Statistics Lecture 1: Introduction and Descriptive Statistics, Lecture notes of Statistics

Download Statistics Lecture 1: Introduction and Descriptive Statistics and more Lecture notes Statistics in PDF only on Docsity! LECTURE 1 INTRODUCTION & DESCRIPTIVE STATISTICS I PROBABILITY AND STATISTICS Adapted from http://www.prenhall.com/mcclave OUTLINE 1. Introduce Course Objectives and Requirements 2. Introduce Statistics and its Applications 3. Describe Types of Data, Ways of Collecting Data 4. Introduce Graphical Methods for Describing Data of 1 variable STUDY MATERIALS  Study materials: lecture notes, required readings, tutorial exercises, etc.  Please note that the materials will be posted and/or updated on Google classroom.  Google classroom is important for class management, notifications, handling questions, study materials, etc. RECOMMENDED STUDY STRATEGIES • Discuss lecture notes with your peers. Review your lecture notes weekly • Attempt all the tutorial exercises before class • Participate in class: ask questions, contribute ideas, volunteer to present solutions, take notes, etc. • Read the assigned readings in textbook • Work actively on your project and the labs • Do further reading if you have time WHAT IS STATISTICS? 1. Collecting Data 2. Presenting Data 3. Characterizing Data 4. Other activities: estimation, hypothesis testing… Question? Data Analysis Decision- Making © 1984-1994 T/Maker Co. © 1984-1994 T/Maker Co. DESCRIPTIVE STATISTICS 1. Involves  Summarizing Data  Presenting Data  Looking for patterns in data 2. Purpose  Describe Data X = 30.5 S2 = 113 Source: https://chartio.com/learn/charts/grouped-bar-chart-complete-guide/ INFERENTIAL STATISTICS 1. Involves  Estimation  Hypothesis Testing  … 2. Purpose  Make Decisions About Population Characteristics Population? STATISTICAL METHODS 1- Descriptive Statistics utilizes numerical and graphical methods to look for patterns in a data set, to summarize the information revealed in a data set and to present the information in a convenient form. 2- Inferential Statistics utilizes sample data to make estimates, decisions, predictions, or other generalizations about a larger set of data. EXAMPLE If we are interested in the number of hours per day the average high school Vietnamese student spends sending text messages? Work in pairs and answer the following questions:  What would be the population?  Why would a sample be necessary?  What could be the variables of interest? DATA TYPES • Why data types are important? • Basic types of data:  Quantitative (numerical) versus Qualitative (categorical) • Examples • Are there numbers that are not quantitative? SCALES OF MEASUREMENT Ratio Interval Ordinal Nominal Quantitative Qualitative DESCRIPTIVE STATISTICS Graphical Methods Numerical Methods Descriptive Statistics We will now explore graphical methods GRAPHICAL METHODS FOR 1 CATEGORICAL VARIABLE 1 categorical variable Graphing Data Pie Chart Pareto Diagram Bar Chart Frequency Distribution Table Tabulating Data SOME TERMS 1- A class is one of the categories into which qualitative data can be classified. 2- The class frequency is the number of observations in the data set falling into a particular class. (Frequency = Count). 3- The class relative frequency is the class frequency divided by the total number of observations in the data set. 0 50 100 150 Acct. Econ. Mgmt. BAR CHART Horizontal Bars for Categorica l Variables Bar Length Shows Frequency or % 1/2 to 1 Bar Width Equal Bar Widths Zero Point Frequency Major Percent Used Also Note that we may wish to use a vertical bar chart Econ. 10% Mgmt. 25% Acct. 65% PIE CHART 1. Shows Breakdown of Total Quantity into Categories 2. Angle Size  (360°)(Percent) Majors (360°) (10%) = 36° 36° SMALL DISCUSSION When to use bar chart or pie chart? EXAMPLE: HUDSON AUTO REPAIR  The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in her shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed below. FREQUENCY DISTRIBUTION TABLE STEPS  1. Determine Range  2. Select Number of Classes  Usually Between 5 & 15 Inclusive  3. Compute Class Width  4. Determine Class Boundaries (Limits)  5. Compute Class Midpoints  6. Count Observations & Assign to Classes FREQUENCY DISTRIBUTION 50-60 60-70 70-80 80-90 90-100 100-110 2 13 16 7 7 5 50 4 26 32 14 14 10 100 Parts Cost ($) Frequency Percent Note: in this example, class 50-60 means parts costs from $50 up to but not including $60. Other classes can be interpreted similarly. DESCRIBING DISTRIBUTIONS Frequency -24 Score (a) Normal (b) Bimodal Frequency Frequency 5 10 15 20 25 Score 0 (d) Positively skewed (c) Negatively skewed © Cengage Leaming Figure 3.9 Shapes of frequency distributions: (a) normal, (b) bimodal, (c) negatively skewed, (d) positively skewed, DESCRIBING DISTRIBUTIONS Start of analysis: plot data Look for  Overall pattern  Shape  Center  Spread  Outliers  Modality  Possible groups SOME GUIDELINES ON GRAPHS •Provide a main title •Label the axes •Try to start both X and Y axis at 0. •Avoid distorting data •Abolish chartjunk: don’t use patterns, 3-D effects, shadows, pictures… •Avoid excess ink