Analyzing OneVariable Data Lesson 1 1 Statistics The

Analyzing One-Variable Data Lesson 1. 1 Statistics: The Science and Art of Data Statistics and Probability with Applications, 3 rd Edition Starnes & Tabor Bedford Freeman Worth Publishers

Statistics: The Science and Art of Data Learning Targets After this lesson, you should be able to: ü Identify the individuals and variables in a data set, then classify the variables as categorical or quantitative. ü Summarize the distribution of a variable with a frequency table or a relative frequency table. Statistics and Probability with Applications, 3 rd Edition 2

Statistics: The Science and Art of Data We live in a world of data. Every day, we encounter data from scientific studies to poll results to test scores to analyses about sports. To understand what the data are saying, you need to learn more about statistics. An understanding of statistics will help you make good decisions based on data. Statistics is the science and art of collecting, analyzing, and drawing conclusions from data. Statistics and Probability with Applications, 3 rd Edition 3

Statistics: The Science and Art of Data Statistical Problem-Solving Process � Ask Questions: Clarify the research problem and ask one or more valid statistics questions. � Collect Data: Design and carry out an appropriate plan to collect the data. � Analyze Data: Use appropriate graphical and numerical methods to analyze the data. � Interpret Results: Draw conclusions based on the data analysis. Be sure to answer the research question(s)! Statistics and Probability with Applications, 3 rd Edition 4

Statistics: The Science and Art of Data Individual, Variable • An individual is a person, animal, or thing described in a set of data. • A variable is any attribute that can take different values for different individuals. Statistics and Probability with Applications, 3 rd Edition 5

Statistics: The Science and Art of Data Variable • A variable is any attribute that can take different values for different individuals. Categorical Variable Quantitative Variable A categorical variable assigns labels that place individuals into particular groups. A quantitative variable takes number values for which it makes sense to find an average. Statistics and Probability with Applications, 3 rd Edition 6

S l i d e 2 7 Types of Variables Qualitative or Categorical Variables Consists of attributes, labels, or nonnumerical entries. Major Place of birth Eye color Common statistic calculated: percentages rd Edition Larson/Farber 4 th ed. Statistics and Probability with Applications, 3 77

S l i d e 2 8 Quantitative Variables Measured with units and answers questions about the quantity of what is measured. Age Weight of a letter Temperature Common statistic calculated: averages rd Edition Larson/Farber 4 th ed. Statistics and Probability with Applications, 3 88

S l i d e 2 9 BEWARE!! Not all numerical variables can be classified as quantitative variables. For example, consider the following list of zip codes: 07446 08204 07028 10704 These data values of the variable zip codes are certainly Numerical, however, they are labeling locations and do Not have units of measure. Therefore zip code is a Categorical variable!! Statistics and Probability with Applications, 3 rd Edition 9

Statistics: The Science and Art of Data Statistics and Probability with Applications, 3 rd Edition 10

Statistics: The Science and Art of Data • A variable generally takes values that vary from one individual to another. The distribution of a variable describes the pattern of variation of these values. Distribution The distribution of a variable tells us what values the variable takes and how often it takes these values. Statistics and Probability with Applications, 3 rd Edition 11

Statistics: The Science and Art of Data • We can summarize a variable’s distribution with a frequency table or a relative frequency table. Frequency Table A frequency table shows the count of individuals having each data value. Relative Frequency Table A relative frequency table shows the proportion or percent of individuals having each data value. Statistics and Probability with Applications, 3 rd Edition 12

LESSON APP 1. 1 What are my classmates like? On the first day of a statistics course, the instructor gave all 40 students in the class a survey. The table below shows data from the first 10 students on the class roster. Identify the individuals and variables in this data set. Classify each variable as either categorical or quantitative. Dominant Hand Children in Family Homework Last Night (min) Sleep (hours) Have a Smartphone? Gender Class GPA Pulse Rate F Fr 3. 22 72 R 3 0 -14 10 Y F Fr 2. 3 110 L 3 0 -14 8 N M Ju 3. 8 60 L 6 15 -29 7 Y M So 3. 1 72 R 2 15 -29 7. 5 Y F So 4 51 R 1 45 -59 7 Y F So 3. 4 68 R 4 0 -14 8. 5 Y F So 3 80 R 3 30 -44 7 Y M So 3. 5 59 R 2 30 -44 7 Y M Fr 3. 9 65 R 2 15 -29 6 Y M Sr 3. 5 144 R 2 0 -14 7 N … Statistics and Probability with Applications, 3 rd Edition 13

Statistics: The Science and Art of Data Learning Targets After this lesson, you should be able to: ü Identify the individuals and variables in a data set, then classify the variables as categorical or quantitative. ü Summarize the distribution of a variable with a frequency table or a relative frequency table. Statistics and Probability with Applications, 3 rd Edition 14