This document contains slides summarizing concepts for summarizing qualitative and quantitative data. For qualitative data, it discusses frequency distributions, relative frequency distributions, bar graphs, and pie charts. For quantitative data, it discusses frequency distributions, histograms, measures of central tendency including mean, median, and mode, and measures of variability. Examples are provided to illustrate these concepts using data on guest ratings at a hotel and costs of car repairs.
This document discusses various methods for summarizing and exploring qualitative and quantitative data through tabular and graphical techniques, including frequency distributions, relative frequency distributions, bar graphs, pie charts, histograms, scatter plots, and cross-tabulations. It provides examples and explanations of how to construct and interpret these summaries and graphs using sample customer satisfaction and automobile repair data. The goal is to gain insights about relationships within the data that are not evident from just looking at the original values.
Descriptive Statistics Part II: Graphical Descriptiongetyourcheaton
The document provides information on descriptive statistics and graphical descriptions of data, including bar charts, pie charts, histograms, and cumulative frequency distributions. It discusses how to construct these various graphs using Excel and includes examples and questions to describe and interpret the graphs. Key information that can be obtained from these graphs includes the mode, range, percentages of observations within certain classes or below/above certain values, and comparing values across categories.
This document provides an introduction to quantitative methods and statistics. It defines key terms like descriptive statistics, measures of central tendency, measures of dispersion, probability, random events, and probability distributions. Examples are given to illustrate concepts like mean, median, mode, variance, and objective vs. subjective probability. Scales of measurement are explained including nominal, ordinal, interval, and ratio scales. The document is intended to introduce foundational statistical concepts.
This document summarizes chapter 3 section 2 of an elementary statistics textbook. It discusses measures of variation, including range, variance, and standard deviation. The standard deviation describes how spread out data values are from the mean and is used to determine consistency and predictability within a specified interval. Several examples demonstrate calculating range, variance, and standard deviation for data sets. Chebyshev's theorem and the empirical rule relate standard deviations to the percentage of values that fall within certain intervals of the mean.
This document provides an overview of key numerical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It defines each measure, provides examples of calculating them, and discusses their characteristics, uses, and advantages/disadvantages. The document also covers weighted means, geometric means, Chebyshev's theorem, and calculating measures for grouped data.
The document discusses various graphical methods for describing data, including bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It provides examples of each using sample student data on vision correction, weights, ages, and GPAs to illustrate how to construct and interpret the different graph types.
This document discusses analytical representation of data through descriptive statistics. It begins by showing raw, unorganized data on movie genre ratings. It then demonstrates organizing this data into a frequency distribution table and bar graph to better analyze and describe the data. It also calculates averages for each movie genre. The document then discusses additional descriptive statistics measures like the mean, median, mode, and percentiles to further analyze data through measures of central tendency and dispersion.
This document provides an overview of measures of central tendency including the mean, median, and mode. It discusses how to calculate and interpret each measure using examples with data sets. The mean is calculated by adding all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently. Other measures discussed include the midrange and calculating the mean from a frequency distribution. Proper rounding of measures is also covered.
This document discusses various methods for summarizing and exploring qualitative and quantitative data through tabular and graphical techniques, including frequency distributions, relative frequency distributions, bar graphs, pie charts, histograms, scatter plots, and cross-tabulations. It provides examples and explanations of how to construct and interpret these summaries and graphs using sample customer satisfaction and automobile repair data. The goal is to gain insights about relationships within the data that are not evident from just looking at the original values.
Descriptive Statistics Part II: Graphical Descriptiongetyourcheaton
The document provides information on descriptive statistics and graphical descriptions of data, including bar charts, pie charts, histograms, and cumulative frequency distributions. It discusses how to construct these various graphs using Excel and includes examples and questions to describe and interpret the graphs. Key information that can be obtained from these graphs includes the mode, range, percentages of observations within certain classes or below/above certain values, and comparing values across categories.
This document provides an introduction to quantitative methods and statistics. It defines key terms like descriptive statistics, measures of central tendency, measures of dispersion, probability, random events, and probability distributions. Examples are given to illustrate concepts like mean, median, mode, variance, and objective vs. subjective probability. Scales of measurement are explained including nominal, ordinal, interval, and ratio scales. The document is intended to introduce foundational statistical concepts.
This document summarizes chapter 3 section 2 of an elementary statistics textbook. It discusses measures of variation, including range, variance, and standard deviation. The standard deviation describes how spread out data values are from the mean and is used to determine consistency and predictability within a specified interval. Several examples demonstrate calculating range, variance, and standard deviation for data sets. Chebyshev's theorem and the empirical rule relate standard deviations to the percentage of values that fall within certain intervals of the mean.
This document provides an overview of key numerical measures used to describe data, including measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation). It defines each measure, provides examples of calculating them, and discusses their characteristics, uses, and advantages/disadvantages. The document also covers weighted means, geometric means, Chebyshev's theorem, and calculating measures for grouped data.
The document discusses various graphical methods for describing data, including bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It provides examples of each using sample student data on vision correction, weights, ages, and GPAs to illustrate how to construct and interpret the different graph types.
This document discusses analytical representation of data through descriptive statistics. It begins by showing raw, unorganized data on movie genre ratings. It then demonstrates organizing this data into a frequency distribution table and bar graph to better analyze and describe the data. It also calculates averages for each movie genre. The document then discusses additional descriptive statistics measures like the mean, median, mode, and percentiles to further analyze data through measures of central tendency and dispersion.
This document provides an overview of measures of central tendency including the mean, median, and mode. It discusses how to calculate and interpret each measure using examples with data sets. The mean is calculated by adding all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the value that occurs most frequently. Other measures discussed include the midrange and calculating the mean from a frequency distribution. Proper rounding of measures is also covered.
The document contains a frequency distribution table that summarizes data from a questionnaire regarding a university computer service system. The table includes frequencies and percentages for respondent demographics like gender (72% male, 28% female), age group (50% between 21-23 years old, 34% 24-26, 16% over 26), GPA range, and academic program of study. A second section of the questionnaire assessed satisfaction levels of system quality on a 5-point scale.
This chapter discusses methods for describing and exploring data, including dot plots, stem-and-leaf displays, quartiles, box plots, and other statistical techniques. It provides examples of how to construct and interpret these graphical representations of data distribution, and how they can be used to analyze sets of observations and identify patterns. Key concepts covered are quartiles, interquartile range, outliers, and using box plots to visualize the spread and central tendency of data.
This document provides an overview of measures of relative standing and boxplots. It defines key terms like percentiles, quartiles, and outliers. Percentiles and quartiles divide a data set into groups based on the number of data points that fall below each value. The document also provides examples of calculating percentiles and quartiles for a data set of cell phone data speeds. Boxplots use the five-number summary (minimum, Q1, Q2, Q3, maximum) to visually depict a data set's center and spread through its quartiles and outliers.
- The document discusses different statistical measures including the mean, median, and mode.
- It provides examples of calculating the mean, median, and mode from sets of data. For example, it calculates the mean number of days students were absent from school based on attendance records.
- The examples demonstrate how to determine the measure, possible limitations, and common uses of each statistical measure.
This document provides information about various statistical concepts including variables, probability, distributions, hypothesis testing, and Python libraries for statistical analysis. It defines different types of variables, such as continuous, discrete, categorical, and their examples. It also explains concepts like population, sample, central tendency, dispersion, probability, distributions, hypothesis testing, t-test, z-test, ANOVA. Finally, it mentions commonly used Python libraries like SciPy for conducting statistical tests and analysis.
1) The document discusses concepts related to probability distributions including uniform, normal, and binomial distributions.
2) It provides examples of calculating probabilities and values using the uniform, normal, and binomial distributions as well as the normal approximation to the binomial.
3) Key concepts covered include means, standard deviations, z-values, areas under the normal curve, and the continuity correction factor for approximating binomial with normal.
This document summarizes the key topics and concepts covered in Chapter 2 of the 9th edition of the business statistics textbook "Presenting Data in Tables and Charts". The chapter discusses guidelines for analyzing data and organizing both numerical and categorical data. It then covers various methods for tabulating and graphing univariate and bivariate data, including tables, histograms, frequency distributions, scatter plots, bar charts, pie charts, and contingency tables.
This document outlines key concepts about discrete probability distributions. It defines probability distributions and random variables, distinguishing between discrete and continuous distributions. It describes how to calculate the mean, variance, and standard deviation of discrete distributions. The document also provides details on the binomial and Poisson probability distributions, including their characteristics and how to compute probabilities using them. Examples are provided to illustrate calculating probabilities and distribution properties.
The median is the middle value when values are ordered from lowest to highest. It divides the data set such that half the values are lower than the median and half are higher. For an even number of values, the median is the average of the two middle values. The mode is the most frequently occurring value. It indicates the most common result. Both the median and mode are less influenced by outliers than the mean. They provide a more representative central value for skewed or irregularly distributed data sets.
Quantitative Methods for Lawyers - Class #20 - Regression Analysis - Part 3Daniel Katz
This document discusses multiple regression analysis and some key assumptions and issues that can arise. It provides an example of using multiple regression to estimate SAT scores based on various state-level factors like expenditures, income levels, education levels etc. It discusses how to detect issues like heteroskedasticity and multicollinearity that can violate the assumptions of regression analysis. It demonstrates how to use robust standard errors to account for heteroskedasticity and examines variance inflation factors to check for multicollinearity issues.
1) The document discusses density curves and normal distributions, which are important mathematical models for describing the overall pattern of data. A density curve describes the distribution of a large number of observations.
2) It specifically covers the normal distribution and some of its key properties, including that about 68%, 95%, and 99.7% of observations fall within 1, 2, and 3 standard deviations of the mean, respectively.
3) The document shows how to work with normal distributions using techniques like standardizing data, finding areas under the normal curve using the standard normal table, and assessing normality with a normal quantile plot.
Applied Business Statistics ,ken black , ch 3 part 1AbdelmonsifFadl
This document provides an overview of descriptive statistics concepts including measures of central tendency (mean, median, mode), measures of variability (range, standard deviation, variance), and how to calculate these measures from both ungrouped and grouped data. It defines key terms, explains how to compute various statistics, and includes example problems and solutions. The learning objectives are to understand and be able to compute different descriptive statistics and apply concepts like the empirical rule and Chebyshev's theorem.
This document discusses various measures of dispersion used in statistics. It defines dispersion as measuring how varied or spread out data values are from the average. The document outlines both absolute measures like range and interquartile range, and relative measures like coefficient of range and coefficient of variation. It provides examples of calculating each measure and discusses their properties, merits, limitations, and uses. The key measures covered are range, interquartile range, mean deviation, and how to calculate them from both raw data and frequency distributions.
This document discusses measures of position such as percentile rank and quartiles. It provides examples of calculating percentile rank for a data value and finding the data value that corresponds to a given percentile. Quartiles (Q1, Q2, Q3) divide a data set into quarters. The second quartile is the median. Examples demonstrate finding quartiles for a data set and drawing and interpreting a box plot.
The document discusses the importance and key concepts of statistics. It introduces three main reasons to study statistics: to be an informed consumer of information, to understand and make decisions, and to evaluate decisions that affect one's life. It then defines important statistical terms like population, sample, variable, and data types. It also provides examples of different data sets and ways to organize data, such as through frequency distributions, bar charts, and dot plots.
This document provides a summary of key statistical concepts and practice test questions. It covers topics such as types of variables, populations and samples, measures of central tendency and variation, frequency distributions, and levels of measurement. Several questions from a practice test on introductory statistics are presented and answered, involving calculations of mean, median, mode, variance, standard deviation, and interpreting frequency tables and distributions. Examples of different sampling methods and types of studies are also defined.
This document provides information about descriptive statistics including measures of central tendency (mean, median, mode) and measures of variation (range, interquartile range, variance, standard deviation). It defines these terms and provides examples using IQ score data from two classes (Class A and Class B) to illustrate how to calculate and interpret these descriptive statistics. The key takeaway is that descriptive statistics are useful for summarizing and comparing characteristics of different groups or datasets in a concise manner.
This document discusses descriptive statistics and measures of central tendency. It defines raw data and descriptive measures. It describes organizing data through ordered arrays and grouped data using frequency distributions. Methods for determining the number of class intervals and class width are provided. Common measures of central tendency - the mean, median and mode - are defined. The mean is the sum of all values divided by the total number. The median is the middle value of ordered data. Examples are given to demonstrate calculating these statistics.
This document discusses different measures of variability in data, including range, interquartile range, standard deviation, and variance. It provides examples calculating each measure using students' quiz scores. Range is the distance between the highest and lowest values, while interquartile range describes the middle 50% of scores. Standard deviation and variance measure how dispersed all values are from the mean by taking the average of squared deviations from the mean. Standard deviation is the square root of variance and is commonly used in inferential statistics.
This document defines key terms and formulas related to circles. It defines a circle as having a center and radius, and defines diameter as the longest chord passing through the center. It provides the formulas for calculating the perimeter and area of a circle using radius and pi. It also defines arc length as the length of an arc based on the central angle, and defines a sector as part of a circle extending to the center, providing the formula to calculate sector area.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document contains a frequency distribution table that summarizes data from a questionnaire regarding a university computer service system. The table includes frequencies and percentages for respondent demographics like gender (72% male, 28% female), age group (50% between 21-23 years old, 34% 24-26, 16% over 26), GPA range, and academic program of study. A second section of the questionnaire assessed satisfaction levels of system quality on a 5-point scale.
This chapter discusses methods for describing and exploring data, including dot plots, stem-and-leaf displays, quartiles, box plots, and other statistical techniques. It provides examples of how to construct and interpret these graphical representations of data distribution, and how they can be used to analyze sets of observations and identify patterns. Key concepts covered are quartiles, interquartile range, outliers, and using box plots to visualize the spread and central tendency of data.
This document provides an overview of measures of relative standing and boxplots. It defines key terms like percentiles, quartiles, and outliers. Percentiles and quartiles divide a data set into groups based on the number of data points that fall below each value. The document also provides examples of calculating percentiles and quartiles for a data set of cell phone data speeds. Boxplots use the five-number summary (minimum, Q1, Q2, Q3, maximum) to visually depict a data set's center and spread through its quartiles and outliers.
- The document discusses different statistical measures including the mean, median, and mode.
- It provides examples of calculating the mean, median, and mode from sets of data. For example, it calculates the mean number of days students were absent from school based on attendance records.
- The examples demonstrate how to determine the measure, possible limitations, and common uses of each statistical measure.
This document provides information about various statistical concepts including variables, probability, distributions, hypothesis testing, and Python libraries for statistical analysis. It defines different types of variables, such as continuous, discrete, categorical, and their examples. It also explains concepts like population, sample, central tendency, dispersion, probability, distributions, hypothesis testing, t-test, z-test, ANOVA. Finally, it mentions commonly used Python libraries like SciPy for conducting statistical tests and analysis.
1) The document discusses concepts related to probability distributions including uniform, normal, and binomial distributions.
2) It provides examples of calculating probabilities and values using the uniform, normal, and binomial distributions as well as the normal approximation to the binomial.
3) Key concepts covered include means, standard deviations, z-values, areas under the normal curve, and the continuity correction factor for approximating binomial with normal.
This document summarizes the key topics and concepts covered in Chapter 2 of the 9th edition of the business statistics textbook "Presenting Data in Tables and Charts". The chapter discusses guidelines for analyzing data and organizing both numerical and categorical data. It then covers various methods for tabulating and graphing univariate and bivariate data, including tables, histograms, frequency distributions, scatter plots, bar charts, pie charts, and contingency tables.
This document outlines key concepts about discrete probability distributions. It defines probability distributions and random variables, distinguishing between discrete and continuous distributions. It describes how to calculate the mean, variance, and standard deviation of discrete distributions. The document also provides details on the binomial and Poisson probability distributions, including their characteristics and how to compute probabilities using them. Examples are provided to illustrate calculating probabilities and distribution properties.
The median is the middle value when values are ordered from lowest to highest. It divides the data set such that half the values are lower than the median and half are higher. For an even number of values, the median is the average of the two middle values. The mode is the most frequently occurring value. It indicates the most common result. Both the median and mode are less influenced by outliers than the mean. They provide a more representative central value for skewed or irregularly distributed data sets.
Quantitative Methods for Lawyers - Class #20 - Regression Analysis - Part 3Daniel Katz
This document discusses multiple regression analysis and some key assumptions and issues that can arise. It provides an example of using multiple regression to estimate SAT scores based on various state-level factors like expenditures, income levels, education levels etc. It discusses how to detect issues like heteroskedasticity and multicollinearity that can violate the assumptions of regression analysis. It demonstrates how to use robust standard errors to account for heteroskedasticity and examines variance inflation factors to check for multicollinearity issues.
1) The document discusses density curves and normal distributions, which are important mathematical models for describing the overall pattern of data. A density curve describes the distribution of a large number of observations.
2) It specifically covers the normal distribution and some of its key properties, including that about 68%, 95%, and 99.7% of observations fall within 1, 2, and 3 standard deviations of the mean, respectively.
3) The document shows how to work with normal distributions using techniques like standardizing data, finding areas under the normal curve using the standard normal table, and assessing normality with a normal quantile plot.
Applied Business Statistics ,ken black , ch 3 part 1AbdelmonsifFadl
This document provides an overview of descriptive statistics concepts including measures of central tendency (mean, median, mode), measures of variability (range, standard deviation, variance), and how to calculate these measures from both ungrouped and grouped data. It defines key terms, explains how to compute various statistics, and includes example problems and solutions. The learning objectives are to understand and be able to compute different descriptive statistics and apply concepts like the empirical rule and Chebyshev's theorem.
This document discusses various measures of dispersion used in statistics. It defines dispersion as measuring how varied or spread out data values are from the average. The document outlines both absolute measures like range and interquartile range, and relative measures like coefficient of range and coefficient of variation. It provides examples of calculating each measure and discusses their properties, merits, limitations, and uses. The key measures covered are range, interquartile range, mean deviation, and how to calculate them from both raw data and frequency distributions.
This document discusses measures of position such as percentile rank and quartiles. It provides examples of calculating percentile rank for a data value and finding the data value that corresponds to a given percentile. Quartiles (Q1, Q2, Q3) divide a data set into quarters. The second quartile is the median. Examples demonstrate finding quartiles for a data set and drawing and interpreting a box plot.
The document discusses the importance and key concepts of statistics. It introduces three main reasons to study statistics: to be an informed consumer of information, to understand and make decisions, and to evaluate decisions that affect one's life. It then defines important statistical terms like population, sample, variable, and data types. It also provides examples of different data sets and ways to organize data, such as through frequency distributions, bar charts, and dot plots.
This document provides a summary of key statistical concepts and practice test questions. It covers topics such as types of variables, populations and samples, measures of central tendency and variation, frequency distributions, and levels of measurement. Several questions from a practice test on introductory statistics are presented and answered, involving calculations of mean, median, mode, variance, standard deviation, and interpreting frequency tables and distributions. Examples of different sampling methods and types of studies are also defined.
This document provides information about descriptive statistics including measures of central tendency (mean, median, mode) and measures of variation (range, interquartile range, variance, standard deviation). It defines these terms and provides examples using IQ score data from two classes (Class A and Class B) to illustrate how to calculate and interpret these descriptive statistics. The key takeaway is that descriptive statistics are useful for summarizing and comparing characteristics of different groups or datasets in a concise manner.
This document discusses descriptive statistics and measures of central tendency. It defines raw data and descriptive measures. It describes organizing data through ordered arrays and grouped data using frequency distributions. Methods for determining the number of class intervals and class width are provided. Common measures of central tendency - the mean, median and mode - are defined. The mean is the sum of all values divided by the total number. The median is the middle value of ordered data. Examples are given to demonstrate calculating these statistics.
This document discusses different measures of variability in data, including range, interquartile range, standard deviation, and variance. It provides examples calculating each measure using students' quiz scores. Range is the distance between the highest and lowest values, while interquartile range describes the middle 50% of scores. Standard deviation and variance measure how dispersed all values are from the mean by taking the average of squared deviations from the mean. Standard deviation is the square root of variance and is commonly used in inferential statistics.
This document defines key terms and formulas related to circles. It defines a circle as having a center and radius, and defines diameter as the longest chord passing through the center. It provides the formulas for calculating the perimeter and area of a circle using radius and pi. It also defines arc length as the length of an arc based on the central angle, and defines a sector as part of a circle extending to the center, providing the formula to calculate sector area.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document summarizes a lesson plan for teaching 8th standard students about adding negative numbers. The teacher uses various activities like grouping students, using sequences and coins to demonstrate positive and negative numbers, and a chart to record results of coin tosses. Students actively participate in the group activities and coin toss game. They solve practice problems and homework assignments on adding negative numbers. An enrichment activity asks students to represent a financial situation using negative numbers.
1. The document is an innovative English lesson plan submitted by a teacher named Smitha A. It includes details about the lesson such as the subject, unit, learning outcomes, content analysis, and classroom activities.
2. The lesson focuses on the one-act play "The Princess on the Road" and teaches students about analyzing literature, group work, and raising awareness about women's issues.
3. The classroom activities include introducing the playwright and title, modeling reading aloud, group discussions, answering scaffolding questions, and presenting summaries. The goal is for students to understand the themes and characters in the play.
This lesson plan is for teaching a unit from the short story "The Tattered Blanket" by Kamala Das. The plan outlines teaching the first two paragraphs, which show the pathetic condition of an old mother who has lost her memory and the arrival of her son after a long time. The plan details the objectives, prerequisites, resources, procedures, and activities that will be used to help students read and analyze the literary text to understand the theme of weakening family ties and the importance of one's roots. Activities include reading aloud, vocabulary work, group discussion, writing assignments, and using online resources.
This lesson plan introduces 8th grade students to the concept of another multiplication using negative numbers. The teacher uses examples like (-3)*4*(-5) and asks students to work through the steps to solve it. Students learn that -*-=+ and -+-=-. They work in groups on a "magic square" activity involving multiplying negatives. The lesson reinforces that multiplying negatives results in multiples of odds or evens. Homework assignments are provided practicing negative number multiplication.
The document discusses the three main types of weathering that cause rocks to break into small pieces. Mechanical weathering is caused by temperature changes that make rocks expand and contract, causing them to peel off in layers. Chemical weathering results from chemical reactions between minerals in rocks and rainwater that cause the rocks to disintegrate. Biological weathering is driven by tree roots and small creatures penetrating cracks in rocks and breaking them apart.
This document describes an innovative learning aid for teaching vocabulary to students. The aid uses pictures with words and their meanings to help students easily learn and remember new vocabulary. It consists of sheets with pictures in holes and windows covering the words and meanings. Teachers rotate the sheets to reveal the pictures, words, and meanings to students one by one. This keeps students engaged and makes vocabulary learning an enjoyable activity. The goal is to help students better understand and retain difficult words from their textbooks in a memorable way.
This document outlines the steps in staffing which include manpower planning, recruitment, selection, placement, orientation, training, performance appraisal, promotions, and compensation. It provides details on each step. Manpower planning involves quantitative and qualitative analysis to determine personnel needs. Recruitment identifies sources for employees within and outside the organization. Selection involves choosing applicants through an elimination process. Placement assigns selected candidates to positions. Orientation introduces new employees. Training empowers employees with skills. Performance appraisal evaluates employee performance. Promotions move employees to higher level jobs. Compensation considers work, skills, risks, and qualifications in designing fair pay plans.
The document discusses the importance of integrating information and communication technology (ICT) into teacher education programs. It notes that both pre-service and in-service teacher training are currently inadequate. ICT can help improve teacher training by providing new ways for teachers to access information and changing relationships between teachers and students. The document outlines different approaches to using ICT in the classroom, such as integrated, enhancement, and complementary approaches. It also discusses the National Council for Teacher Education's curriculum areas and how ICT and e-learning are transforming education through tools like MOOCs, online resources, and educational software. Overall, the document advocates for improving teacher training through the strategic integration of ICT.
1. The document discusses various methods for summarizing categorical and quantitative data through tables and graphs, including frequency distributions, relative frequency distributions, bar charts, pie charts, dot plots, histograms, and ogives.
2. An example using data on customer ratings from a hotel illustrates frequency distributions and pie charts.
3. Another example using costs of auto parts demonstrates frequency distributions, histograms, and ogives.
The document provides information about descriptive statistics, summarizing qualitative and quantitative data, and various methods for presenting data visually. It discusses frequency distributions, relative and percent frequency distributions, bar graphs, pie charts, dot plots, histograms, and cumulative distributions as ways to summarize data in a clear manner. Guidelines are given for selecting class widths and numbers when creating frequency distributions. Examples using data on hotel ratings and auto repair part costs are presented to illustrate the various statistical and graphical techniques.
The document provides information on methods for summarizing qualitative and quantitative data through tables, graphs, and exploratory data analysis techniques. Key methods discussed include frequency distributions, relative frequency distributions, bar graphs, pie charts, histograms, cumulative distributions, ogives, stem-and-leaf displays, and exploratory data analysis techniques. Worked examples using guest rating and auto repair cost data illustrate how to construct and interpret these various summarization methods.
This document provides examples and explanations of various graphical methods for describing data, including frequency distributions, bar charts, pie charts, stem-and-leaf diagrams, histograms, and cumulative relative frequency plots. It demonstrates how to construct these graphs using sample data on student weights, grades, ages, and other examples. The goal is to help readers understand different ways to visually represent data distributions and patterns.
This document discusses various methods for summarizing and presenting data, including:
- Frequency distributions to summarize qualitative and quantitative data using tables.
- Graphical representations like bar graphs, pie charts, dot plots, histograms and ogives to visualize patterns in the data.
- Cross tabulations and scatter diagrams to understand relationships between two variables.
Examples using data from hotels, auto repair shops, and football are provided to illustrate each method. The goal is to gain insights from the data that cannot be seen from the raw numbers alone.
This document discusses frequency distributions and how to construct them from raw data. It provides examples of creating stem-and-leaf displays, frequency tables, relative frequency tables, and cumulative frequency tables from various data sets. Key concepts covered include class width, class boundaries, tallying data, and calculating relative frequencies and percentages. Overall, the document serves as a tutorial on how to organize and summarize data using various types of frequency distributions.
It's about statistical methods.
Data analysis,Grouped-Ungrouped data,Mean,Median,Mode,Percentile,Standard Deviation,Variance,Frequency Distribution Graphs,Corelation
The document provides examples and explanations of different types of graphs and charts used to represent qualitative data, including bar charts, pie charts, histograms, frequency polygons, cumulative frequency polygons, and stem-and-leaf displays. It gives step-by-step instructions on constructing each graph or chart using sample data sets and how to interpret the results.
The document discusses organizing and presenting data through descriptive statistics. It covers types of data, constructing frequency distribution tables, calculating relative frequencies and percentages, and using graphical methods like bar graphs, pie charts, histograms and polygons to summarize categorical and quantitative data. Examples are provided to demonstrate how to organize data into frequency distributions and calculate relative frequencies to graph the results.
This document discusses frequency distributions and graphic presentations of data. It defines a frequency distribution as a grouping of data into categories showing the number of observations in each category. It describes the steps to construct a frequency distribution and provides examples using employee salary data. It also discusses types of graphic presentations like histograms, frequency polygons, cumulative frequency distributions, bar charts, and pie charts that can be used to visually display frequency distribution data.
The document describes descriptive statistics and methods for presenting qualitative and quantitative data. It discusses frequency distributions, relative frequencies, percentages and graphs including bar charts, pie charts, and line graphs. Examples show how to construct these graphs and calculate values for datasets. Exercises provide practice creating frequency tables, determining relative frequencies and percentages, and representing data using pie charts.
The document outlines key concepts in statistics including frequency distributions, measures of central tendency, dispersion, position, and distribution. It discusses grouped and ungrouped data, mean, median, mode, range, variance, standard deviation, quartiles, percentiles, skewness, kurtosis, and z-scores. Graphs like histograms, pie charts, and ogives are presented as ways to visually represent data. Formulas and examples are provided for calculating various statistical measures.
This chapter discusses numerical measures used to describe data, including measures of center (mean, median, mode), location (percentiles, quartiles), and variation (range, variance, standard deviation, coefficient of variation). It defines these terms and how to calculate and interpret them, as well as how to construct and use box and whisker plots to graphically display data distributions.
This document discusses frequency distributions and graphical presentations of data. It defines frequency distributions as the pattern of frequencies of a variable's values or grouped values. There are four main types of frequency distributions: ungrouped, grouped, relative, and cumulative. The document also describes three common graphical presentations: pie charts to show relative frequencies of categorical variables, bar charts to display frequency distributions of categorical variables, and histograms to illustrate quantitative variable distributions. The purpose of graphical presentations is to visually compare and relate data.
1. The document discusses different topics related to data collection and presentation including sources of data, data collection methods, processing data, and presenting data through graphs, tables, frequency distributions, and other visual formats.
2. Common data collection methods are surveys, observation, interviews, and existing sources; data must then be processed, organized, and cleaned before analysis.
3. Data can be presented visually through tables, graphs, frequency distributions and other charts to reveal patterns and insights in the data in a clear, understandable format.
TSTD 6251 Fall 2014SPSS Exercise and Assignment 120 PointsI.docxnanamonkton
TSTD 6251 Fall 2014
SPSS Exercise and Assignment 1
20 Points
In this class, we are going to study descriptive summary statistics and learn how to construct box plot. We are still working with univariate variable for this exercise.
Practice Example:
Admission receipts (in million of dollars) for a recent season are given below for the
n =
30 major league baseball teams:
19.4 26.6 22.9 44.5 24.4 19.0 27.5 19.9 22.8 19.0 16.9 15.2 25.7 19.0 15.5 17.1 15.6 10.6 16.2 15.6 15.4 18.2 15.5 14.2 9.5 9.9
10.7 11.9 26.7 17.5
Require:
a. Compute the mean, variance and standard deviation.
b. Find the sample median, first quartile, and third quartile.
c. Construct a boxplot and interpret the distribution of the data.
d. Discuss the distribution of this set of data by examining kurtosis and skewness
statistics, such as if the distribution is skewed to one side of the distribution, and if the
distribution shows a peaked/skinny curve or a spread out/flat curve.
SPSS Procedures for Computing Summary Statistics
:
Enter the 30 data values in the first column of SPSS
Data View
Tab
Variable View
and name this variable
receipts
Adjust
Decimals
to 3 decimal points
Type
Admission Receipts
($ mn)
in the
Label
column for output viewer
Return to
Data View
and click
A
nalyze
on the menu bar
Click the second menu
D
e
scriptive Statistics
Click
F
requencies …
Move
Admission Receipts
to the
Variable(s)
list by clicking the arrow button
Click
S
tatistics …
button at the top of the dialog box
Now, you can select the descriptive statistics according to what the question requires. For this practice question, it requires central tendency, dispersion, percentile and distribution statistics, so we click all the boxes
except for
P
ercentile(s): and Va
l
ues are group midpoints
.
Click
Continue
to return to the
Frequencies
dialog box
Click
OK
to generate descriptive statistic output which is pasted below:
The first table provides summary statistics and the second table lists frequencies, relative frequencies and cumulative frequencies. The statistics required for solving this problem are highlighted in red.
Statistics
Admission Receipts
N
Valid
30
Missing
0
Mean
18.76333
Std. Error of Mean
1.278590
Median
17.30000
Mode
19.000
Std. Deviation
7.003127
Variance
49.043782
Skewness
1.734
Std. Error of Skewness
.427
Kurtosis
5.160
Std. Error of Kurtosis
.833
Range
35.000
Minimum
9.500
Maximum
44.500
Sum
562.900
Percentiles
10
10.61000
20
14.40000
25
15.35000
30
15.50000
40
15.84000
50
17.30000
60
19.00000
70
19.75000
75
22.82500
80
24.10000
90
26.69000
Admission Receipts
Frequency
Percent
Valid Percent
Cumulative Percent
Valid
9.500
1
3.3
3.3
3.3
9.900
1
3.3
3.3
6.7
10.600
1
3.3
3.3
10.0
10.700
1
3.3
3.3
13.3
11.900
1
3.3
3.3
16.7
14.200
1
3.3
3.3
20.0
15.2.
This document provides an overview and examples of various statistical concepts and tools, including:
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Keynote presentation to the Educational Leaders hui Kōkiritia Marautanga held in Auckland on 26 June 2024. Provides a high level overview of the history and development of the science of learning, and implications for the design of learning in our modern schools and classrooms.
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This session represents an opportunity for the author to reflect on a volume he has just finished editing entitled Decolonizing UDL and to highlight and share insights into the key innovations, promising practices, and calls for change, originating from the Global South and Indigenous Communities, that have woven the canvas of this book. The session seeks to create a space for critical dialogue, for the challenging of existing power dynamics within the UDL scholarship, and for the emergence of transformative voices from underrepresented communities. The workshop will use the UDL principles scrupulously to engage participants in diverse ways (challenging single story approaches to the narrative that surrounds UDL implementation) , as well as offer multiple means of action and expression for them to gain ownership over the key themes and concerns of the session (by encouraging a broad range of interventions, contributions, and stances).
Information and Communication Technology in EducationMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 2)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐈𝐂𝐓 𝐢𝐧 𝐞𝐝𝐮𝐜𝐚𝐭𝐢𝐨𝐧:
Students will be able to explain the role and impact of Information and Communication Technology (ICT) in education. They will understand how ICT tools, such as computers, the internet, and educational software, enhance learning and teaching processes. By exploring various ICT applications, students will recognize how these technologies facilitate access to information, improve communication, support collaboration, and enable personalized learning experiences.
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐫𝐞𝐥𝐢𝐚𝐛𝐥𝐞 𝐬𝐨𝐮𝐫𝐜𝐞𝐬 𝐨𝐧 𝐭𝐡𝐞 𝐢𝐧𝐭𝐞𝐫𝐧𝐞𝐭:
-Students will be able to discuss what constitutes reliable sources on the internet. They will learn to identify key characteristics of trustworthy information, such as credibility, accuracy, and authority. By examining different types of online sources, students will develop skills to evaluate the reliability of websites and content, ensuring they can distinguish between reputable information and misinformation.
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 3)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
Lesson Outcomes:
- students will be able to identify and name various types of ornamental plants commonly used in landscaping and decoration, classifying them based on their characteristics such as foliage, flowering, and growth habits. They will understand the ecological, aesthetic, and economic benefits of ornamental plants, including their roles in improving air quality, providing habitats for wildlife, and enhancing the visual appeal of environments. Additionally, students will demonstrate knowledge of the basic requirements for growing ornamental plants, ensuring they can effectively cultivate and maintain these plants in various settings.
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This is a great way to be more productive but a few things to
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3. Slide 3
NATIONAL ANTHEM
Jana-gana-mana-adhinayaka,jaya he
Bharata-bhagya-vidhata.
Punjab-Sindh-Gujarat-Maratha
Dravida-Utkala-Banga
Vindhya-Himachala-Yamuna-Ganga
Uchchala –Jaladhi-taranga.
Tava shubha asisa jage,
Tava subha asisa mage,
Gahe tava jaya gatha,
Jana-gana-mangala-dayaka jaya he
Bharata-bhagya-vidhata.
Jaya he, jaya he, jaya he,
Jaya jaya jaya , jaya he!
PLEDGE
India is my country. All Indians are my brothers and sisters. I love my country, and I am proud
of its rich and varied heritage. I shall always strive to be worthy of it. I shall give respect to my
parents, teachers and all elders and treat everyone with courtesy. I pledge my devotion to my
country and my people. In their well-being and prosperity alone lies my happiness
4. Slide 4
INDEX
REVIEW ON OWN
• Summarizing Qualitative Data
• Summarizing Quantitative Data
• Measures of Location and Variability/Dispersion
5. Slide 5
Summarizing Qualitative Data
Frequency Distribution
Relative Frequency
Percent Frequency Distribution
Bar Graph
Pie Chart
6. Slide 6
Frequency Distribution
A frequency distribution is a tabular summary of
data showing the frequency (or number) of items in
each of several nonoverlapping classes.
The objective is to provide insights about the data
that cannot be quickly obtained by looking only at
the original data.
7. Slide 7
Example: Marada Inn
Guests staying at Marada Inn were asked to rate the
quality of their accommodations as being excellent,
above average, average, below average, or poor. The
ratings provided by a sample of 20 guests are shown
below.
Below Average Average Above Average
Above Average Above Average Above Average
Above Average Below Average Below Average
Average Poor Poor
Above Average Excellent Above Average
Average Above Average Average
Above Average Average
How many rated worse than average?
How many rated better than average?
8. Slide 8
Example: Marada Inn
Frequency Distribution
Rating Frequency
Poor 2
Below Average 3
Average 5
Above Average 9
Excellent 1
Total 20
How many rated worse than average?
How many rated better than average?
9. Slide 9
Example: Marada Inn
Frequency Distribution
Rating Frequency
Poor 2
Below Average 3
Average 5
Above Average 9
Excellent 1
Total 20
The GM of Marada Inn has a goal that no more than 10% of
all guests will rate their stay as worse than average.
How is the inn doing?
10. Slide 10
Relative Frequency and
Percent Frequency Distributions
The relative frequency of a class is the fraction or
proportion of the total number of data items
belonging to the class.
A relative frequency distribution is a tabular
summary of a set of data showing the relative
frequency for each class.
The percent frequency of a class is the relative
frequency multiplied by 100.
A percent frequency distribution is a tabular
summary of a set of data showing the percent
frequency for each class.
11. Slide 11
Example: Marada Inn
Relative Frequency and Percent Frequency
Distributions
Relative Percent
Rating Frequency Frequency
Poor .10 10
Below Average .15 15
Average .25 25
Above Average .45 45
Excellent .05 5
Total 1.00 100
12. Slide 12
Bar Graph
A bar graph is a graphical device for depicting
qualitative data that have been summarized in a
frequency, relative frequency, or percent frequency
distribution.
On the horizontal axis we specify the labels that are
used for each of the classes.
A frequency, relative frequency, or percent frequency
scale can be used for the vertical axis.
Using a bar of fixed width drawn above each class
label, we extend the height appropriately.
The bars are separated to emphasize the fact that
each class is a separate category.
13. Slide 13
Two Definitions
HISTOGRAM
• Quantitative data
BAR GRAPH
• Qualitative (non-numerical) data
• See examples that follow
14. Slide 14
Example: Marada Inn
Bar Graph
9
8
7
6
5
4
3
2
1
Poor Below
Average
Average Above
Average
Excellent
Frequency
Rating
15. Slide 15
ECO 6416 Grade Distribution
0% 0%
25%
50%
25%
60%
40%
20%
0%
A B C D F
16. Slide 16
3D BAR GRAPH
ECO 6416 Grade Distribution
100%
0% 0% 0% 0%
100%
50%
0%
A B C D F
17. Slide 17
Pie Chart
The pie chart is a commonly used graphical device
for presenting relative frequency distributions for
qualitative data.
First draw a circle; then use the relative frequencies
to subdivide the circle into sectors that correspond to
the relative frequency for each class.
Since there are 360 degrees in a circle, a class with a
relative frequency of .25 would consume .25(360) =
90 degrees of the circle.
19. Slide 19
Example: Marada Inn
Pie Chart
Poor
10%
Below
Average
15%
Average
25%
Above
Average
45%
Exc.
5%
Quality Ratings
20. Slide 20
Summarizing Quantitative Data
Frequency Distribution
Relative Frequency and Percent Frequency
Distributions
Histogram
21. Slide 21
Example: Hudson Auto Repair
The manager of Hudson Auto would like to get a
better picture of the distribution of costs for engine
tune-up parts. A sample of 50 customer invoices has
been taken and the costs of parts, rounded to the
nearest dollar, are listed below.
91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 74
62 82 98 101 79 105 79 69 62 73
22. Example: Frequency Distribution Table
Slide 22
This is what a frequency distribution table looks like
Cumulative
Relative Cumulative Percent
Cost ($) Frequency Frequency Frequency Frequency
50-59 2 .04 2 4
60-69 13 .26 15 30
70-79 16 .32 31 62
80-89 7 .14 38 76
90-99 7 .14 45 90
100-109 5 .10 50 100
Totals 50 1.00
23. Slide 23
Frequency Distribution
Guidelines for Selecting Number of Classes
• Use between 5 and 20 classes.
• Data sets with a larger number of elements
usually require a larger number of classes.
• Smaller data sets usually require fewer classes.
Guidelines for Selecting Width of Classes
• USE CLASSES OF EQUAL WIDTH
• Approximate Class Width =
Largest Data Value
Smallest Data Value
Number of Classes
24. Slide 24
Example: Hudson Auto Repair
Frequency Distribution
If we choose six classes:
Approximate Class Width = (109 - 52)/6 = 9.5 10
Cost ($) Frequency
50-59 2
60-69 13
70-79 16
80-89 7
90-99 7
100-109 5
Total 50
Would it be wrong if 50-59,60-79,80-89,90-99,100-109?
25. Slide 25
Example: Hudson Auto Repair
Relative Frequency and Percent Frequency
Distributions
Relative Percent
Cost ($) Frequency Frequency
50-59 .04 4
60-69 .26 26
70-79 .32 32
80-89 .14 14
90-99 .14 14
100-109 .10 10
Total 1.00 100
26. Slide 26
Histogram
Another common graphical presentation of
quantitative data is a histogram.
The variable of interest is placed on the horizontal
axis and the frequency, relative frequency, or percent
frequency is placed on the vertical axis.
A rectangle is drawn above each class interval with
its height corresponding to the interval’s frequency,
relative frequency, or percent frequency.
Unlike a bar graph, a histogram has no natural
separation between rectangles of adjacent classes.
30. Slide 30
Example: Apartment Rents
Given below is a sample of monthly rent values ($)
for one-bedroom apartments. The data is a sample of 70
apartments in a particular city. The data are presented
in ascending order.
425 430 430 435 435 435 435 435 440 440
440 440 440 445 445 445 445 445 450 450
450 450 450 450 450 460 460 460 465 465
465 470 470 472 475 475 475 480 480 480
480 485 490 490 490 500 500 500 500 510
510 515 525 525 525 535 549 550 570 570
575 575 580 590 600 600 600 600 615 615
31. Slide 31
Mean
The mean of a data set is the average of all the data
values.
If the data are from a sample, the mean is denoted by
.
If the data are from a population, the mean is
denoted by (mu).
x
x
n
i
x
N
i
x
33. Slide 33
Median
The median of a data set is the value in the middle
when the data items are arranged in ascending order.
If there is an odd number of items, the median is the
value of the middle item.
If there is an even number of items, the median is the
average of the values for the middle two items.
34. Slide 34
Example: Apartment Rents
Median
Since 70 is even and ½ of 70 = 35, average 35th and
36th data values:
Median = (475 + 475)/2 = 475
425 430 430 435 435 435 435 435 440 440
440 440 440 445 445 445 445 445 450 450
450 450 450 450 450 460 460 460 465 465
465 470 470 472 475 475 475 480 480 480
480 485 490 490 490 500 500 500 500 510
510 515 525 525 525 535 549 550 570 570
575 575 580 590 600 600 600 600 615 615
35. Slide 35
Example: Apartment Rents
ALTERNATIVE METHOD - Median
Median = 50% percentile
i = (p/100)n = (50/100)70 = 35, average 35th and 36th
data values: (see later slide)
Median = (475 + 475)/2 = 475
36. Slide 36
Mode
The mode of a data set is the value that occurs with
greatest frequency.
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