SCS 1104: Probability and Statistics Lecture 1 PDF

SCS 1104: Probability and Statistics Lecture 1 1 Introduction to Statistics The primary role of statistics is to provide decision makers with methods for obtaining and analyzing information to help make these decisions. Statistics therefore, is an invest...

SCS 1104: Probability and Statistics Lecture 1 1 Introduction to Statistics The primary role of statistics is to provide decision makers with methods for obtaining and analyzing information to help make these decisions. Statistics therefore, is an investigative scientific technique that deals with problems capable of being answered, to some degree, by numerical information which is obtained by measuring or counting. 2 Formal Definition of Statistics Statistics is the science that deals with the collection, organization, analysis and interpretation of both numerical and non-numerical data. 3 Formal Definition of Statistics Collection of Data: is the process of obtaining measurements or counts or observations. Organization of Data is the task of presenting the collected data in a form suitable for deriving logical conclusions. 4 Formal Definition of Statistics Analysis of Data: is the process of extracting from the given measurements, counts or observations relevant information from which a summarized and comprehensive numerical description can be formulated. The most important measures used for this purpose are the mean, median, range and standard deviation. 5 Formal Definition of Statistics Interpretation of Data: is the task of drawing logical conclusions from the analysis of the data. It usually involves formulation of prediction formulation of predictions concerning a large collection of objects from information available for a small collection of similar objects. 6 Application of Statistics Accounting Public accounting firms use statistical sampling procedures when conducting audits for their clients. Finance Financial advisors use a variety of statistical information to guide their investment recommendations. 7 Application of Statistics Marketing Electronic scanners at retail checkout counters are being used to date for a variety of marketing research applications. Production With today's emphasis on quality, quality control is an important application of statistics in production. 8 Application of Statistics Economics Economists are frequently asked to provide forecast about the future of the economy or some aspect of it. They use a variety of statistical information in making such forecasts. 9 Types of Statistics There are two types of statistics 1. Descriptive Statistics is concerned with summary calculations, graphs, charts and tables. 2. Inferential Statistics is a method used to generalize from a sample to a population. 10 Types of Statistics Example: Population vs Sample For example, the average income of all families (the population) in a country can be estimated from figures obtained from a few hundred (the sample) families. 11 Population and Sample Population: is the collection of all possible observations (measurements or counts) of a specified characteristic of interest. An example is all of the students in COM 311 course in this semester. Sample: is a subset of the population. An example is the number of foreign students in the COM311 course in this semester. 12 Types of Variables Variable: A variable is an item of interest that can take on many different numerical values. 1. Qualitative Variables: are nonnumeric variables and can't be measured. Examples include: gender, religious affiliation, state of birth. 13 Types of Variables 2. Quantitative Variables: are numerical variables and can be measured. Examples include: balance in your bank account, number of children in your family, number of students in COM 311, etc. 14 Types of Variables 2. Quantitative Variables: Note that quantitative variables are either : - discrete: can assume only certain values, and there are usually "gaps" between the values, such as the number of bedrooms in a house, or - continuous: can assume any value within a specific range, such as the air pressure in a car tyre. 15 Types of Quantitative Data There are four (4) types of quantitative data: 16  Types of Quantitative Data 1. Nominal Data: Numbers are used to represent an item or characteristic. The weakest data measurement. Examples include: a university or college may designate third year students by numbers, i.e., BSC in CS=1, BSC in IT=04, or male=1 and female=2. Note: such data SHOULD NOT be treated as numerical, since relative size has no meaning. 17 Types of Quantitative Data 2. Ordinal or Rank Data: Numbers are used to rank. An example is wind forces at sea. A gentle breeze is rated at 3, a strong breeze is rated at 6. Another example is excellent, good, fair and poor. Note: Simple arithmetic operations are NOT meaningfully applied to ordinal data. 18 Types of Quantitative Data The main difference between ordinal data and nominal data is that : ordinal data contain both an equality (=) and a greater-than (>) relationship, whereas the nominal data contain only an equality (=) relationship. 19 Types of Quantitative Data 3. Interval Data: If we have data with ordinal properties (> & =) and can also measure the distance between two data items, we have an interval measurement. 20 Types of Quantitative Data Interval data are preferred over ordinal data because, with them, decision makers can precisely determine the difference between two observations, i.e., distances between numbers can be measured. For example, frozen-food packagers have daily contact with a common interval measurement-- temperature. 21 Types of Quantitative Data 4. Ratio Data: is the highest level of measurement and allows for all basic arithmetic operations, including division and multiplication. Data measured on a ratio scale have a fixed or non- arbitrary zero point. Examples include: business data, such as cost, revenue and profit. 22 Types of Data Data may be categorized as: 1. Secondary: Data which are already available. An example: statistical abstract Economic Review, data in books, journals or any other storage medium, etc. Advantage: less expensive. Disadvantage: may not satisfy one’s needs. 2. Primary Data: Data which must be collected. 23 Data Collection Methods Methods for collecting primary data include: 1. Focus Group 2. Interview 3. Questionnaires 4. Experimental designs. 24 Sampling Methods There are many ways to collect a sample. The most commonly used methods are: A. Statistical Sampling 1. Simple Random Sampling: is a method of selecting items from a population such that every possible sample of specific size has an equal chance of being selected. In this case, sampling may be with or without replacement. 25 Sampling Methods A. Statistical Sampling 2. Stratified Random Sampling: is obtained by selecting simple random samples from strata (or mutually exclusive sets). Some of the criteria for dividing a population into strata are: Sex (male, female); Age (under 18, 18 to 28, 29 to 39). 26 Sampling Methods A. Statistical Sampling 3. Cluster Sampling: Is a simple random sample of groups or cluster of elements. Cluster sampling is useful when it is difficult or costly to generate a simple random sample. 27 Sampling Methods A. Statistical Sampling 3. Cluster Sampling: Example: To estimate the average annual household income in a large city we use cluster sampling, because: to use simple random sampling we need a complete list of households in the city from which to sample. 28 Sampling Methods A. Statistical Sampling 3. Cluster Sampling: Example: To estimate the average annual household income in a large city we use cluster sampling, because: To use stratified random sampling, we would again need the list of households. 29 Sampling Methods A. Statistical Sampling 3. Cluster Sampling: Example: To estimate the average annual household income in a large city we use cluster sampling. It is a less expensive way that lets each block within the city represent a cluster. 30 Sampling Methods A. Statistical Sampling 3. Cluster Sampling: Example: To estimate the average annual household income in a large city we use cluster sampling. A sample of clusters could then be randomly selected, and every household within these clusters could be interviewed to find the average annual household income. 31 Sampling Methods B. Non-Statistical Sampling 1. Judgment Sampling: In this case, the person taking the sample has direct or indirect control over which items are selected for the sample. 32 Sampling Methods B. Non-Statistical Sampling 2. Convenience Sampling: In this method, the decision maker selects a sample from the population in a manner that is relatively easy and convenient. 33 Sampling Methods B. Non-Statistical Sampling 3. Quota Sampling: In this method, the decision maker requires the sample to contain a certain number of items with a given characteristic. Many political polls are, in part, quota sampling. 34