STAT 1053 Week One: Chapters 1 - 2
STAT 1053 Week One: Chapters 1 - 2 STAT 1053
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This 6 page Class Notes was uploaded by Morgan Routman on Wednesday January 14, 2015. The Class Notes belongs to STAT 1053 at George Washington University taught by Professor Balaji in Winter2015. Since its upload, it has received 384 views. For similar materials see Intro to Statistics for Social Sciences in Statistics at George Washington University.
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STAT 1053 Ch 1 Introduction 11415 820 PM What is Statistics 0 The Science of Collection and Analysis of Data 9 handling data 0 Aspects Classifying Summarizing Organizing Analyzing Interpreting first three descriptive last two inferential 2 Types Numerical and Graphical methods used to look for patterns in a set of data and present them in a convenient form covered in Chapter 2 Used to make estimates decisions and predictions about a given population Ie probability exercises covered in Chapter 3 main part of the course 0 Terms to know 0 a collection of individuals or objects in a study 0 a subset of the population 0 a characteristic of interest about an individual of a population or sample 0 Number or information with a context Different characteristics are measured for different individuals in the population or sample 0 Applications of Statistics 0 Ranges from calculating the average height or females in America to income variance or effectiveness of drugs etc Essentially statistics can be used in all sorts of different ways to find specific data for a specific population two types 0 Variables that can assume numerical Values 0 Must be able to add and subtract this data Ie number of students enrolled in GW between 95 and now 0 Variables that are not numerical 0 Observations are categorized into different groups 0 Cannot be added or subtracted Ie Blood Types 0 data can be obtained in several ways depending on the situation Published source Designed experiment Surveys Observational study 0 should be representative of the populationshould have the characteristics of the population 0 Can be done in different ways 0 O O O a Each element of the population has the same chance of being selected a Can be done either with or without replacement a The first element is picked at random and the rest are picked systematically at every Kth interval a Stratify the sample frame and then a select fixed number is selected from the population a Sampling some of but not all of the possible subdivisions of the population STAT 1053 Ch 2 Descriptive Stats 11415 820 PM 0 Observations can be classified 0 Not Numerical o Tabular System Frequency Distribution Relative Freq Distribution 0 Graphical System Pie Chart Bar Chart o Tabular summary of data showing how the values in a sample are distributed 0 Objective is to provide insight about data that can t be quickly obtained by looking at the data itself Number of times a value occurs in a set FrequencyTotal Number of Values a Total of relative frequency should add up to 1 EXAMPLE The following is a set of ratings that students gave of a writing class Average Bad Good Good Bas Good Good Average Poor Good Excellent Average Good Average Good Excellent Average Good Good Poor A frequency table for this data would look like this Rating Tallies Frequency Relative Freq Poor ll 2 01 Bad ll 2 01 Average lllll 5 025 Good lllll llll 9 045 ExceHent ll 2 01 TOTAL 20 1 o Graphical method of depicting Qualitative data from frequency distributions and relative frequency distributions Xaxis represents the categories or classes Yaxis represents the frequency Fixed Width for all of the bars There should be gaps between each of the bars o Graphical method of depicting Qualitative data from frequency distributions and relative frequency distributions 0 The circle represents the entire data set Every sector represents the relative frequency of the class its representing Multiply the relative frequency by 360 to get the angle for each sector a The larger the relative frequency the larger the angle and vice versa 0000 O 0 Numerical Data 0 ie SAT Scores salaries unemployment rates 0 When summarizing we want to see distribution of variables shown via different kinds of plots Essentially a bar graph with dots The more often a variable appears in a set of data the more dots go above the value on the Xaxis The leading digits go into the left column to make up the stem while the following digits go into the right column to create the leaves Arrange the stems from smallest to largest number and the leaves in order of magnitude The units of the stems can change as well EXAMPLE Use this set of data to create a stem and leaf plot 35 36 42 06 21 27 32 O 6 2 17 3 256 4 2 Essentially splits the left column into more rows so that if one stem has a lot of leaves it can be separated into two or more stems Essentially just a bar graph with the bars being connected Can be skewed positively if the slope leans to the left negatively if the slope leans to the right or be symmetrical Frequency Distribution is constructed by counting the number of observations and putting them into classes I There should be between 5 and 20 classes a The larger the dataset the more classes there should be and vice versa a Class width largest observation smallest observation the number of classes a The number of classes the square root of total observation EXAMPLE Determine classes for the following set of data 85 89 74 76 78 88 96 94 99 76 63 51 57 67 79 89 93 727778 There are 20 data points total Take the square root of 20 and you get a value somewhere between 4 and 5 The class width must be greater or equal to the range of the dataset and the number of classes 99575 96 Round this to the nearest whole number and we get 10 as our class width Therefore the classes for this histogram would be 5060 6070 7080 8090 90100 These are the points that are marked on the xaxis of the histogram so that the bars are attached The yaxis is the frequency