This chapter discusses descriptive statistics including organizing and graphing qualitative and quantitative data, measures of central tendency, and measures of dispersion. It covers frequency distributions, histograms, polygons, measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), skewness, and cumulative frequency distributions. The objectives are to describe and interpret graphical displays of data, compute various statistical measures, and identify shapes of distributions.
This document summarizes key concepts from Chapter 1 of an introductory statistics textbook. It defines statistics, distinguishes between populations and samples, parameters and statistics, and descriptive and inferential statistics. It also classifies data types and levels of measurement, and discusses experimental design concepts like data collection methods and sampling techniques.
The document provides an introduction to statistics, describing key concepts such as:
- Descriptive statistics involves collecting and summarizing sample data, while inferential statistics uses sample results to draw conclusions about a population.
- A population is all individuals of interest, a sample is a subset of the population, and variables are characteristics measured about each individual.
- There are qualitative variables that categorize data and quantitative variables that quantify data numerically using scales like nominal, ordinal, interval, and ratio.
- Common statistical techniques involve gathering primary data through surveys, experiments, and observations or secondary data from published sources.
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.
The document provides information about measures of central tendency and dispersion in statistics. It discusses finding the mode, median, and mean of ungrouped and grouped data. It also discusses determining the range and interquartile range of ungrouped and grouped data. Formulas are provided for calculating the mean, median, mode, range, interquartile range, and variance of data sets. Examples are worked through to demonstrate calculating these statistical measures from raw data sets and frequency distribution tables.
This document provides information on simple and compound interest. It defines simple and compound interest, and outlines the key formulas used to calculate simple interest, simple amount, present value, and compound interest/future value. Several examples are provided to demonstrate calculating simple and compound interest for different scenarios involving principal amounts, interest rates, and time periods. Practice problems are also included for readers to work through.
Ringkasan dokumen tersebut adalah:
BAB 2 membahas teori dan konsep dasar hubungan antaretnik, meliputi teori ekologi, Freudian, struktur fungsionalisme, kelas, masyarakat majmuk, pasaran buruh terpisah, dan pilihan rasional. Juga dibahas konsep masyarakat, kebudayaan, ras, etnik, dan integrasi.
This document summarizes key concepts from Chapter 1 of an introductory statistics textbook. It defines statistics, distinguishes between populations and samples, parameters and statistics, and descriptive and inferential statistics. It also classifies data types and levels of measurement, and discusses experimental design concepts like data collection methods and sampling techniques.
The document provides an introduction to statistics, describing key concepts such as:
- Descriptive statistics involves collecting and summarizing sample data, while inferential statistics uses sample results to draw conclusions about a population.
- A population is all individuals of interest, a sample is a subset of the population, and variables are characteristics measured about each individual.
- There are qualitative variables that categorize data and quantitative variables that quantify data numerically using scales like nominal, ordinal, interval, and ratio.
- Common statistical techniques involve gathering primary data through surveys, experiments, and observations or secondary data from published sources.
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.
The document provides information about measures of central tendency and dispersion in statistics. It discusses finding the mode, median, and mean of ungrouped and grouped data. It also discusses determining the range and interquartile range of ungrouped and grouped data. Formulas are provided for calculating the mean, median, mode, range, interquartile range, and variance of data sets. Examples are worked through to demonstrate calculating these statistical measures from raw data sets and frequency distribution tables.
This document provides information on simple and compound interest. It defines simple and compound interest, and outlines the key formulas used to calculate simple interest, simple amount, present value, and compound interest/future value. Several examples are provided to demonstrate calculating simple and compound interest for different scenarios involving principal amounts, interest rates, and time periods. Practice problems are also included for readers to work through.
Ringkasan dokumen tersebut adalah:
BAB 2 membahas teori dan konsep dasar hubungan antaretnik, meliputi teori ekologi, Freudian, struktur fungsionalisme, kelas, masyarakat majmuk, pasaran buruh terpisah, dan pilihan rasional. Juga dibahas konsep masyarakat, kebudayaan, ras, etnik, dan integrasi.
The document discusses annuities and provides examples of calculating future and present values of ordinary annuity certain. It also discusses amortization schedules. Some key points:
- An annuity is a series of equal payments made at equal time intervals.
- Formulas are provided to calculate the future and present values of annuities based on interest rate, payment amount, number of periods.
- Examples demonstrate using the formulas to solve various annuity problems, including multi-rate annuities.
- Amortization schedules show the breakdown of principal and interest over the payment periods of a loan.
Financial Account group assignment on Financial statement of Golden Agricultureamykua
ย
This document provides an overview and examples of key financial statements including:
1) The balance sheet reports a company's assets, liabilities, and owner's equity at a point in time. It divides assets into current and long-term categories.
2) The income statement reports a company's revenues, expenses, and profits over a period of time. It follows revenue recognition and expense matching principles.
3) An example income statement from Golden Agri is presented showing revenues, expenses, and net income.
4) Financial statements provide important information to both internal and external users about a company's financial performance and health.
Kebebasan beragama di malaysia & hubungkait dengan perlembagaan Mel Cassie
ย
assalamua'laikum semua,
sedikit info berkaitan kebebasan agama dan hubungkait dgn perlembagaan. slide sy share ni hanyalah basic info. Banyak lagi yg perlu dikaji berkaitan isu kebebasan agama. Semoga slide ini sedikit sebanyak membantu anda dalam apa jua perkara
~ by melcassie ~
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.
Chapter 8 Measure of Dispersion of DataMISS ESTHER
ย
This document discusses measures of dispersion for ungrouped data. It defines dispersion as how scattered the values in a data set are. Measures of dispersion include range, interquartile range, variance and standard deviation. These measures quantify how spread out the data is by looking at the differences between values. Examples are provided to demonstrate calculating the range and comparing the dispersion of two data sets using dot plots.
The document lists various discourse markers used in the Malay language to structure ideas and indicate relationships between parts of speech. It categorizes discourse markers according to their function, such as adding information, expressing opinions, sequencing events, illustrating examples, indicating causes and effects, making comparisons, and emphasizing or contrasting ideas. Some common terms with similar meanings are also outlined.
The document is a list of 44 companies that have applied for sponsorship funding. It provides the company name, contact details including address, phone number and estimated amount of sponsorship funding requested ranging from RM200 to RM5000. The total estimated funding requested is RM36,500. The list is sorted alphabetically by company name and includes large Malaysian corporations across various industries such as petroleum, banking, telecommunications and food & beverage.
This document discusses the calculation of quartile deviation from both ungrouped and grouped data. It defines quartiles as values that divide a data distribution into four equal parts (Q1, Q2, Q3). The quartile deviation is half the difference between the first (Q1) and third (Q3) quartiles. It provides the steps to find Q1, Q3, and quartile deviation from ungrouped data by ranking scores and using quartile locators. For grouped data, it uses formulas involving class limits and cumulative frequencies to determine Q1 and Q3, then takes half their difference. An example calculation is shown.
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 discusses various types of graphic representations of data including graphs, diagrams, and charts. It describes graphs as a pictorial presentation of data using lines, bars, and dots. It explains the meaning and significance of graphs, compares tabular and graphic representations, and outlines general rules for constructing graphs. The document also discusses one variable graphs, two variable graphs, time series graphs, and different types of charts including histograms, frequency polygons, box plots, Pareto charts, fishbone diagrams, and more. It covers the merits, demerits, and limitations of using graphs.
The document discusses annuities and provides examples of calculating future and present values of ordinary annuity certain. It also discusses amortization schedules. Some key points:
- An annuity is a series of equal payments made at equal time intervals.
- Formulas are provided to calculate the future and present values of annuities based on interest rate, payment amount, number of periods.
- Examples demonstrate using the formulas to solve various annuity problems, including multi-rate annuities.
- Amortization schedules show the breakdown of principal and interest over the payment periods of a loan.
Financial Account group assignment on Financial statement of Golden Agricultureamykua
ย
This document provides an overview and examples of key financial statements including:
1) The balance sheet reports a company's assets, liabilities, and owner's equity at a point in time. It divides assets into current and long-term categories.
2) The income statement reports a company's revenues, expenses, and profits over a period of time. It follows revenue recognition and expense matching principles.
3) An example income statement from Golden Agri is presented showing revenues, expenses, and net income.
4) Financial statements provide important information to both internal and external users about a company's financial performance and health.
Kebebasan beragama di malaysia & hubungkait dengan perlembagaan Mel Cassie
ย
assalamua'laikum semua,
sedikit info berkaitan kebebasan agama dan hubungkait dgn perlembagaan. slide sy share ni hanyalah basic info. Banyak lagi yg perlu dikaji berkaitan isu kebebasan agama. Semoga slide ini sedikit sebanyak membantu anda dalam apa jua perkara
~ by melcassie ~
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.
Chapter 8 Measure of Dispersion of DataMISS ESTHER
ย
This document discusses measures of dispersion for ungrouped data. It defines dispersion as how scattered the values in a data set are. Measures of dispersion include range, interquartile range, variance and standard deviation. These measures quantify how spread out the data is by looking at the differences between values. Examples are provided to demonstrate calculating the range and comparing the dispersion of two data sets using dot plots.
The document lists various discourse markers used in the Malay language to structure ideas and indicate relationships between parts of speech. It categorizes discourse markers according to their function, such as adding information, expressing opinions, sequencing events, illustrating examples, indicating causes and effects, making comparisons, and emphasizing or contrasting ideas. Some common terms with similar meanings are also outlined.
The document is a list of 44 companies that have applied for sponsorship funding. It provides the company name, contact details including address, phone number and estimated amount of sponsorship funding requested ranging from RM200 to RM5000. The total estimated funding requested is RM36,500. The list is sorted alphabetically by company name and includes large Malaysian corporations across various industries such as petroleum, banking, telecommunications and food & beverage.
This document discusses the calculation of quartile deviation from both ungrouped and grouped data. It defines quartiles as values that divide a data distribution into four equal parts (Q1, Q2, Q3). The quartile deviation is half the difference between the first (Q1) and third (Q3) quartiles. It provides the steps to find Q1, Q3, and quartile deviation from ungrouped data by ranking scores and using quartile locators. For grouped data, it uses formulas involving class limits and cumulative frequencies to determine Q1 and Q3, then takes half their difference. An example calculation is shown.
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 discusses various types of graphic representations of data including graphs, diagrams, and charts. It describes graphs as a pictorial presentation of data using lines, bars, and dots. It explains the meaning and significance of graphs, compares tabular and graphic representations, and outlines general rules for constructing graphs. The document also discusses one variable graphs, two variable graphs, time series graphs, and different types of charts including histograms, frequency polygons, box plots, Pareto charts, fishbone diagrams, and more. It covers the merits, demerits, and limitations of using graphs.
This document discusses various methods of graphically representing data, including:
1. It defines graphs and diagrams, and compares tabular and graphical representation. General rules for constructing graphs are also outlined.
2. One variable and two variable graphs are described. Specific types of graphs discussed include time series graphs, histograms, frequency polygons, cumulative frequency curves, range charts, and band diagrams.
3. Additional graph types analyzed are Pareto diagrams, fishbone diagrams, and box plots. Merits, limitations and uses of different graphs are mentioned.
This document discusses methods for organizing and presenting qualitative and quantitative data, including:
1. Organizing qualitative data into frequency tables and presenting them as bar charts or pie charts.
2. Organizing quantitative data into frequency distributions by grouping data into classes and showing the number of observations in each class. Frequency distributions can be presented as histograms, frequency polygons, or cumulative frequency distributions.
3. An example is provided of constructing a frequency distribution table by determining the number of classes, class interval, class limits, and tallying data into classes using vehicle selling prices. Relative frequency distributions are also discussed.
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.
The document discusses methods for organizing and presenting both qualitative and quantitative data, including frequency tables, bar charts, pie charts, and different types of frequency distributions. It provides examples of how to construct a frequency table by determining the number of classes, class intervals, and class limits based on a set of data. It also describes how to create histograms, frequency polygons, and cumulative frequency distributions to graphically display a frequency distribution and highlights key terms such as class frequency, class interval, and relative frequency.
This chapter discusses how to organize and present both qualitative and quantitative data using frequency tables, bar charts, pie charts, histograms, frequency polygons, and cumulative frequency distributions. It provides examples of how to construct frequency tables by determining the number of classes, class width, and class limits. It also explains how to convert frequency distributions to relative frequency distributions and how to represent the distributions graphically.
This document provides an introduction to descriptive statistics. It discusses organizing and presenting both qualitative and quantitative data. For qualitative data, it describes frequency distribution tables, relative frequencies, percentages, and graphs like bar charts and pie charts. For quantitative data, it covers stem-and-leaf displays, frequency distributions, class widths and midpoints, relative frequencies and percentages. It also discusses histograms for presenting grouped quantitative data. Examples are provided to illustrate these concepts and techniques.
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.
Frequency Tables, Frequency Distributions, and Graphic PresentationConflagratioNal Jahid
ย
This document provides an overview of key concepts for describing data through frequency tables, distributions, and graphs. It defines important terms like frequency table, distribution, class, interval and discusses how to organize both qualitative and quantitative data. Guidelines for data collection are provided. Examples are given to demonstrate how to construct frequency tables and distributions and convert them to relative frequencies. Finally, different types of graphs for presenting frequency distributions are described, including histograms, polygons and cumulative distributions.
Graphical Presentation of Data - Rangga Masyhuri Nuur LLU 27.pptxRanggaMasyhuriNuur
ย
The document discusses various graphical methods for presenting data, including histograms, polygons, pie charts, ogives, and stem-and-leaf plots. Histograms display the frequency distribution of data using bars of varying heights. Polygons connect the midpoints of histogram bars with straight lines. Pie charts represent proportions using circular slices. Ogives show cumulative frequencies with class limits on the x-axis and cumulative counts on the y-axis. Stem-and-leaf plots break values into "stems" and "leaves" for an organized display of the raw data. Examples are provided for constructing each type of graph using sample data sets.
1. This document discusses various quantitative techniques used in business, including measures of central tendency (mean, median, mode), cumulative frequency distributions, different types of graphs (pie charts, bar charts, histograms, frequency polygons), and methods for determining trends in time series data.
2. Measures of central tendency include the mean, median, and mode. Different measures are more appropriate depending on the data. The document also defines the arithmetic mean, geometric mean, median, and mode.
3. Graphs covered include pie charts, single/grouped/stacked bar charts, histograms, and frequency polygons. Trend analysis discusses using the method of least squares to fit a straight line trend to time series data.
This document discusses different types of graphs used to represent frequency distributions: bar graphs, histograms, frequency polygons, pie charts, and OGIVE charts. It provides instructions on how to construct each graph type, including labeling axes, ensuring proportionality, and adding titles and legends. Examples of each graph type are shown using sample data on family sizes. The document concludes that bar graphs, histograms, frequency polygons and pie charts are common ways to show frequency distributions, while OGIVE charts illustrate less than and greater than cumulative frequencies.
Graphs are used to visually represent data and relationships between variables. There are various types of graphs that can be used for different purposes. Histograms represent the distribution of continuous variables. Bar graphs display the distribution of categorical variables or allow for comparisons between categories. Line graphs show trends and patterns over time. Pie charts summarize categorical data as percentages of a whole. Cubic graphs refer to graphs where all vertices have a degree of three. Response surface plots visualize the relationship between multiple independent variables and a response variable.
Graphs, charts, and tables ppt @ bec domsBabasab Patil
ย
This document discusses various methods for organizing and presenting quantitative data, including frequency distributions, histograms, stem-and-leaf diagrams, pie charts, bar charts, line charts, scatter plots, and strategies for grouping continuous data into classes. Key topics covered include constructing frequency distributions, interpreting relative frequencies, guidelines for determining class widths and intervals, and using graphs and charts to visualize categorical and multivariate data.
This document discusses methods for organizing and presenting qualitative and quantitative data using frequency tables, charts, and graphs. It covers:
1. Creating frequency tables to organize qualitative and quantitative data, and presenting qualitative data as bar charts or pie charts.
2. Constructing frequency distributions to organize quantitative data into class intervals and determining class frequencies, and presenting quantitative data using histograms, frequency polygons, and cumulative frequency polygons.
3. An example of creating a frequency table and histogram based on sales price data from 80 vehicles to compare typical selling prices on dealer lots.
This document discusses graphs that can effectively and objectively summarize data versus graphs that can potentially mislead or deceive the viewer. Effective graphs discussed include dot plots, stem-and-leaf plots, time-series graphs, bar graphs, Pareto charts, pie charts, histograms, frequency polygons and ogives. Potentially deceptive graphs discussed are those that do not start the vertical axis at zero, exaggerating differences, and pictographs that depict one-dimensional data with multi-dimensional objects.
This document discusses methods for organizing and presenting data through frequency tables, distributions, and graphs. It covers creating frequency tables to organize qualitative and quantitative data. Frequency distributions group quantitative data into classes with class limits, frequencies, and midpoints. These distributions can be presented as histograms, frequency polygons, or cumulative frequency distributions. The document provides an example using data on vehicle selling prices to demonstrate constructing a frequency table and distribution, calculating relative frequencies, and graphing the results as a histogram.
This document discusses techniques for presenting data through tables and graphs. It provides examples of different types of tables including univariate, bivariate, and multivariate tables. It also discusses various types of graphs for presenting qualitative and quantitative data, including bar graphs, pie charts, line graphs, histograms, ogives, and scatter diagrams. Examples are given of each type of table and graph to demonstrate how they can be used to organize and communicate data in a clear and understandable way.
Dokumen ini membahas tentang perniagaan francais di Malaysia. Ia menyebutkan contoh-contoh perniagaan francais seperti McDonalds dan 7-Eleven. Dokumen ini juga membahas perkembangan francais di Malaysia sejak 1960-an dan peraturan terkait seperti Akta Francais 1998. Kelebihan dan tantangan bagi francaisor dan francaisi juga dibahas.
Dokumen tersebut membahas konsep kreativiti dan inovasi, proses kreativiti, kepentingannya dalam keusahawanan, dan cara untuk membangunkan kreativiti dan inovasi. Ia juga menjelaskan halangan terhadap kreativiti dan inovasi serta kaedah untuk mengatasinya seperti teknik sumbangsiaran dan analisis masalah.
Dokumen tersebut membahas mengenai jenis-jenis usaha teroka, faktor kegagalan usaha teroka, proses mengenal pasti peluang bisnis, dan kelebihan serta kelemahan memulai usaha sendiri. Dokumen ini memberikan panduan lengkap bagi para calon entrepreneur dalam memulai bisnis mereka.
Bab 8 membahaskan etika dan nilai-nilai murni di Malaysia serta aplikasinya dalam etika pengurusan, bisnis, dan lingkungan. Dokumen ini menjelaskan nilai-nilai utama Malaysia seperti kejujuran, kerjasama, dan kesederhanaan, serta nilai-nilai Barat dan Timur yang mempengaruhi masyarakat Malaysia. Dokumen ini juga membahas prinsip-prinsip pengurusan beretika seperti amanah, disiplin, dan produktiv
Teori etika deontologi dan teleologi digunakan untuk menilai tingkah laku manusia. Teori deontologi fokus pada tindakan itu sendiri tanpa mempertimbangkan akibatnya, sementara teori teleologi melihat akibat tindakan. Kant menekankan kewajiban dan peraturan universal dalam teori deontologinya. Aristotle menyarankan keperibadian mulia sebagai jalan tengah antara ekstrem.
Dokumen tersebut membahas tentang berfikir kritis dan kreatif. Berfikir kritis merupakan proses mental untuk memahami lingkungan melalui interaksi pengetahuan, keterampilan, dan sikap. Seseorang yang berfikir secara kritis selalu menilai ide secara sistematis sebelum menerimanya. Berfikir kreatif adalah kemampuan menghasilkan ide baru dan menggunakannya untuk menyelesaikan masalah. Terdapat
Dokumen tersebut membahas tentang konsep agama sebagai sistem kepercayaan dan etika dalam kehidupan. Agama didefinisikan sebagai sistem kepercayaan yang dianuti oleh kelompok atau masyarakat dalam menafsirkan dan merespon apa yang dianggap suci dan gaib. Agama berperan penting dalam memberikan penjelasan tentang kehidupan manusia dan cara mengatasi berbagai masalah yang dihadapi. Kelompok agama berperan dalam melestarikan dan
Dokumen tersebut membahas empat aliran utama dalam pemikiran Islam, yaitu:
1. Aliran yang hanya mengambil wahyu sebagai sumber, tanpa mempertimbangkan akal.
2. Aliran yang mengambil wahyu dan akal sebagai sumber.
3. Aliran yang mengambil akal dan wahyu sebagai sumber.
4. Aliran yang hanya mengambil akal sebagai sumber, tanpa mempertimbangkan wahyu.
Dokumen tersebut membahas tentang falsafah, pemikiran, etika, dan agama dalam konteks pendidikan bersepadu di Malaysia. Dokumen ini terbagi menjadi 10 bagian yang mendiskusikan berbagai konsep, aliran pemikiran, tokoh-tokoh, dan pendekatan etika dalam agama-agama besar serta sejarah pendidikan di Malaysia.
How to Create User Notification in Odoo 17Celine George
ย
This slide will represent how to create user notification in Odoo 17. Odoo allows us to create and send custom notifications on some events or actions. We have different types of notification such as sticky notification, rainbow man effect, alert and raise exception warning or validation.
Artificial Intelligence (AI) has revolutionized the creation of images and videos, enabling the generation of highly realistic and imaginative visual content. Utilizing advanced techniques like Generative Adversarial Networks (GANs) and neural style transfer, AI can transform simple sketches into detailed artwork or blend various styles into unique visual masterpieces. GANs, in particular, function by pitting two neural networks against each other, resulting in the production of remarkably lifelike images. AI's ability to analyze and learn from vast datasets allows it to create visuals that not only mimic human creativity but also push the boundaries of artistic expression, making it a powerful tool in digital media and entertainment industries.
How to Create a Stage or a Pipeline in Odoo 17 CRMCeline George
ย
Using CRM module, we can manage and keep track of all new leads and opportunities in one location. It helps to manage your sales pipeline with customizable stages. In this slide letโs discuss how to create a stage or pipeline inside the CRM module in odoo 17.
(๐๐๐ ๐๐๐) (๐๐๐ฌ๐ฌ๐จ๐ง 3)-๐๐ซ๐๐ฅ๐ข๐ฆ๐ฌ
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.
1. QQS1013 ELEMENTARY STATISTIC CHAPTER 2 DESCRIPTIVE STATISTICS 2.1Introduction 2.2Organizing and Graphing Qualitative Data 2.3Organizing and Graphing Quantitative Data 2.4Central Tendency Measurement 2.5Dispersion Measurement 2.6Mean, Variance and Standard Deviation for Grouped Data 2.7Measure of Skewness OBJECTIVES After completing this chapter, students should be able to: Create and interpret graphical displays involve qualitative and quantitative data. Describe the difference between grouped and ungrouped frequency distribution, frequency and relative frequency, relative frequency and cumulative relative frequency. Identify and describe the parts of a frequency distribution: class boundaries, class width, and class midpoint. Identify the shapes of distributions. Compute, describe, compare and interpret the three measures of central tendency: mean, median, and mode for ungrouped and grouped data. Compute, describe, compare and interpret the two measures of dispersion: range, and standard deviation (variance) for ungrouped and grouped data. Compute, describe, and interpret the two measures of position: quartiles and interquartile range for ungrouped and grouped data. Compute, describe and interpret the measures of skewness: Pearson Coefficient of Skewness. Introduction Raw data - Data recorded in the sequence in which there are collected and before they are processed or ranked. Array data - Raw data that is arranged in ascending or descending order. Example 1 Here is a list of question asked in a large statistics class and the โraw dataโ given by one of the students: What is your sex (m=male, f=female)? Answer (raw data): m How many hours did you sleep last night? Answer: 5 hours Randomly pick a letter โ S or Q. Answer: S What is your height in inches? Answer: 67 inches Whatโs the fastest youโve ever driven a car (mph)? Answer: 110 mph Example 2 Quantitative raw data Qualitative raw data These data also called ungrouped data 2.2Organizing and Graphing Qualitative Data 2.2.1Frequency Distributions/ Table 2.2.2Relative Frequency and Percentage Distribution 2.2.3Graphical Presentation of Qualitative Data 2.2.1Frequency Distributions / Table A frequency distribution for qualitative data lists all categories and the number of elements that belong to each of the categories. It exhibits the frequencies are distributed over various categories Also called as a frequency distribution table or simply a frequency table. The number of students who belong to a certain category is called the frequency of that category. 457200185420 Relative Frequency and Percentage Distribution A relative frequency distribution is a listing of all categories along with their relative frequencies (given as proportions or percentages). It is commonplace to give the frequency and relative frequency distribution together. Calculating relative frequency and percentage of a category Relative Frequency of a category = Frequency of that category Sum of all frequencies Percentage = (Relative Frequency)* 100 Example 3 A sample of UUM staff-owned vehicles produced by Proton was identified and the make of each noted. The resulting sample follows (W = Wira, Is = Iswara, Wj = Waja, St = Satria, P = Perdana, Sv = Savvy): WWPIsIsPIsWStWjIsWWWjIsWWIsWWjWjIsWjSvWWWWjStWWjSvWIsPSvWjWjWWStWWWWStStPWjSv Construct a frequency distribution table for these data with their relative frequency and percentage. Solution: CategoryFrequencyRelative FrequencyPercentage (%)Wira1919/50 = 0.380.38*100= 38Iswara80.1616Perdana40.088Waja100.2020Satria50.1010Savvy40.088Total501.00100 Graphical Presentation of Qualitative Data Bar Graphs A graph made of bars whose heights represent the frequencies of respective categories. Such a graph is most helpful when you have many categories to represent. Notice that a gap is inserted between each of the bars. It has =>simple/ vertical bar chart => horizontal bar chart => component bar chart => multiple bar chart Simple/ Vertical Bar Chart To construct a vertical bar chart, mark the various categories on the horizontal axis and mark the frequencies on the vertical axis Refer to Figure 2.1 and Figure 2.2, 27432004445 Figure 2.1 Figure 2.2 Horizontal Bar Chart To construct a horizontal bar chart, mark the various categories on the vertical axis and mark the frequencies on the horizontal axis. Example 4: Refer Example 3, left15240 Figure 2.3 Another example of horizontal bar chart: Figure 2.4 center635 Figure 2.4: Number of students at Diversity College who are immigrants, by last country of permanent residence Component Bar Chart To construct a component bar chart, all categories is in one bar and every bar is divided into components. The height of components should be tally with representative frequencies. Example 5 Suppose we want to illustrate the information below, representing the number of people participating in the activities offered by an outdoor pursuits centre during Jun of three consecutive years. 200420052006Climbing213436Caving101221Walking7585100Sailing363640Total142167191 Solution: Figure 2.5 Mulztiple Bar Chart To construct a multiple bar chart, each bars that representative any categories are gathered in groups. The height of the bar represented the frequencies of categories. Useful for making comparisons (two or more values). Example 6: Refer example 5, center165100Figure 2.6 Another example of horizontal bar chart: Figure 2.7 457200100330 Figure 2.7: Preferred snack choices of students at UUM The bar graphs for relative frequency and percentage distributions can be drawn simply by marking the relative frequencies or percentages, instead of the class frequencies. Pie Chart A circle divided into portions that represent the relative frequencies or percentages of a population or a sample belonging to different categories. An alternative to the bar chart and useful for summarizing a single categorical variable if there are not too many categories. The chart makes it easy to compare relative sizes of each class/category. The whole pie represents the total sample or population. The pie is divided into different portions that represent the different categories. To construct a pie chart, we multiply 360o by the relative frequency for each category to obtain the degree measure or size of the angle for the corresponding categories. Example 7 (Table 2.6 and Figure 2.8): 0482603314700581660 Table 2.6 Figure 2.8 Example 8 (Table 2.7 and Figure 2.9): Movie GenresFrequencyRelative FrequencyAngle SizeComedyActionRomanceDramaHorrorForeignScience Fiction543628282216160.270.180.140.140.110.080.08 360*0.27=97.2o 360*0.18=64.8o360*0.14=50.4o360*0.14=50.4o360*0.11=39.6o360*0.08=28.8o360*0.08=28.8o2001.00360o left24765 Figure 2.9Figure 2.9 Line Graph/Time Series Graph A graph represents data that occur over a specific period time of time. Line graphs are more popular than all other graphs combined because their visual characteristics reveal data trends clearly and these graphs are easy to create. When analyzing the graph, look for a trend or pattern that occurs over the time period. Example is the line ascending (indicating an increase over time) or descending (indicating a decrease over time). Another thing to look for is the slope, or steepness, of the line. A line that is steep over a specific time period indicates a rapid increase or decrease over that period. Two data sets can be compared on the same graph (called a compound time series graph) if two lines are used. Data collected on the same element for the same variable at different points in time or for different periods of time are called time series data. A line graph is a visual comparison of how two variablesโshown on the x- and y-axesโare related or vary with each other. It shows related information by drawing a continuous line between all the points on a grid. Line graphs compare two variables: one is plotted along the x-axis (horizontal) and the other along the y-axis (vertical). The y-axis in a line graph usually indicates quantity (e.g., RM, numbers of sales litres) or percentage, while the horizontal x-axis often measures units of time. As a result, the line graph is often viewed as a time series graph Example 9 A transit manager wishes to use the following data for a presentation showing how Port Authority Transit ridership has changed over the years. Draw a time series graph for the data and summarize the findings. YearRidership(in millions)1990199119921993199488.085.075.776.675.4 Solution: The graph shows a decline in ridership through 1992 and then leveling off for the years 1993 and 1994. Exercise 1 The following data show the method of payment by 16 customers in a supermarket checkout line. Here, C = cash, CK = check, CC = credit card, D = debit and O = other. CCKCKCCCDOCCKCCDCCCCKCKCC Construct a frequency distribution table. Calculate the relative frequencies and percentages for all categories. Draw a pie chart for the percentage distribution. The frequency distribution table represents the sale of certain product in ZeeZee Company. Each of the products was given the frequency of the sales in certain period. Find the relative frequency and the percentage of each product. Then, construct a pie chart using the obtained information. Type of ProductFrequencyRelative FrequencyPercentageAngle SizeABCDE13125911 Draw a time series graph to represent the data for the number of worldwide airline fatalities for the given years. Year1990199119921993199419951996No. of fatalities4405109908017325571132 A questionnaire about how people get news resulted in the following information from 25 respondents (N = newspaper, T = television, R = radio, M = magazine). NNRTTRNTMRMMNRNTRMNMTRRNN Construct a frequency distribution for the data. Construct a bar graph for the data. The given information shows the export and import trade in million RM for four months of sales in certain year. Using the provided information, present this data in component bar graph. MonthExportImportSeptemberOctoberNovemberDecember2830322420281714 The following information represents the maximum rain fall in millimeter (mm) in each state in Malaysia. You are supposed to help a meteorologist in your place to make an analysis. Based on your knowledge, present this information using the most appropriate chart and give your comment. StateQuantity (mm)PerlisKedahPulau PinangPerakSelangorWilayah Persekutuan Kuala LumpurNegeri SembilanMelakaJohorPahangTerengganuKelantanSarawakSabah435512163721664100339022387610501255986878456 2.3Organizing and Graphing Quantitative Data 2.3.1Stem and Leaf Display 2.3.2Frequency Distribution 2.3.3Relative Frequency and Percentage Distributions. 2.3.4 Graphing Grouped Data 2.3.5Shapes of Histogram 2.3.6Cumulative Frequency Distributions. Stem-and-Leaf Display In stem and leaf display of quantitative data, each value is divided into two portions โ a stem and a leaf. Then the leaves for each stem are shown separately in a display. Gives the information of data pattern. Can detect which value frequently repeated. Example 10 12 9 10 5 12 23 7 13 11 12 31 28 37 6 41 38 44 13 22 18 19 Solution: 09 5 7 6 12 0 2 3 1 2 4 3 8 9 25 3 8 2 36 1 7 8 41 4 Frequency Distributions A frequency distribution for quantitative data lists all the classes and the number of values that belong to each class. Data presented in form of frequency distribution are called grouped data. 0163830 The class boundary is given by the midpoint of the upper limit of one class and the lower limit of the next class. Also called real class limit. To find the midpoint of the upper limit of the first class and the lower limit of the second class, we divide the sum of these two limits by 2. e.g.: class boundary Class Width (class size) Class width = Upper boundary โ Lower boundary e.g. : Width of the first class = 600.5 โ 400.5 = 200 Class Midpoint or Mark e.g: Constructing Frequency Distribution Tables 1.To decide the number of classes, we used Sturgeโs formula, which is c = 1 + 3.3 log n where c is the no. of classes n is the no. of observations in the data set. 2. Class width, This class width is rounded to a convenient number. 3.Lower Limit of the First Class or the Starting Point Use the smallest value in the data set. Example 11 The following data give the total home runs hit by all players of each of the 30 Major League Baseball teams during 2004 season Solution: Number of classes, c = 1 + 3.3 log 30 = 1 + 3.3(1.48) = 5.89 6 class Class width, Starting Point = 135 Table 2.10 Frequency Distribution for Data of Table 2.9 Total Home RunsTallyf135 โ 152153 โ 170171 โ 188189 โ 206207 โ 224225 โ 242|||| |||||||||| |||| ||||||||1025634 Relative Frequency and Percentage Distributions Example 12 (Refer example 11) Table 2.11: Relative Frequency and Percentage Distributions Total Home RunsClass BoundariesRelative Frequency%135 โ 152153 โ 170171 โ 188189 โ 206207 โ 224225 โ 242134.5 less than 152.5152.5 less than 170.5170.5 less than 188.5188.5 less than 206.5206.5 less than 224.5224.5 less than 242.50.33330.06670.16670.20.10.133333.336.6716.67201013.33Sum1.0100% Graphing Grouped Data Histograms A histogram is a graph in which the class boundaries are marked on the horizontal axis and either the frequencies, relative frequencies, or percentages are marked on the vertical axis. The frequencies, relative frequencies or percentages are represented by the heights of the bars. In histogram, the bars are drawn adjacent to each other and there is a space between y axis and the first bar. Example 13 (Refer example 11) 134.5 152.5 170.5 188.5 206.5 224.5 242.5 Figure 2.10: Frequency histogram for Table 2.10 Polygon A graph formed by joining the midpoints of the tops of successive bars in a histogram with straight lines is called a polygon. Example 13 34290082550 134.5 152.5 170.5 188.5 206.5 224.5 242.5 134.5 152.5 170.5 188.5 206.5 224.5 242.5Figure 2.11: Frequency polygon for Table 2.10 For a very large data set, as the number of classes is increased (and the width of classes is decreased), the frequency polygon eventually becomes a smooth curve called a frequency distribution curve or simply a frequency curve. Figure 2.12: Frequency distribution curve Shape of Histogram Same as polygon. For a very large data set, as the number of classes is increased (and the width of classes is decreased), the frequency polygon eventually becomes a smooth curve called a frequency distribution curve or simply a frequency curve. The most common of shapes are: (i) Symmetric Figure 2.13 & 2.14: Symmetric histograms (ii) Right skewed and (iii) Left skewed Figure 2.15 & 2.16: Right skewed and Left skewed Describing data using graphs helps us insight into the main characteristics of the data. When interpreting a graph, we should be very cautious. We should observe carefully whether the frequency axis has been truncated or whether any axis has been unnecessarily shortened or stretched. Cumulative Frequency Distributions A cumulative frequency distribution gives the total number of values that fall below the upper boundary of each class. Example 14: Using the frequency distribution of table 2.11, Total Home RunsClass BoundariesCumulative Frequency135 โ 152153 โ 170171 โ 188189 โ 206207 โ 224225 โ 242134.5 less than 152.5152.5 less than 170.5170.5 less than 188.5188.5 less than 206.5206.5 less than 224.5224.5 less than 242.51010+2=1210+2+5=1710+2+5+6=2310+2+5+6+3=2610+2+5+6+3+4=30 Ogive An ogive is a curve drawn for the cumulative frequency distribution by joining with straight lines the dots marked above the upper boundaries of classes at heights equal to the cumulative frequencies of respective classes. Two type of ogive: (i) ogive less than (ii)ogive greater than First, build a table of cumulative frequency. Example 15 (Ogive Less Than) 56633730 โ 3940 โ 4950 โ 5960 - 6970 โ 7980 - 8930Number of students (f)TotalEarnings (RM)Earnings (RM) Cumulative Frequency (F)Less than 29.5Less than 39.5Less than 49.5Less than 59.5Less than 69.5Less than 79.5Less than 89.5051117202330 0510152025303529.539.549.559.569.579.589.5EarningsCumulative Frequency Figure 2.17 Example 16 (Ogive Greater Than) 56633730 โ 3940 โ 4950 โ 5960 - 6970 โ 7980 - 8930Number of students (f)TotalEarnings (RM) Cumulative Frequency (F)Earnings (RM) 302519131070More than 29.5More than 39.5More than 49.5More than 59.5More than 69.5More than 79.5More than 89.5 0510152025303529.539.549.559.569.579.589.5EarningsCumulative Frequency Figure 2.18 Figure 2.18 2.3.7Box-Plot Describe the analyze data graphically using 5 measurement: smallest value, first quartile (K1), second quartile (median or K2), third quartile (K3) and largest value. Smallest valueLargest value K1 Median K3Largest value K1 Median K3Largest value K1 Median K3Smallest valueSmallest valueFor symmetry data For left skewed data For right skewed data 2.4Measures of Central Tendency 2.4.1 Ungrouped Data (1) Mean (2) Weighted mean (3) Median (4) Mode Grouped Data (1) Mean (2) Median (3) Mode Relationship among mean, median & mode 2.4.1 Ungrouped Data Mean Mean for population data: Mean for sample data: where: = the sum af all values N = the population size n = the sample size, ยต = the population mean = the sample mean Example 17 The following data give the prices (rounded to thousand RM) of five homes sold recently in Sekayang. 158189265127191 Find the mean sale price for these homes. Solution: Thus, these five homes were sold for an average price of RM186 thousand @ RM186 000. The mean has the advantage that its calculation includes each value of the data set. Weighted Mean Used when have different needs. Weight mean : where w is a weight. Example 18 Consider the data of electricity components purchasing from a factory in the table below: TypeNumber of component (w)Cost/unit (x)12345120050025001000800RM3.00RM3.40RM2.80RM2.90RM3.25Total6000 Solution: Mean cost of a unit of the component is RM2.97 Median Median is the value of the middle term in a data set that has been ranked in increasing order. Procedure for finding the Median Step 1: Rank the data set in increasing order. Step 2: Determine the depth (position or location) of the median. Step 3: Determine the value of the Median. Example 19 Find the median for the following data: 10 5 19 8 3 Solution: (1) Rank the data in increasing order 3 5 8 10 19 (2) Determine the depth of the Median (3) Determine the value of the median Therefore the median is located in third position of the data set. 3 5 8 10 19 Hence, the Median for above data = 8 Example 20 Find the median for the following data: 10 5 19 8 3 15 Solution: (1) Rank the data in increasing order 35810 15 19 (2) Determine the depth of the Median (3) Determine the value of the Median Therefore the median is located in the middle of 3rd position and 4th position of the data set. Hence, the Median for the above data = 9 The median gives the center of a histogram, with half of the data values to the left of (or, less than) the median and half to the right of (or, more than) the median. The advantage of using the median is that it is not influenced by outliers. Mode Mode is the value that occurs with the highest frequency in a data set. Example 21 1. What is the mode for given data? 77 69 74 81 71 68 74 73 2. What is the mode for given data? 77 69 68 74 81 71 68 74 73 Solution: 1. Mode = 74 (this number occurs twice): Unimodal 2.Mode = 68 and 74: Bimodal A major shortcoming of the mode is that a data set may have none or may have more than one mode. One advantage of the mode is that it can be calculated for both kinds of data, quantitative and qualitative. Grouped Data Mean Mean for population data: Mean for sample data: Where the midpoint and f is the frequency of a class. Example 22 The following table gives the frequency distribution of the number of orders received each day during the past 50 days at the office of a mail-order company. Calculate the mean. Numberof orderf10 โ 1213 โ 1516 โ 1819 โ 214122014ย n = 50 Solution: Because the data set includes only 50 days, it represents a sample. The value of is calculated in the following table: Numberof orderfxfx10 โ 1213 โ 1516 โ 1819 โ 2141220141114172044168340280ย n = 50 = 832 The value of mean sample is: Thus, this mail-order company received an average of 16.64 orders per day during these 50 days. Median Step 1: Construct the cumulative frequency distribution. Step 2: Decide the class that contain the median. Class Median is the first class with the value of cumulative frequency is at least n/2. Step 3: Find the median by using the following formula: Where: n = the total frequency F = the total frequency before class median i = the class width = the lower boundary of the class median = the frequency of the class median Example 23 Based on the grouped data below, find the median: Time to travel to workFrequency1 โ 1011 โ 2021 โ 3031 โ 4041 โ 508141297 Solution: 1st Step: Construct the cumulative frequency distribution Time to travel to workFrequency Cumulative Frequency1 โ 1011 โ 2021 โ 3031 โ 4041 โ 508141297822344350 Class median is the 3rd class So, F = 22, = 12, = 21.5 and i = 10 Therefore, Thus, 25 persons take less than 24 minutes to travel to work and another 25 persons take more than 24 minutes to travel to work. Mode Mode is the value that has the highest frequency in a data set. For grouped data, class mode (or, modal class) is the class with the highest frequency. To find mode for grouped data, use the following formula: Where: is the lower boundary of class mode is the difference between the frequency of class mode and the frequency of the class before the class mode is the difference between the frequency of class mode and the frequency of the class after the class mode i is the class width Example 24 Based on the grouped data below, find the mode Time to travel to workFrequency1 โ 1011 โ 2021 โ 3031 โ 4041 โ 508141297 Solution: Based on the table, = 10.5, = (14 โ 8) = 6, = (14 โ 12) = 2 and i = 10 We can also obtain the mode by using the histogram; Figure 2.19 2.4.3 Relationship among mean, median & mode As discussed in previous topic, histogram or a frequency distribution curve can assume either skewed shape or symmetrical shape. Knowing the value of mean, median and mode can give us some idea about the shape of frequency curve. For a symmetrical histogram and frequency curve with one peak, the value of the mean, median and mode are identical and they lie at the center of the distribution.(Figure 2.20) 2971800961390228600951865For a histogram and a frequency curve skewed to the right, the value of the mean is the largest that of the mode is the smallest and the value of the median lies between these two. Figure 2.20: Mean, median, and mode for a symmetric histogram and frequency distribution curve Figure 2.21: Mean, median, and mode for a histogram and frequency distribution curve skewed to the right 2971800168275 For a histogram and a frequency curve skewed to the left, the value of the mean is the smallest and that of the mode is the largest and the value of the median lies between these two. Figure 2.22: Mean, median, and mode for a histogram and frequency distribution curve skewed to the left 2.5Dispersion Measurement The measures of central tendency such as mean, median and mode do not reveal the whole picture of the distribution of a data set. Two data sets with the same mean may have a completely different spreads. The variation among the values of observations for one data set may be much larger or smaller than for the other data set. 2.5.1 Ungrouped data (1) Range (2) Standard Deviation 2.5.2 Grouped data (1) Range (2) Standard deviation 2.5.3 Relative Dispersion Measurement Ungrouped Data Range RANGE = Largest value โ Smallest value Example 25: Find the range of production for this data set, Solution: Range = Largest value โ Smallest value = 267 277 โ 49 651 = 217 626 Disadvantages: being influenced by outliers. Based on two values only. All other values in a data set are ignored. Variance and Standard Deviation Standard deviation is the most used measure of dispersion. A Standard Deviation value tells how closely the values of a data set clustered around the mean. Lower value of standard deviation indicates that the data set value are spread over relatively smaller range around the mean. Larger value of data set indicates that the data set value are spread over relatively larger around the mean (far from mean). Standard deviation is obtained the positive root of the variance: VarianceStandard DeviationPopulationSample Example 26 Let x denote the total production (in unit) of company CompanyProductionABCDE62931267534 Find the variance and standard deviation, Solution: CompanyProduction (x)x2ABCDE629312675343844864915 87656251156ย 1156ย Since s2 = 1182.50; Therefore, The properties of variance and standard deviation: (1) The standard deviation is a measure of variation of all values from the mean. (2)The value of the variance and the standard deviation are never negative. Also, larger values of variance or standard deviation indicate greater amounts of variation. (3)The value of s can increase dramatically with the inclusion of one or more outliers. (4) The measurement units of variance are always the square of the measurement units of the original data while the units of standard deviation are the same as the units of the original data values. Grouped Data Range Range = Upper bound of last class โ Lower bound of first class ClassFrequency41 โ 5051 โ 6061 โ 7071 โ 8081 โ 9091 - 10013713106 Total40 Upper bound of last class = 100.5 Lower bound of first class = 40.5 Range = 100.5 โ 40.5 = 60 Variance and Standard Deviation VarianceStandard DeviationPopulationSample Example 27 Find the variance and standard deviation for the following data: No. of orderf10 โ 1213 โ 1516 โ 1819 โ 214122014 Totaln = 50 Solution: No. of orderfxfxfx210 โ 1213 โ 1516 โ 1819 โ 2141220141114172044168340280484235257805600 Totaln = 5085714216 Variance, Standard Deviation, 320040048260 Thus, the standard deviation of the number of orders received at the office of this mail-order company during the past 50 days is 2.75. 2.5.3 Relative Dispersion Measurement To compare two or more distribution that has different unit based on their dispersion Or To compare two or more distribution that has same unit but big different in their value of mean. Also called modified coefficient or coefficient of variation, CV. Example 28 Given mean and standard deviation of monthly salary for two groups of worker who are working in ABC company- Group 1: 700 & 20 and Group 2 :1070 & 20. Find the CV for every group and determine which group is more dispersed. Solution: The monthly salary for group 1 worker is more dispersed compared to group 2. Measure of Position Determines the position of a single value in relation to other values in a sample or a population data set. Ungrouped Data Quartiles Interquatile Range Grouped Data Quartile Interquartile Range Quartiles Quartiles are three summary measures that divide ranked data set into four equal parts. The 1st quartiles โ denoted as Q1 The 2nd quartiles โ median of a data set or Q2 The 3rd quartiles โ denoted as Q3 Example 29 Table below lists the total revenue for the 11 top tourism company in Malaysia 109.7 79.9 21.2 76.4 80.2 82.1 79.4 89.3 98.0 103.5 86.8 Solution: Step 1: Arrange the data in increasing order 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Step 2: Determine the depth for Q1 and Q3 Step 3: Determine the Q1 and Q3 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Q1 = 79.9 Q3 = 103.5 Table below lists the total revenue for the 12 top tourism company in Malaysia 109.7 79.9 74.1 121.2 76.4 80.2 82.1 79.4 89.3 98.0 103.5 86.8 Solution: Step 1: Arrange the data in increasing order 74.1 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Step 2: Determine the depth for Q1 and Q3 Step 3: Determine the Q1 and Q3 74.1 76.4 79.4 79.9 80.2 82.1 86.8 89.3 98.0 103.5 109.7 121.2 Q1 = 79.4 + 0.25 (79.9 โ 79.4) = 79.525 Q3 = 98.0 + 0.75 (103.5 โ 98.0) = 102.125 Interquartile Range The difference between the third quartile and the first quartile for a data set. IQR = Q3 โ Q1 Example 30 By referring to example 29, calculate the IQR. Solution: IQR = Q3 โ Q1 = 102.125 โ 79.525 = 22.6 2.6.2 Grouped Data Quartiles From Median, we can get Q1 and Q3 equation as follows: ; Example 31 Refer to example 23, find Q1 and Q3 Solution: 1st Step: Construct the cumulative frequency distribution Time to travel to workFrequency Cumulative Frequency1 โ 1011 โ 2021 โ 3031 โ 4041 โ 508141297822344350 2nd Step: Determine the Q1 and Q3 Class Q1 is the 2nd class Therefore, Class Q3 is the 4th class Therefore, Interquartile Range IQR = Q3 โ Q1 Example 32: Refer to example 31, calculate the IQR. Solution: IQR = Q3 โ Q1 = 34.3889 โ 13.7143 = 20.6746 Measure of Skewness To determine the skewness of data (symmetry, left skewed, right skewed) Also called Skewness Coefficient or Pearson Coefficient of Skewness If Sk +ve right skewed If Sk -ve left skewed If Sk = 0 ๏ symmetry If Sk takes a value in between (-0.9999, -0.0001) or (0.0001, 0.9999) approximately symmetry. Example 33 The duration of cancer patient warded in Hospital Seberang Jaya recorded in a frequency distribution. From the record, the mean is 28 days, median is 25 days and mode is 23 days. Given the standard deviation is 4.2 days. What is the type of distribution? Find the skewness coefficient Solution: This distribution is right skewed because the mean is the largest value So, from the Sk value this distribution is right skewed. Exercise 2: A survey research company asks 100 people how many times they have been to the dentist in the last five years. Their grouped responses appear below. Number of VisitsNumber of Responses0 โ 4165 โ 92510 โ 144815 โ 1911 What are the mean and variance of the data? A researcher asked 25 consumers: โHow much would you pay for a television adapter that provides Internet access?โ Their grouped responses are as follows: Amount ($)Number of Responses0 โ 992100 โ 1992200 โ 2493250 โ 2993300 โ 3496350 โ 3993400 โ 4994500 โ 9992 Calculate the mean, variance, and standard deviation. The following data give the pairs of shoes sold per day by a particular shoe store in the last 20 days. 85 90 89 70 79 80 83 83 75 76 89 86 71 76 77 89 70 65 90 86 Calculate the mean and interpret the value. median and interpret the value. mode and interpret the value. standard deviation. 4. The followings data shows the information of serving time (in minutes) for 40 customers in a post office: 2.04.52.52.94.22.93.52.83.22.94.03.03.82.52.33.52.13.13.64.34.72.64.13.14.62.85.12.72.64.43.53.02.73.92.92.92.53.73.32.4 Construct a frequency distribution table with 0.5 of class width. Construct a histogram. Calculate the mode and median of the data. Find the mean of serving time. Determine the skewness of the data. Find the first and third quartile value of the data. Determine the value of interquartile range. 5. In a survey for a class of final semester student, a group of data was obtained for the number of text books owned. Number of studentsNumber of text book owned1291115108553210 Find the average number of text book for the class. Use the weighted mean. The following data represent the ages of 15 people buying lift tickets at a ski area. 1525261738166021 30532840203531 Calculate the quartile and interquartile range. A student scores 60 on a mathematics test that has a mean of 54 and a standard deviation of 3, and she scores 80 on a history test with a mean of 75 and a standard deviation of 2. On which test did she perform better? The following table gives the distribution of the shareโs price for ABC Company which was listed in BSKL in 2005. Price (RM)Frequency12 โ 1415 โ 1718 โ 2021 โ 2324 โ 2627 - 2951425763 Find the mean, median and mode for this data.