Giao trinh bai tap statistics 1

STATISTICS FREQUENCY DISTRIBUTIONS & GRAPHS Vuong Ba Thinh Statistics ACKNOWLEDMENT  This slides are composed using the book: Allan G Bluman , Elementary Statistics: A Step by Step Approach, eighth edition 2012 Statistics OUTLINE  Organizing Data  Histograms, Frequency Polygons, and Ogives  Other Types of Graphs  R functions  Q&A Statistics Introduction  Raw Data  Organizing Data  Presenting Data  Example: a study on the ages of the top 50 wealthiest people in the world  raw data Statistics Organizing Data  How? Statistics Organizing Data (1)  Frequency Distribution  A frequency distribution consists of classes and their corresponding frequencies  Each raw data value is placed into a quantitative or qualitative category called a class  The frequency of a class then is the number of data values contained in a specific class Statistics Organizing Data (2)  A frequency distribution is the organization of raw data in table form, using classes and frequencies  Two types of frequency distributions: frequency distribution, grouped frequency distribution Statistics Organizing Data (3)  Categorical Frequency Distributions  nominal or ordinal-level data  EX: Twenty-five army inductees were given a blood test to determine their blood type The data set is Construct a frequency distribution for the data Statistics Organizing Data (4) Statistics Organizing Data (5)  Grouped Frequency Distributions  grouped frequency distribution: When the range of the data is large, the data must be grouped into classes that are more than one unit in width  EX: a distribution of the number of hours that boat batteries lasted is the following 10 Statistics Histograms, Frequency Polygons, & Ogives  A picture is worth a thousand words 15 Statistics Histograms  The histogram is a graph that displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes  EX: Construct a histogram to represent the data shown for the record high temperatures for each of the 50 states 16 Statistics Frequency Polygons  The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes The frequencies are represented by the heights of the points  EX: 17 Statistics Ogives  The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution  Cumulative frequency graphs are used to visually represent how many values are below a certain upper class boundary  EX: 18 Statistics 19 Statistics Relative Frequency Graphs 20 Statistics Other Types of Graphs  Bar graph, Pareto chart, time series graph, and pie graph  A bar graph represents the data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data 21 Statistics Other Types of Graphs (2)  A Pareto chart is used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest  EX: Number of Homeless 22 Statistics Other Types of Graphs (3)  A time series graph represents data that occur over a specific period of time  EX: Workplace Homicides 23 Statistics Other Types of Graphs (4)  A pie graph is a circle that is divided into sections according to the percentage of frequencies in each category of the distribution  EX: blood types of the army inductees 24 Statistics Misleading Graphs 25 Statistics Misleading Graphs (2) 26 Statistics Misleading Graphs (3) 27 Statistics R functions  ???  R Studio, or Google 28 Statistics Q&A 29 Statistics [...]... equal in width 11 Statistics Organizing Data (7) 12 Statistics Applying the Concepts  The data represent the ages of our Presidents at the time they were first inaugurated 1 Were the data obtained from a population or a sample? Explain your answer 2 What was the age of the oldest President? 3 What was the age of the youngest President? 4 Construct a frequency distribution for the data 13 Statistics Applying... many values are below a certain upper class boundary  EX: 18 Statistics 19 Statistics Relative Frequency Graphs 20 Statistics Other Types of Graphs  Bar graph, Pareto chart, time series graph, and pie graph  A bar graph represents the data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data 21 Statistics Other Types of Graphs (2)  A Pareto chart is... the data shown for the record high temperatures for each of the 50 states 16 Statistics Frequency Polygons  The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes The frequencies are represented by the heights of the points  EX: 17 Statistics Ogives  The ogive is a graph that represents the cumulative frequencies... any peaks in the distribution? 6 ldentify any possible outliers 7 Write a brief summary of the nature of the data as shown in the frequency distribution 14 Statistics Histograms, Frequency Polygons, & Ogives  A picture is worth a thousand words 15 Statistics Histograms  The histogram is a graph that displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various... 22 Statistics Other Types of Graphs (3)  A time series graph represents data that occur over a specific period of time  EX: Workplace Homicides 23 Statistics Other Types of Graphs (4)  A pie graph is a circle that is divided into sections according to the percentage of frequencies in each category of the distribution  EX: blood types of the army inductees 24 Statistics Misleading Graphs 25 Statistics. .. in each category of the distribution  EX: blood types of the army inductees 24 Statistics Misleading Graphs 25 Statistics Misleading Graphs (2) 26 Statistics Misleading Graphs (3) 27 Statistics R functions  ???  R Studio, or Google 28 Statistics Q&A 29 Statistics ... inductees 24 Statistics Misleading Graphs 25 Statistics Misleading Graphs (2) 26 Statistics Misleading Graphs (3) 27 Statistics R functions  ???  R Studio, or Google 28 Statistics Q&A 29 Statistics. .. represent how many values are below a certain upper class boundary  EX: 18 Statistics 19 Statistics Relative Frequency Graphs 20 Statistics Other Types of Graphs  Bar graph, Pareto chart, time series... continuous  The classes must be exhaustive  The classes must be equal in width 11 Statistics Organizing Data (7) 12 Statistics Applying the Concepts  The data represent the ages of our Presidents