Chapter 1 Introduction to Statistics PDF

CHAPTER 1 1 An Introduction to Statistics  Key concepts to understand You must be able to define these concepts and provide examples of each. ∙ Statistics ∙ Population ∙ Parameter ∙ Sample ∙ Sample statistic ∙ Variable ∙ Values...

CHAPTER 1 1 An Introduction to Statistics  Key concepts to understand You must be able to define these concepts and provide examples of each. ∙ Statistics ∙ Population ∙ Parameter ∙ Sample ∙ Sample statistic ∙ Variable ∙ Values ∙ Data ∙ Random Variable (RV) ∙ Discrete RV ∙ Continuous RV ∙ Types of Data (Qualitative; Quantitative) ∙ Scales of measurement (Nominal; Ordinal; Interval; Ratio) ∙ Descriptive Statistics 2 ∙ Inferential Statistics ⮚ What is Statistics? - Statistics is used everywhere, every day, in every field of study – business, education, politics, sports, retail etc. - It’s a tool used to make sense (understand) of information that is collected. - Information is collected in many different ways like when you surf the internet / when you buy something using an account / voting at an election / watching TV OR in a more formal way through surveys or censuses. - That information or observations collected is called raw data and is then organised, analysed and interpreted in a systematic way. - This process of collecting, organising, analysing and disseminating of data is basically what Statistics is all about. 3  Statistics ⮚ Descriptive Statistics ⮚ Inferential Statistics - Collection, arrangement, - Process of inferring an estimate, summarisation and presentation of prediction or decision about a data population based on sample data - Methods used are graphs, tables and - Methods are measuring the reliability numerical measures of conclusions based on the - Ch’s 1 to 5 information from a sample of the population - Ch’s 6 to 8 4  Definitions and concepts ⮚ Population (N) - Total number of objects/subjects being studied - Finite population = limited or fixed size – countable - Infinite population = impossible to measure - no limit – uncountable ⮚ Parameter ( µ , σ, σ2 etc) - A number that describes a characteristic of the population - P goes with P Example: The average age of 1000 registered BUS132 students in 2016 was 19. What is the population? What is the population size? What is the parameter? What is the size of the parameter? 5 ⮚ Sample (n) - Subset drawn/taken from the population - Must be representative of the population and not a biased sample – random selection 6  How do we link sample statistics to parameters? We use the sample statistics to do calculations and analyses to then make a decision or conclusion or inference about the population parameters. Example 1.3; Pg 2 The 49 numbers from which the lotto numbers are drawn constitutes a population of 49 items. The six numbers that are randomly drawn are a sample from the population. The largest number in the population is 49 and it is a population parameter which could be denoted by the Greek letter α, thus α = 49. If the sample consists of the numbers 5, 21, 3, 42, 10 and 11 the sample maximum is 42 and could be denoted by the Roman letter a, thus a = 42.. 7 ⮚ Variable (age, gender, test scores) A characteristic being observed that can take on different values in different people or objects. ⮚ Values (Test scores between 0 & 100) All possible observations of a variable. The actual number representing each person or object. ⮚ Data (All the marks of Test 1 for the entire class = data) The observed values of a variable or information collected or attained. ⮚ Random Variable (Corresponding lower case letters and a subscript) A characteristic being observed or measured that is collected randomly. 8 Example 1.5; Pg 5 Let the RV represent tree height Y a) If the height of the tenth tree in the population of trees is 3 metres, then y10 = 3 b) If the height of the second tree is 4 meters, then y2 = 4 Example 1.6; Pg 5 In a candy shop, let the RV be the price of sweets X a) If the price of the first packet of sweets on the shelf is R4.50, then x1 = R4.50 b) If the price of the second packet of sweets on the shelf is R6.75, then x2 = R6.75 9 ⮚ Discrete RV (integers / whole numbers) A variable that can only assume distinct values. A constant = variable that can assume only 1 value. ⮚ Continuous RV (a fraction / decimal) A variable that can assume any value within a specified interval. Height, mass, etc. Qualitative Variable Quantitative Variable - Described by non-numeric/ - Described by numbers. categorical responses. Usually - Suitable for performing calculations described by words and referred to on data values. as attribute variables. - Discrete and continuous RV - e.g. eye colour, place of residence, - e.g. age, height, weight, etc. marital status etc. 10  Quantitative Qualitative Scales of Measurement ⮚ Nominal Scale ⮚ Ordinal Scale ⮚ Interval Scale ⮚ Ratio Scale - Words describing - Appears nominal - Numeric - Numeric categories - Non-Numeric - > or < - > or < - Non-numeric - Only one category - Has a unit of - Has a unit of - Categories are mutually - Categories are ranked or measurement – can measurement – can exclusive ordered calculate the distance or calculate the distance or - Not ranked or ordered - When coding, maintain difference between difference between - Min 2 categories the order or ranking categories categories - Can be coded but no - Can only order the data - Has no meaningful zero - Has a meaningful or calculations can be done and then split into equal point or absolute zero absolute zero point – not with these codes parts like percentiles, point present or not observable - Can only count number deciles, quartiles etc. Eg: Temperature; Time Eg: Age, height, weight, of occurrences - Can construct a box plot etc. - Pie chart or bar graph - No unit of measurement Eg: marital status, place of Eg: marathon rankings; birth, favourite colour world tennis rankings, rating the restaurant service etc. 11 Readings: Ch. 1 & 2 Exercises: End of Ch. 1 (Pgs. 15 – 16)