, Data that can be Data that can only be mutually exclusive mutually exclusice counted precisely approximate to or e.g: Blood group, e.g: Shirt size (S, e.g: no. of Facebook measured Eye colour, Gender M, L, XL), likes, e.g: distance, Zip code Likert scale no. of patience tyre pressure, temperature17 1.3.1 Quantitative and Qualitative 22 1.3 Types of Data and Variable 1. The following information is obtained from 2. Determine whether the following data customers upon existing the shopping are discrete or continuous variables. mall. Classify each of these variables as qualitative or quantitative: a) The distance (in kilometer) driven annually by employees in company a) Amount of money spent on clothing cars. b) Pairs of shoes owned b) The number of students in KPMB. c) Favorite department store. c) The final marks score received by students in a statistics course. d) Amount of time spent shopping for clothing. d) The height of 50 children in a kinder garden.. e) Method of payment for purchases. e) The number of cars in a parking lot. 23 1.3.3 Level of Measurements 24 1.4 Survey Methodology Learning Objectives: 1. Define population, sample, sample survey and sample frame 2. Identify Probability Sampling Techniques and Non-Probability Sampling Techniques. 3. Apply appropriate sampling techniques 25 1.4 Survey Methodology 26 27 1.4 Survey Methodology ii. Sample Size number of participants/elements or observations included in a study influences two statistical properties: 1) the precision of our estimates and 2) the power of the study to draw conclusions. sample size which is too small may produce inconclusive results too large will waste scarce resources 28 1.4 Survey Methodology iii. Sampling Error Sampling errors occur due to a disparity (different) in the representativeness of the respondents. happens when the researcher does not plan his sample carefully. Can be controlled and eliminated by creating a careful sample design, having a large enough sample to reflect the entire population 29 1.4 Survey Methodology iv. Sample Frame Tool used to get access to the sample Lists the items from which the sample can be obtained. any list, material or device that delimits, identifies, and allows access to the elements of the survey population 30 1.4.1 What is Sampling SAMPLING? Procedure of selecting a sample from the population. The sample must be selected in such a way that it will accurately represent the population 31  1.4.2 Reason for Sampling To contact the whole The cost of studying population would be time all the items in consuming population may be prohibitive The physical The destructive impossibility of nature of certain checking all items in test the population The sample result are adequate 32 1.4.3 Sampling Techniques / Methods 33  Non-probability / Probability / Non-Random Sampling Random Sampling Sample item are chosen every item in the depending on the population has an equal judgment or the opinion of chance of being chosen as the person conducting the the sample survey. 34 (a) Probability Sampling Techniques i. Simple Random Sampling Make a list Assign a Choose Steps to sequential sample size conduct SRS number Use random number table/ generator 35  e.g: Simple Random Sampling Scenario: Step 1 & 2: List and assign number The college management is No. Students’ Name Class interested in obtaining information 001 Abdullah DIB1B on problems that affected students’ 002 Ahmad Kassim DEC1A performance on academic. The total 003 Baharudin DMK1A number of students is 879 and the 004 Daud DEC2D number of sample required is 150. How to conduct the sampling 005 Hisham DMK3C technique by using simple random … … … method? 500 Rashid DBIT4B … … … 879 Zack DIB3A 36  e.g: Simple Random Sampling Step 3: a) Use Lottery Method b) Random Number Table c) Generated Random Number 37  e.g: Simple Random Sampling Step 4: Identify sample from the list No. Students’ Name Class No. Students’ Name Class 001 Abdullah DIB1B 312 Mariam DIB6A 002 Ahmad Kassim DEC1A … … … 003 Baharudin DMK1A 433 Mohd DBIT5B 004 Daud DEC2D … … … 005 Hisham DMK3C 511 Rashid DBIT4B … … … … … … 125 Kamal DIB2C 680 Suhaimi DMK5C … … … … … … 237 Nora DEC4C 879 Zack DIB3A 38 (a) Probability Sampling Techniques ii. Systematic Random Sampling There is a gap or interval, between each selected unit in the sample. Selection of unit is based on sample interval, k starting from a determined point, where k= N/n. 39  e.g: Systematic Random Sampling Scenario: Step 1: List and assign number The college management is No. Students’ Name Class interested in obtaining information 001 Abdullah DIB1B on problems that affected students’ 002 Ahmad Kassim DEC1A performance on academic. The 003 Baharudin DMK1A total number of students is 879 and 004 Daud DEC2D the number of sample required is 005 Hisham DMK3C 150. … … … How to conduct the sampling 500 technique using systematic random Rashid DBIT4B … method? … … 879 Zack DIB3A 40  e.g: Systematic Random Sampling No. Students’ Name Class Step 2: 001 Abdullah DIB1B Select 1 Calculate sample interval... … … sample randomly k = N/n 004 Baharudin DMK1A e.g: No. 4 005 Bahrin DEC3B k = 879/150 (random 006 Hisham DMK3C start) k = 5.86 … k ≈ 5 (rounding down) 010 Hashim DMK3A … Step 3: 016 Lokman DIB1B … … … Select a starting point by 500 Rashid DBIT4B randomly select an item from 1 to … … … kth 879 Zack DIB3A 41  e.g: Systematic Random Sampling No. Students’ Name Class Step 4: 001 Abdullah DIB1B Select 1 Select every kth unit after that first... … … sample number. 004 Baharudin 1st samp DleMK1A randomly e.g: No. 4 e.g: 4, 9 (4 + 5), 14 (9 + 5), 19 … (random (14 + 5) , 24 (19 + 5), until you 006 Hisham DMK3C start) get all the samples you need. … 009 Hashim 2 nd sampl DMK3A e … 014 Lokman 3th DIB1B sampl e … … … 4th 019 Rashid DBIT4B sampl e 42 … … …  e.g: Systematic Random Sampling Other examples of Systematic Random Sampling The market researcher might select every 5th person who enters a particular store, after selecting the The surveyor may interview first person at the occupants of every fifth random house on a street, after randomly selecting one of the first five houses. 43  e.g: Systematic Random Sampling Suppose you run a large grocery store and have a list of the employees in each stores The grocery store is divided into the following 10 section: Deli Counter, Bakery, Cashiers, Stock, Meat Counter, Production, Pharmacy, Photo Shop, Flower Shop and Dry Cleaning. Each section has 10 employees, including a manager (making 100 employees in total) Your list is ordered by section, with the manager listed first and then, the employees by descending order of seniority. You wanted to survey your employees about their thoughts on their work environment. 44  e.g: Systematic Random Sampling Would you use Systematic Random Sampling Technique? If you use a systematic sampling approach and your sampling interval, k = 10, then you could end up selecting only managers or the newest employees in each section. Possible error: This type of sample would not give you a complete or appropriate picture of your employees’ thoughts. 45 (a) Probability Sampling Techniques iii. Stratified Random Sampling A population is divided into homogeneous, mutually exclusive subgroups called strata and a sample is selected from each stratum. GOAL: To guarantee that all groups in the population are adequately represented. Within stratum – uniformity (homogeneous) Between strata – difference (heterogeneous) 46 (a) Probability Sampling Techniques Stratum 1 iii. Stratified Random Sampling Can be stratified by any variable that is available e.g: Gender: Male & Female Education Level: SPM, Diploma, 1st Degree etc Number of sample from each stratum – select Stratum 2 randomly = 𝑁𝑜.𝑜𝑓 𝑒𝑙 𝑒𝑚 𝑒 𝑛𝑡 𝑖 𝑛 𝑡ℎ𝑒 𝑠 𝑡 𝑟 𝑎 𝑡 𝑢 𝑚 ,𝑛 1 × 𝑁𝑜. 𝑜𝑓 𝑠𝑎𝑚𝑝𝑙𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒 𝑁𝑜.𝑜𝑓 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛, 𝑁 47  e.g: Stratified Random Sampling Scenario: Step 1: The college management is Stratify the population e.g by Gender, interested in obtaining Stratum 1: Male Stratum 2: Female information on problems that affected students’ performance on academic. The total number Step 2: of students is 879 and the Calculate number of sample from each stratum number of sample required is Suppose number of male student is 368 and 150. How to conduct the female student is 511. sampling technique using 368 Male = × 150 = 62.7 ≈ 63 stratified random method? 879 Female = 511 × 150 = 87.2 ≈ 87 879 48  e.g: Stratified Random Sampling Strata (by Gender) Male (368) - 63 Female (511) - 87 No. Students’ Name Class No. Students’ Name Class 001 Abdullah DIB1B 001 Aminah DMK3A 002 Ahmad Kassim DEC1A 002 Atiqah DIB5B … 003 Aliya DEC1C … … 257 Zafran DMK3A … … 511 Zaqiah DEC4B 49  (a) Probability Sampling Techniques iv. Cluster Random Sampling To reduce the cost of sampling a population scattered over a large geographical area. To gather data quickly and cheaply at the expense of possible over or underrepresenting certain groups of people. Step 1: Divide the population into subpopulations or cluster Step 2: Select few clusters at random. All units within selected cluster are included in the sample and no units from non-selected cluster are included in the sample. 46  e.g: Cluster Random Sampling Scenario: Step 1: The Secondary Education Divide population into subgroup e.g: states Division of MARA is interested in studying the performance of Step 2: MRSM students in SPM for the year 2019. How to conduct the Randomly choose 5 (example) states. sampling technique using All MRSM students from the selected state will cluster random method? be the sample of study. 51 e.g: Stratified Random Sampling 01 Perlis 02 Kedah 03 Pulau Pinang 04 Perak 05 Selangor 06 Putrajaya 07 Kuala Lumpur 08 Negeri Sembilan 09 Melaka 10 Johor 11 Pahang 12 Terengganu 13 Kelantan 14 Sarawak 15 Sabah 52 (a) Probability Sampling Techniques v. Multi-stage Sampling Combination of any (atleast) 2 methods describe before. Involve in selecting samples in at least two stages e.g: Stage 1: Stratified sampling Stage 2: Systematic sampling Stage 1: Cluster sampling Stage 2: Stratified sampling * Can also be combined with Non-probability sampling techniques (to be discussed in the next sub-topic) 53 Probability Sampling Techniques 54 55  (b) Non-Probability Sampling Techniques i. ConvenienceSampling The selection of sample elements is left to the Interviewer. Often, the respondents are selected because They happened to be there at that specific time. e.g: an interviewer may look for respondents at a shopping complex, airport or stadium to interview. Advantage: 1. Less expensive, less time consuming, most convenient Disadvantage: 1. Selection bias, sample may not be representative, not recommended for descriptive or causal research. 56 (b) Non-Probability Sampling Techniques ii. Judgmental Sampling The sample elements are selected based on the judgement of the researcher. The researcher selects a respondent whom the feels the possess certain characteristics that represents the population. Advantage: 1. Low cost, convenient, not time consuming Disadvantage: 1. Subjective, does not allow generalization 57  (b) Non-Probability Sampling Techniques iii. Snowball Sampling An initial group of respondents is selected (usually at random). After being interviewed, the respondents are asked to identify others who belong to the target population interest. The procedure is applied until the researcher obtains the required number of respondents. Advantage: 1. Can estimate rare characteristics Disadvantage: 1. Time consuming in locating respondents. 58 (b) Non-Probability Sampling Techniques iv. Quota Sampling The procedure is similar to convenience sampling except that the number (size) allocated for each group of respondents with specific characteristics are based on population statistics. The interviewers has the flexibility to choose whoever he wants provided he abides by the specifications. Advantage: 1. Sample can be control for certain characteristics Disadvantage: 55 1. Selection bias, no assurance of representativeness. Non- Probability Sampling Techniques 60  1. Identify the sampling method used in the following cases: a. Using a table random numbers to select a sample of people entering an amusement park. b. Interviewing every 100th person entering an Survey amusement park, randomly starting at 55th person to enter the park. Methodology: c. Estimating the voting preferences of the region by interviewing those who live in various neighborhoods. Discussion 2. A statistics professor wanted to find out the average GPA for all the students in her university. She used all the students enrolled in her statistics class as the sample and collected information on their GPAs to get the average GPA. 61  3. Suggest an appropriate sampling method for the following: a. Passengers’ view on the efficiency of public transportation. b. The attitudes towards the administration of the Survey company. c. The percentage of defects in finished items from a Methodology: production line. Discussion d. The view of car drivers on compulsory use of car seats for children under 3 years old. e. The view of schoolchildren on the food served in the school canteen. f. The effects of new hormones on the growth of poultry. g. The public’s view on the use of monosodium glutamate in foods. 62  Pre-numbered sales invoices are kept in a sales journal. The invoices are numbered 001 to 500. Beginning with the first row, column 1 and proceeding horizontally in the given table of random numbers below, select a simple random sample of 10 invoice numbers. Survey 02711 08182 75997 79866 58095 83319 Methodology: 80295 79741 74599 84379 94873 90935 Discussion 31684 63952 09865 14491 99518 93394 34691 14985 13748 04742 92460 85801 53444 65626 58710 55406 17173 69776 09899 57409 91185 10200 61411 23392 47797 56377 71935 08601 63 1.5 METHOD OF COLLECTING DATA At the end of the lesson, student should be able to: 1. Briefly explain type each type of data sources and. 2. Briefly explain each type of statistical collecting data methods. 3. Discuss the advantages/disadvantages of the collecting data method. 4. Design relevant questions for the objectives of survey. 5. Briefly explain the important of pilot study. 65  1.5.1 What is Collecting Data? Data collection is defined as the “process of gathering and measuring information on variables of interest, in an established systematic fashion that enables one to answer queries, stated research questions, test hypotheses, and evaluate outcomes.” In most cases, data collection is the primary and most important step for research, irrespective of the field of research. The approach of data collection is different for different fields of study, depending on the required information. 66  1.5.2 Data Sources https://youtu.be/VKR1EgfcKdQ 1.5.2 Data Sources https://youtu.be/fbYjaE6Ybpc 1.5.2 Data Sources Before we dive deeper into different data collection techniques and methods, let’s just briefly differentiate between the two main types of data sources – primary and secondary. Primary data sources: Secondary data sources: also known as firsthand data. also known as secondhand data. freshly collected for a specific collected by other parties. purpose. usually in the form of published data. more accurate and consistent with the easily accessible, save time objectives handle with caution: outdated, lack requires more time, manpower, high accuracy, unsuitable and maybe cost biased. 69  1.5.3 General Categories of Collecting Data Methods SURVEY EXPERIMENT DIRECT Face-to-face OBSERVATION interview ABSTRACT FROM Telephone interview PUBLISHED Mailed Interview / MATERIALS Google Form 70 71 72 73 74 75 76 77 Method chosen depends on: Accuracy Cost Time Location Type of data to be gathered ✓ There is no one “best” data collection method. ✓ Each method has its pros and cons. Which one you choose depends on what kind of data you have (i.e. qualitative data or quantitative data) and which pros/cons are important for your study. 78  1.5.4 Designing Questionnaire A set of questions prepared on paper/form and will be given to respondents to be answered. 79 1.5.4 Designing Questionnaire Tips on writing a questionnaire: ✓ Questions should be short and easy to understand ✓ Questions should not be ambiguous ✓ No calculation are needed to be done ✓ Questionnaire must not be to long ✓ Wherever possible, use questions with choice of responses ✓ Questions must not be too personal irrelevant ✓ No leading questions may be asked 80  1.5.5 Pilot Study A pilot study is a small-scale preliminary study conducted before any large-scale quantitative research in order to evaluate the potential for a future, full-scale project. Sometimes the task is too hard, and A pilot study can help the the researcher may get a floor effect, It involves selecting a few people researcher spot any because none of the participants can and trying out the study on them. ambiguities (i.e. unusual score at all or can complete the task – It is possible to save time, and in things) or confusion in the all performances are low. The opposite some cases, money, by identifying effect is a ceiling effect, when the task information given to any flaws in the procedures is so easy that all achieve virtually full participants or problems designed by the researcher. marks or top performances and are with the task devised. “hitting the ceiling”. 81 1.5.5 Pilot Study It is important to conduct a questionnaire pilot study for the following reasons: Check that emotive questions Check that respondents have not been used as they understand the terminology make people defensive and used in the questionnaire. could invalidate their answers. Check that leading questions Ensure the questionnaire can be have not been used as they completed in an appropriate could bias the respondent's time frame answer. (i.e., it's not too long). 82 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS At the end of the lesson, student should be able to: 1. Explain the “business analytics” 1. Explain the importance and the role of business analytics. 83 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS 1.6.1 What is Business Analytics? Refining past or present business data using modern technologies. They are used to build sophisticated models for driving future growth. General Business Analytics process may include Data Collection, Data Mining, Sequence Identification, Text Mining, Forecasting, Predictive Analytics, Optimization, and Data Visualization. Every business today produces a considerable amount of data in a specific way. Business Analytics now are leveraging the benefits of statistical methods and technologies to analyze their past data. This is used to uncover new insights to help them make a strategic decision for the future. 84 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS 1.6.1 What is Business Analytics? Business Intelligence, a subset of the Business Analytics field, plays an essential role in utilizing various tools and techniques such as machine learning and artificial intelligence technologies to predict and implement insights into daily operations. Thus, Business Analytics brings together fields of business management, and computing to get actionable insights. These values and inputs are then used to remodel business procedures to generate more efficiency and build a productive system. 85 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS 1.6.2 Types of Business Analytics Techniques Business analytics techniques can be segmented in the following four ways: 1. Descriptive This technique describes the past or present situation of Analytics: the organization’s activities. 2. Diagnostic This technique discovers factors or reasons for past or Analytics: current performance. 3. Predictive This technique predicts figures and results using a Analytics: combination of business analytics tools. 4. Prescriptive This technique recommends specific solutions for Analytics: businesses to drive their growth forward. 86 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS 1.6.3 Importance of Business Analytics 1. Business analytics can transform raw data into more valuable inputs to leverage this information in decision making. 2. With Business Analytics tools, we can have a more profound understanding of primary and secondary data emerging from their activities. This helps businesses refine their procedures further and be more productive. 3. To stay competitive, companies need to be ahead of their peers and have all the latest toolsets to assist their decision making in improving efficiency as well as generating more profits. 87 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS 1.6.4 1.6.5 Business Analytics Business Analytics Applications Life Cycle 1. supply chain management 2. Customer relationship management 3. financial management 4. human resources 5. Manufacturing 6. smart strategies for sports many more…… 88 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS 1.6.6 The Benefits of Business Analytics Business Analytics brings actionable insights for businesses. However, here are the main benefits of Business Analytics: 1. Improve operational efficiency through their daily activities. 2. Assist businesses to understand their customers more precisely. 3. Business uses data visualization to offer projections for future outcomes. 4. These insights help in decision making and planning for the future. 5. Business analytics measures performance and drives growth. 6. Discover hidden trends, generate leads, and scale business in the right direction. 89 1.6 INTRODUCTION TO ROLE OF BUSINESS ANALYTICS 1.6.7 The Role of Business Analytics Enhance Customer Experience M ake Informed Decisions Reduce Employee Turnover Improve Efficiency Cut Manufacturing Costs Better Product M anagement Tackle Problems 90