Introduction to Probability & Statistics

1. Introduction to Probability & Statistics Dhon G. Dungca, M.Eng’g.

2. STATISTICS • The branch of mathematics that deals with the systematic method of collecting, classifying, presenting, analyzing and interpreting quantitative or numerical data.

3. IMPORTANCE • Research • Forecasting business trends and sales • Economic activities such as investments • Production • Quality control

4. I HOPE THIS ISN’T STATISTICS

5. Realities about Statistics • The man in the street distrusts statistics and despises [his image of] statisticians, those who diligently collect irrelevant facts and figures and use them to manipulate society. “There are three kinds of lies: lies, damned lies, and statistics” – Mark Twaine • One can not go about without statistics. “Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital.” – Aaron Levenstein

6. Florence Nightingale on Statistics • “...the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, all organization based on experience, for it only gives results of our experience.” • “To understand God's thoughts, we must study statistics, for these are the measures of His purpose.”

7. Statistics (not Stat-is-eeks) • Data is the foundation of any statistical analysis • Purpose of using statistics: • Use data to describe, explain, predict, make decisions

8. Come on! It can‘t go wrong every time...

9. DIVISION OF STATISTICS • Descriptive Statistics • Collection, organization, summarization, and presentation of data. • Inferential Statistics • Generalizing from samples to populations using probabilities. Performing hypothesis testing, determining relationships between variables, and making predictions.

10. STEPS IN A STATISTICAL INQUIRY OR INVESTIGATION • Collection of data • Processing of data • Presentation of data • Analysis of data • Interpretation of data

11. CLASSIFICATION OF COLLECTED DATA • Primary Data • refer to the data obtained directly from an original source by means of actual observations or by conducting interviews. • Secondary Data • refer to data or information that come from existing records (published or unpublished) in usable form such as surveys, census, business journals, magazines, newspapers, commercial publications, theses, research papers, etc. • Internal Data • data taken from the company’s own records of operations such as sales records, production records, personnel records, etc. • External Data • data that come from outside sources and not from the company’s own records.

12. METHODS OF DATA COLLECTION • Interview or Direct Method • The research worker gets the needed data from the respondent verbally and directly in a face-to-face contact. • Questionnaire or Indirect Method • The questionnaire is a data-gathering instrument to acquire the needed data. • Registration Method • Examples are records of births, marriages, and deaths at the National Census and Statistics Office. • Observation • Is employed when certain information cannot be secured through the use of the other methods of data collection. • Experimentation

13. SOME STATISTICAL TERMS Population vs Sample The population (N) includes all objects of interest whereas the sample (n) is only a portion of the population. Parameters are associated with populations and statistics with samples. Parameters are usually denoted using Greek letters (, ) while statistics are usually denoted using Roman letters (x, s). There are several reasons why we don't work with populations. They are usually large, and it is often impossible to get data for every object we're studying. Sampling does not usually occur without cost, and the more items surveyed, the larger the cost. We compute statistics, and use them to estimate parameters. The computation is the first part of the statistics course (Descriptive Statistics) and the estimation is the second part (Inferential Statistics)

14. SOME STATISTICAL TERMS Variables and Constants • Variable • Characteristic or attribute that can assume different values • Random Variable • A variable whose values are determined by chance. • Qualitative Variables • Variables which assume non-numerical values. • Quantitative Variables • Variables which assume numerical values.

15. LEVELS OF MEASUREMENT • Nominal Level • Level of measurement which classifies data into mutually exclusive, all inclusive categories in which no order or ranking can be imposed on the data. • Ordinal Level • Level of measurement which classifies data into categories that can be ranked. Differences between the ranks do not exist. • Interval Level • Level of measurement which classifies data that can be ranked and differences are meaningful. However, there is no meaningful zero, so ratios are meaningless. • Ratio Level • Level of measurement which classifies data that can be ranked, differences are meaningful, and there is a true zero. True ratios exist between the different units of measure.

16. TYPES OF SAMPLING • Random sampling is analogous to putting everyone's name into a hat and drawing out several names. Each element in the population has an equal chance of occuring. While this is the preferred way of sampling, it is often difficult to do. It requires that a complete list of every element in the population be obtained. Computer generated lists are often used with random sampling. • Systematic sampling is easier to do than random sampling. In systematic sampling, the list of elements is "counted off". That is, every kth element is taken. This is similar to lining everyone up and numbering off "1,2,3,4; 1,2,3,4; etc". When done numbering, all people numbered 4 would be used. • Convenience sampling is very easy to do, but it's probably the worst technique to use. In convenience sampling, readily available data is used. That is, the first people the surveyor runs into.

17. TYPES OF SAMPLING • Cluster sampling is accomplished by dividing the population into groups -- usually geographically. These groups are called clusters or blocks. The clusters are randomly selected, and each element in the selected clusters are used. • Stratified sampling also divides the population into groups called strata. However, this time it is by some characteristic, not geographically. For instance, the population might be separated into males and females. A sample is taken from each of these strata using either random, systematic, or convenience sampling.

18. PRESENTATION OF DATA • Textual Presentation • Combines text and figures in a statistical report. An example of this is a news item in the newspaper. • Tabular Presentation • The data are presented through tables consisting of vertical columns and horizontal rows with headings describing these rows and columns. • Graphic Presentation • Use of graphs as most effective means of presenting statistical data. • Bar Graph • Line Graph • Pie Chart • Scatter Diagram • Pictogram