SESSION 1 & 2

1. SESSION 1 & 2 Last Update 15th February 2011 Introduction to Statistics

3. Learning Unit 1 (10 Sessions) • Give a description of statistical techniques • Construct a frequency distribution table • Represent data in tabular or graphical form • Distinguish between different graphical representation forms

4. Session 1 & 2 • Concepts and Definitions • Terminology • Data types • Graphical representations

5. Definitions Statistics is the name given to the science of collecting facts, typically in numerical form, and studying or analysing them. The facts, or data, can cover a wide range of subjects. The science of statistics deals with the methods used in the collection, presentation, analysis and interpretation of data.

6. Definitions cont. Statistics is a way to get information from data.

7. Descriptive Statistics • Methods of organizing, summarizing and presenting data in a convenient and informative way. • Numerical techniques to summarize data: Measure of Central location or Measure of Variability.

8. Inferential Statistics • Body of methods used to draw conclusions or inferences about characteristics of a population based on sample data. • “Estimation”

9. Statistical Concepts • The Population is Group of all items of interest to the statistical practitioner. • The Sample is a set of data drawn from the population. A descriptive measure of the sample is called a statistic. • Statistical Inference is the process of making an estimate, prediction, or decision about a population based on sample data.

10. Statistical Concepts • A Variable is some characteristic of a population or sample. • The values of the variable are the possible observations of the variable. • Data are the observed values of a variable.

11. Example Stock Statistical Inference

12. Example Test Marks Statistical Inference

13. Data Types • Interval data are real numbers, such as heights, weights, incomes, and distance. • Example stock performance in %:

14. Data Types • The values of nominal data are categories. Nominal data is often recorded by arbitrarily assigning a number to each category • Example Marital Status:

15. Data Types • Ordinal data appear nominal but their values are in order. • Example students evaluating course: Codes are arbitrary. Thus, no meaningful interpretation of the results.

16. Calculations Data Types • All calculations are allowed on interval data (e.g. calculating the average). • Codes in nominal data are arbitrary. Averages are not meaningful; Observations can be described counting the number of each category and report the frequencies frequencies.

17. Example Frequencies • Original responses: 1 2 2 2 4 1 2 2 1 3 4 4 4 3 • Frequency table / Proportions:

18. Calculations Data Types • The only permissible calculations for ordinal data are ones involving a ranking process (e.g. the median).

19. Data Collection Primary Data vs Secondary Data

20. Primary Data • Questionnaires / Surveys • Cannot be looked up elsewhere • The collection is performed by observation, survey, experimental research conducted for a part of total population under consideration - sample

21. Data Collection Discrete Data vs Continuous Data

22. Discrete Data • A random variable whose observations can take on only specific values, usually only integer (whole number) values, is referred to as a discrete random variable. • Example • Statistic test marks (0 to 100) • Number of students in a class room • The outcomes of tossing a die • The outcome of tossing a coin (binary)

23. Continuous Data • Data that are measured on a scale, such as mass or temperature, are called continuous data. • Example • Time it takes a student to complete a statistics test • The weight / height of a student • The return on a stock

24. Graphical Techniques • Nominal Data: Bar charts / pie charts • Interval data: Frequency distribution tables and histograms