This document provides information on presenting data through textual, tabular, and graphical methods. It discusses preparing stem-and-leaf plots and frequency distribution tables to organize and summarize data. Frequency distribution tables include elements like class intervals, frequencies, relative frequencies, and cumulative frequencies. The document also introduces contingency tables for enumerating data by cell across rows and columns. The overall purpose is to teach students the various ways of organizing and presenting numerical data through different visual and textual methods.
Here are the class widths, marks and boundaries for the given class intervals:
a. Class interval (ci): 4 – 8
Class Width: 4
Class Mark: 6
Class Boundary: 3.5 – 8.5
b. Class interval (ci): 35 – 44
Class Width: 9
Class Mark: 39.5
Class Boundary: 34.5 – 43.5
c. Class interval (ci): 17 – 21
Class Width: 4
Class Mark: 19
Class Boundary: 16.5 – 20.5
d. Class interval (ci): 53 – 57
Class Width: 4
Class Mark: 55
Class Boundary: 52.5 –
This document discusses different measures of relative position including percentiles, quartiles, and z-scores. Percentiles indicate the percentage of values below a given score. Quartiles divide a dataset into quarters. The interquartile range is the difference between the first and third quartiles. A z-score standardizes a score by subtracting the mean and dividing by the standard deviation, allowing comparison across different scales.
This document is a lesson on calculating quartiles, deciles, and percentiles from grouped and ungrouped data. It provides examples and step-by-step instructions on arranging data in ascending order and using the Mendenhall-Sincich method and formulas to determine the lower quartile, upper quartile, 5th decile, 50th percentile, and other values. It then provides practice problems for the student to solve involving grouped data from test scores and smoking levels. The document emphasizes rounding rules and identifying the correct interval before applying the formulas.
This section expands on frequency distributions by discussing additional features: midpoints, which are the averages of class limits; relative frequency, which shows what portion of the data falls in each class; and cumulative frequency, which is the running total of all previous classes' frequencies. It provides an example calculating these values for a given
Fractiles are statistical measures used to divide a distribution into equal parts. Common fractiles include quartiles, which divide data into 4 equal parts, deciles which divide into 10 parts, and percentiles which divide into 100 parts. Quartiles (Q1, Q2, Q3) indicate the points where 25%, 50%, and 75% of values lie. Deciles and percentiles are calculated similarly based on dividing the data set into 10 or 100 equal parts. Formulas are provided to calculate fractiles from both ungrouped and grouped frequency distribution data.
The document discusses measures of central tendency for ungrouped and grouped data. It defines mean, median, and mode, and provides examples of calculating each for ungrouped and grouped data sets. Formulas and step-by-step workings are shown for finding the mean, median, and mode of grouped data using frequency distributions.
This document discusses various measures of position for ungrouped data including quartiles, deciles, and percentiles. It provides definitions and formulas for calculating these measures, and works through examples finding the quartiles, deciles, and percentiles for sample data sets.
Here are the class widths, marks and boundaries for the given class intervals:
a. Class interval (ci): 4 – 8
Class Width: 4
Class Mark: 6
Class Boundary: 3.5 – 8.5
b. Class interval (ci): 35 – 44
Class Width: 9
Class Mark: 39.5
Class Boundary: 34.5 – 43.5
c. Class interval (ci): 17 – 21
Class Width: 4
Class Mark: 19
Class Boundary: 16.5 – 20.5
d. Class interval (ci): 53 – 57
Class Width: 4
Class Mark: 55
Class Boundary: 52.5 –
This document discusses different measures of relative position including percentiles, quartiles, and z-scores. Percentiles indicate the percentage of values below a given score. Quartiles divide a dataset into quarters. The interquartile range is the difference between the first and third quartiles. A z-score standardizes a score by subtracting the mean and dividing by the standard deviation, allowing comparison across different scales.
This document is a lesson on calculating quartiles, deciles, and percentiles from grouped and ungrouped data. It provides examples and step-by-step instructions on arranging data in ascending order and using the Mendenhall-Sincich method and formulas to determine the lower quartile, upper quartile, 5th decile, 50th percentile, and other values. It then provides practice problems for the student to solve involving grouped data from test scores and smoking levels. The document emphasizes rounding rules and identifying the correct interval before applying the formulas.
This section expands on frequency distributions by discussing additional features: midpoints, which are the averages of class limits; relative frequency, which shows what portion of the data falls in each class; and cumulative frequency, which is the running total of all previous classes' frequencies. It provides an example calculating these values for a given
Fractiles are statistical measures used to divide a distribution into equal parts. Common fractiles include quartiles, which divide data into 4 equal parts, deciles which divide into 10 parts, and percentiles which divide into 100 parts. Quartiles (Q1, Q2, Q3) indicate the points where 25%, 50%, and 75% of values lie. Deciles and percentiles are calculated similarly based on dividing the data set into 10 or 100 equal parts. Formulas are provided to calculate fractiles from both ungrouped and grouped frequency distribution data.
The document discusses measures of central tendency for ungrouped and grouped data. It defines mean, median, and mode, and provides examples of calculating each for ungrouped and grouped data sets. Formulas and step-by-step workings are shown for finding the mean, median, and mode of grouped data using frequency distributions.
This document discusses various measures of position for ungrouped data including quartiles, deciles, and percentiles. It provides definitions and formulas for calculating these measures, and works through examples finding the quartiles, deciles, and percentiles for sample data sets.
STATISTICS | Measures Of Central TendencyMaulen Bale
The document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. Examples are given to demonstrate calculating the mean, median, and mode for both individual and grouped data. Key properties of each measure are also outlined.
This document discusses different methods for presenting data, including textual, tabular, and graphical presentations. Tabular presentations include frequency distribution tables that are ungrouped, grouped, simple, and complete. Graphical presentations include bar charts, histograms, frequency polygons, pie charts, and pictographs to visually depict quantitative data using bars, rectangles, lines, circles, or pictures. The examples provided demonstrate how to construct different types of tables and graphs for a set of sample data.
This document discusses measures of central tendency and dispersion for ungrouped data, including the mean, quartiles, deciles, and percentiles. It provides formulas for calculating these values and examples worked out step-by-step. The mean is defined as the average value of the data. Quartiles divide the data into four equal parts, with the first quartile being the 25th percentile, second quartile the 50th percentile (median), and third quartile the 75th percentile. Deciles and percentiles further divide the data into 10 and 100 equal parts, respectively, using formulas that calculate the cutoff points.
This document provides an overview of methods for presenting data, including textual, tabular, and graphical methods. It discusses topics such as ungrouped vs. grouped data, frequency distribution tables, stem-and-leaf plots, class boundaries, class midpoints, and class width. The objectives are to describe how to prepare a stem-and-leaf plot, describe data textually, construct a frequency distribution table, create graphs, and interpret graphs and tables. Examples are provided to illustrate these concepts and methods.
Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.
This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and explains their properties and appropriate uses. The mean is the average value obtained by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value. Each measure can be affected differently by outliers, with the median being least affected. The appropriate measure depends on the scale of measurement and distribution of the data.
Data can be presented in three methods: textual, tabular, or graphical. Tabular presentation involves organizing data into a table with columns and rows for classification. Graphical presentation uses visual representations like bar graphs, pie charts, and line graphs to show relationships between data points. Different types of graphs are suited to different types of data and comparisons.
This module introduces key concepts in statistics. It will cover defining statistics and related terms, the history and importance of statistics, summation rules, sampling techniques, organizing data in tables, constructing frequency distributions, and measures of central tendency for ungrouped data. The goal is for students to understand how statistics is used in daily life and to learn techniques for collecting, organizing, and analyzing data.
The document discusses measures of position for ungrouped data including quartiles, deciles, and percentiles. It specifically describes quartiles, which divide a distribution into four equal parts (Q1, Q2, Q3). The Mendenhall and Sincich method is presented for finding quartile values using a formula based on the number of data points. The method involves arranging data in order and determining the quartile positions. Linear interpolation is described for estimating quartile values that fall between data points. An example applies these methods to calculate quartiles for a set of student test scores.
Measures of Central Tendency, Variability and ShapesScholarsPoint1
The PPT describes the Measures of Central Tendency in detail such as Mean, Median, Mode, Percentile, Quartile, Arthemetic mean. Measures of Variability: Range, Mean Absolute deviation, Standard Deviation, Z-Score, Variance, Coefficient of Variance as well as Measures of Shape such as kurtosis and skewness in the grouped and normal data.
The document discusses the steps to construct a frequency distribution table (FDT):
1. Find the range and number of classes or intervals.
2. Estimate the class width and list the lower and upper class limits.
3. Tally the observations in each interval and record the frequencies.
It also describes how to calculate relative frequencies and cumulative frequencies to vary the FDT.
This document provides steps for calculating the median of grouped data:
1. Create a frequency distribution table with class intervals, frequencies, and cumulative frequencies.
2. Find the median class by calculating N/2, where N is the total number of data points.
3. The median is calculated using the formula: x = L + (n2 - F2)/f2 * i, where L is the lower limit of the median class, n2 is the median class, F2 is the cumulative frequency before the median class, f2 is the frequency of the median class, and i is the class interval.
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.
Here are the steps to solve this problem:
1. Find the 3rd quartile, 72nd percentile, and 8th decile from the data:
- 3rd quartile (Q3) = 38
- 72nd percentile = 36
- 8th decile (D8) = 35
2. Find the percentile ranks of Jaja and Krisha:
- Jaja scored 32. From the table, 27 students scored lower than 32. So Jaja's percentile rank is 27/50 x 100 = 54%
- Krisha scored 23. From the table, 20 students scored lower than 23. So Krisha's percentile rank is 20/50 x 100 = 40%
3.
Lesson 1 provides an introduction to the National Service Training Program (NSTP) in the Philippines. It outlines the legal basis of the NSTP as established by RA 9163, which aims to enhance civic consciousness and defense preparedness in youth. The three components of the NSTP are described as Reserve Officer's Training Corps (ROTC), Civic Welfare Training Service (CWTS), and Literacy Training Service (LTS). Details are also provided on student and institutional coverage, duration and units for each component, fees, and program management between educational institutions and relevant government agencies.
Determining measures of central tendency for grouped dataAlona Hall
This document discusses measures of central tendency (mean, median, mode) using grouped data from a sample of 40 students' heights. It provides an example to calculate each measure. The mean height is estimated as 151.25 cm using a frequency table and calculating the mid-point of each height range. The modal class is 155-159 cm as it has the highest frequency. A cumulative frequency table and ogive curve allow estimating the median height as 153.5 cm.
This document explores patterns in polygons based on their number of points. It presents data showing that the maximum number of chords in an n-point polygon is n(n-1)/2, and the maximum number of regions is 2n-1. These formulas are supported by data from diagrams of polygons with 1 to 5 points. While the formulas have been tested against examples, they have not yet been formally proven.
The document discusses frequency distributions and their components. A frequency distribution arranges data into categories and shows the number of observations in each category. Key parts include:
- Class limits, which define the groupings by lower and upper limits.
- Class size, which is the width of each interval. It is calculated as the range divided by the number of classes.
- Class boundaries and marks, which separate and indicate the midpoints of categories.
The document provides steps for constructing a frequency distribution, including computing the range, determining class size, setting limits, tallying scores, and counting frequencies. An example uses exam scores to demonstrate these steps.
This document discusses different methods for presenting data graphically. It begins by listing the objectives of the lesson and identifying textual, tabular, and graphical methods. Examples of various graphs like bar charts, histograms, frequency polygons, pie charts, and ogives are then shown and explained using sample data on examination scores. The document concludes by assigning activities for students to practice constructing these different graphs from sample data sets.
This document provides information about frequency distributions and constructing frequency distribution tables. It defines a frequency distribution as a representation of data in a tabular format showing the number of observations within intervals. It then outlines the general process for constructing a frequency table which includes determining the range, number of classes, class width, and recording the frequencies in a table. An example is provided of constructing a frequency table from data on the ages of 50 men who died from gunfire using 7 classes. Guidelines for constructing frequency tables are also listed.
STATISTICS | Measures Of Central TendencyMaulen Bale
The document discusses measures of central tendency including the mean, median, and mode. It provides definitions and formulas for calculating each measure. Examples are given to demonstrate calculating the mean, median, and mode for both individual and grouped data. Key properties of each measure are also outlined.
This document discusses different methods for presenting data, including textual, tabular, and graphical presentations. Tabular presentations include frequency distribution tables that are ungrouped, grouped, simple, and complete. Graphical presentations include bar charts, histograms, frequency polygons, pie charts, and pictographs to visually depict quantitative data using bars, rectangles, lines, circles, or pictures. The examples provided demonstrate how to construct different types of tables and graphs for a set of sample data.
This document discusses measures of central tendency and dispersion for ungrouped data, including the mean, quartiles, deciles, and percentiles. It provides formulas for calculating these values and examples worked out step-by-step. The mean is defined as the average value of the data. Quartiles divide the data into four equal parts, with the first quartile being the 25th percentile, second quartile the 50th percentile (median), and third quartile the 75th percentile. Deciles and percentiles further divide the data into 10 and 100 equal parts, respectively, using formulas that calculate the cutoff points.
This document provides an overview of methods for presenting data, including textual, tabular, and graphical methods. It discusses topics such as ungrouped vs. grouped data, frequency distribution tables, stem-and-leaf plots, class boundaries, class midpoints, and class width. The objectives are to describe how to prepare a stem-and-leaf plot, describe data textually, construct a frequency distribution table, create graphs, and interpret graphs and tables. Examples are provided to illustrate these concepts and methods.
Here are the modes for the three examples:
1. The mode is 3. This value occurs most frequently among the number of errors committed by the typists.
2. The mode is 82. This value occurs most frequently among the number of fruits yielded by the mango trees.
3. The mode is 12 and 15. These values occur most frequently among the students' quiz scores.
This document discusses measures of central tendency including the mean, median, and mode. It defines each measure and explains their properties and appropriate uses. The mean is the average value obtained by dividing the sum of all values by the total number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the most frequently occurring value. Each measure can be affected differently by outliers, with the median being least affected. The appropriate measure depends on the scale of measurement and distribution of the data.
Data can be presented in three methods: textual, tabular, or graphical. Tabular presentation involves organizing data into a table with columns and rows for classification. Graphical presentation uses visual representations like bar graphs, pie charts, and line graphs to show relationships between data points. Different types of graphs are suited to different types of data and comparisons.
This module introduces key concepts in statistics. It will cover defining statistics and related terms, the history and importance of statistics, summation rules, sampling techniques, organizing data in tables, constructing frequency distributions, and measures of central tendency for ungrouped data. The goal is for students to understand how statistics is used in daily life and to learn techniques for collecting, organizing, and analyzing data.
The document discusses measures of position for ungrouped data including quartiles, deciles, and percentiles. It specifically describes quartiles, which divide a distribution into four equal parts (Q1, Q2, Q3). The Mendenhall and Sincich method is presented for finding quartile values using a formula based on the number of data points. The method involves arranging data in order and determining the quartile positions. Linear interpolation is described for estimating quartile values that fall between data points. An example applies these methods to calculate quartiles for a set of student test scores.
Measures of Central Tendency, Variability and ShapesScholarsPoint1
The PPT describes the Measures of Central Tendency in detail such as Mean, Median, Mode, Percentile, Quartile, Arthemetic mean. Measures of Variability: Range, Mean Absolute deviation, Standard Deviation, Z-Score, Variance, Coefficient of Variance as well as Measures of Shape such as kurtosis and skewness in the grouped and normal data.
The document discusses the steps to construct a frequency distribution table (FDT):
1. Find the range and number of classes or intervals.
2. Estimate the class width and list the lower and upper class limits.
3. Tally the observations in each interval and record the frequencies.
It also describes how to calculate relative frequencies and cumulative frequencies to vary the FDT.
This document provides steps for calculating the median of grouped data:
1. Create a frequency distribution table with class intervals, frequencies, and cumulative frequencies.
2. Find the median class by calculating N/2, where N is the total number of data points.
3. The median is calculated using the formula: x = L + (n2 - F2)/f2 * i, where L is the lower limit of the median class, n2 is the median class, F2 is the cumulative frequency before the median class, f2 is the frequency of the median class, and i is the class interval.
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.
Here are the steps to solve this problem:
1. Find the 3rd quartile, 72nd percentile, and 8th decile from the data:
- 3rd quartile (Q3) = 38
- 72nd percentile = 36
- 8th decile (D8) = 35
2. Find the percentile ranks of Jaja and Krisha:
- Jaja scored 32. From the table, 27 students scored lower than 32. So Jaja's percentile rank is 27/50 x 100 = 54%
- Krisha scored 23. From the table, 20 students scored lower than 23. So Krisha's percentile rank is 20/50 x 100 = 40%
3.
Lesson 1 provides an introduction to the National Service Training Program (NSTP) in the Philippines. It outlines the legal basis of the NSTP as established by RA 9163, which aims to enhance civic consciousness and defense preparedness in youth. The three components of the NSTP are described as Reserve Officer's Training Corps (ROTC), Civic Welfare Training Service (CWTS), and Literacy Training Service (LTS). Details are also provided on student and institutional coverage, duration and units for each component, fees, and program management between educational institutions and relevant government agencies.
Determining measures of central tendency for grouped dataAlona Hall
This document discusses measures of central tendency (mean, median, mode) using grouped data from a sample of 40 students' heights. It provides an example to calculate each measure. The mean height is estimated as 151.25 cm using a frequency table and calculating the mid-point of each height range. The modal class is 155-159 cm as it has the highest frequency. A cumulative frequency table and ogive curve allow estimating the median height as 153.5 cm.
This document explores patterns in polygons based on their number of points. It presents data showing that the maximum number of chords in an n-point polygon is n(n-1)/2, and the maximum number of regions is 2n-1. These formulas are supported by data from diagrams of polygons with 1 to 5 points. While the formulas have been tested against examples, they have not yet been formally proven.
The document discusses frequency distributions and their components. A frequency distribution arranges data into categories and shows the number of observations in each category. Key parts include:
- Class limits, which define the groupings by lower and upper limits.
- Class size, which is the width of each interval. It is calculated as the range divided by the number of classes.
- Class boundaries and marks, which separate and indicate the midpoints of categories.
The document provides steps for constructing a frequency distribution, including computing the range, determining class size, setting limits, tallying scores, and counting frequencies. An example uses exam scores to demonstrate these steps.
This document discusses different methods for presenting data graphically. It begins by listing the objectives of the lesson and identifying textual, tabular, and graphical methods. Examples of various graphs like bar charts, histograms, frequency polygons, pie charts, and ogives are then shown and explained using sample data on examination scores. The document concludes by assigning activities for students to practice constructing these different graphs from sample data sets.
This document provides information about frequency distributions and constructing frequency distribution tables. It defines a frequency distribution as a representation of data in a tabular format showing the number of observations within intervals. It then outlines the general process for constructing a frequency table which includes determining the range, number of classes, class width, and recording the frequencies in a table. An example is provided of constructing a frequency table from data on the ages of 50 men who died from gunfire using 7 classes. Guidelines for constructing frequency tables are also listed.
biostatstics :Type and presentation of datanaresh gill
The document provides an overview of different types of data and methods for presenting data. It discusses qualitative vs quantitative data, primary vs secondary data, and different ways to present data visually including bar charts, histograms, frequency polygons, scatter diagrams, line diagrams and pie charts. Guidelines are provided for tabular presentation of data to make it clear, concise and easy to understand.
Presentation of Data and Frequency DistributionElain Cruz
The document discusses the key components of statistical tables including the table heading, body, stub, box head, footnotes, and source of data. It provides an example of a statistical table showing the enrolment profile of a college by subject with the number and percentage of students. The document also includes examples of different types of graphs that can be used to display statistical data like bar graphs, line graphs, pie charts, and pictographs.
Variables describe attributes that can vary between entities. They can be qualitative (categorical) or quantitative (numeric). Common types of variables include continuous, discrete, ordinal, and nominal variables. Data can be presented graphically through bar charts, pie charts, histograms, box plots, and scatter plots to better understand patterns and trends. Key measures used to summarize data include measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation, interquartile range).
This chapter presents the analysis and results of a study of 200 psychology students at PUP. It includes tables on the demographic profile of respondents and effects of technological development on their socialization, self-esteem, and school performance. It also analyzes whether there is a correlation between technological developments of cellular phones and changes in respondents' behavior.
This document provides an overview of different methods for presenting data, including textual, tabular, and graphical methods. It discusses topics such as ungrouped versus grouped data, frequency distribution tables, stem-and-leaf plots, relative frequency tables, cumulative frequency tables, and contingency tables. Examples are provided to illustrate key concepts and techniques for organizing data using these various presentation methods. The objectives are to be able to prepare different types of tables and graphs, as well as read and interpret the information conveyed by these data visualization tools.
1. The document discusses different methods for presenting data, including textual, tabular, and graphical methods.
2. It provides examples of how to prepare a stem-and-leaf plot, construct a frequency distribution table, and define key terms related to grouped and ungrouped data presentation.
3. The objectives are to describe how to prepare a stem-and-leaf plot, describe data textually, construct a frequency distribution table, create graphs, and interpret graphs and tables.
2. week 2 data presentation and organizationrenz50
Here are the answers to the questions:
A.
1. The variables in the graph are age (x-axis) and frequency (y-axis).
2. The variables are quantitative.
3. The variables are discrete.
4. No, a pie chart could not be used to display this data since it involves quantitative variables rather than categorical variables.
B.
1. A line graph would most appropriately represent the number of students enrolled at a local college for each year during the last 5 years. This involves two quantitative variables - years on the x-axis and enrollments on the y-axis.
2. A bar graph would most appropriately represent the frequency of each type of crime committed in
This document provides information on various methods of presenting data, including tabular, graphical, and textual presentation. It discusses principles of data presentation and different types of tables, charts, and diagrams that can be used including simple tables, frequency distribution tables, bar charts, histograms, line graphs and pie charts. It also covers concepts like class intervals, frequency, relative frequency and discusses worked examples of various methods of data presentation.
Descriptive statistics can summarize and graphically present data. Tabular presentations display data in a grid, with tables showing frequencies of categories. Graphical presentations include bar graphs to show frequencies, pie charts to show proportions, and line graphs to show trends over time. Frequency distributions organize raw data into meaningful patterns for analysis by specifying class intervals and calculating frequencies and cumulative frequencies.
Mathematics 7 Frequency Distribution Table.pptxJeraldelEncepto
The document provides instructions for constructing a frequency distribution table using test score data from 60 students. It explains how to determine the number of class intervals, calculate the class width, tally the scores within each interval, and record the frequencies. The steps include finding the range of scores, dividing the range by the number of intervals, establishing the class limits, and populating the frequency table with tallies and counts.
This document discusses different methods for organizing data in research. It describes data organization as the process of structuring collected factual information in a way that is accepted by the scientific community. Proper data organization is important for research because it allows facts to be represented in context and helps researchers answer questions and hypotheses. The document then explains three common ways to organize data: frequency distribution tables, stem-and-leaf diagrams, and different types of charts including bar charts, pie charts, line charts, and histograms. Guidelines are provided for constructing each of these data organization methods.
Frequency_Distribution-1.ppt *Constructing Frequency Distribution Table)MayFelwa
The document discusses frequency distributions and how to construct them. It provides guidelines for constructing a frequency distribution, including deciding on the number of classes, finding the class width and limits, tallying data points into classes, and counting the tallies to determine frequencies. An example is shown of constructing a frequency distribution for a data set of 30 students' ages, with classes determined to have an interval size of 8 years based on 5 total classes.
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.
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 various methods for presenting data, including tabular form, arrays, simple tables, frequency distributions, and stem-and-leaf displays. It provides examples and tasks to practice each method. Specifically, it discusses how to construct frequency distributions and stem-and-leaf displays, including how to determine class limits, boundaries, widths, and marks. The goal is to organize and present data in a meaningful way that allows for easy interpretation and analysis.
This document provides instructions and examples for creating stem-and-leaf plots, frequency tables, histograms, and cumulative frequency tables from data sets. It includes step-by-step explanations and examples of how to organize and summarize data using these graphical representations. Key terms like stem, leaf, frequency, interval, and cumulative frequency are also defined. Quiz problems at the end ask the reader to apply the methods by creating a stem-and-leaf plot, frequency table, and histogram from sample data sets.
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 descriptive statistics concepts including measures of center (mean, median, mode), measures of variation (range, standard deviation, variance), and properties of distributions (symmetric, skewed). Frequency tables are presented as a method to summarize data, including guidelines for construction and different types (relative frequency and cumulative frequency). Common notation and formulas are provided.
This document provides an overview of key concepts in probability and statistics including:
1. Definitions of experimental units, variables, samples, populations, and types of data.
2. Methods for graphing univariate data distributions including bar charts, pie charts, histograms and more.
3. Techniques for interpreting graphs and describing data distributions based on their shape, proportion of measurements in intervals, and presence of outliers.
The document discusses various methods for organizing and presenting quantitative and qualitative data, including frequency distribution tables, graphs, charts, and diagrams. It provides examples of different types of tables, bar graphs, pie charts, histograms, line graphs, frequency polygons, scatter plots, and more. It also outlines general principles for designing clear and informative tables, such as using titles, labeling rows and columns, and summarizing the presented data.
This document discusses descriptive and inferential statistics, and how to organize data into frequency distribution tables. Descriptive statistics summarize data, while inferential statistics are used to generalize results to populations. Frequency distribution tables arrange data into class intervals to show the distribution of a variable or combination of variables. The tables include the class, frequency, relative frequency, and cumulative frequency. An example frequency distribution table is provided using data on number of children from 20 individuals.
The document defines basic statistics and discusses frequency distribution and types of frequency distributions. It provides steps to construct discrete and continuous frequency distributions, including determining class limits and boundaries. Examples are given to demonstrate creating frequency tables from raw data for discrete and continuous variables. Key concepts discussed include tally marks, frequencies, class intervals, midpoints, and cumulative frequencies.
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You can see the future first in San Francisco.
Over the past year, the talk of the town has shifted from $10 billion compute clusters to $100 billion clusters to trillion-dollar clusters. Every six months another zero is added to the boardroom plans. Behind the scenes, there’s a fierce scramble to secure every power contract still available for the rest of the decade, every voltage transformer that can possibly be procured. American big business is gearing up to pour trillions of dollars into a long-unseen mobilization of American industrial might. By the end of the decade, American electricity production will have grown tens of percent; from the shale fields of Pennsylvania to the solar farms of Nevada, hundreds of millions of GPUs will hum.
The AGI race has begun. We are building machines that can think and reason. By 2025/26, these machines will outpace college graduates. By the end of the decade, they will be smarter than you or I; we will have superintelligence, in the true sense of the word. Along the way, national security forces not seen in half a century will be un-leashed, and before long, The Project will be on. If we’re lucky, we’ll be in an all-out race with the CCP; if we’re unlucky, an all-out war.
Everyone is now talking about AI, but few have the faintest glimmer of what is about to hit them. Nvidia analysts still think 2024 might be close to the peak. Mainstream pundits are stuck on the wilful blindness of “it’s just predicting the next word”. They see only hype and business-as-usual; at most they entertain another internet-scale technological change.
Before long, the world will wake up. But right now, there are perhaps a few hundred people, most of them in San Francisco and the AI labs, that have situational awareness. Through whatever peculiar forces of fate, I have found myself amongst them. A few years ago, these people were derided as crazy—but they trusted the trendlines, which allowed them to correctly predict the AI advances of the past few years. Whether these people are also right about the next few years remains to be seen. But these are very smart people—the smartest people I have ever met—and they are the ones building this technology. Perhaps they will be an odd footnote in history, or perhaps they will go down in history like Szilard and Oppenheimer and Teller. If they are seeing the future even close to correctly, we are in for a wild ride.
Let me tell you what we see.
Codeless Generative AI Pipelines
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https://ml.dssconf.pl/user.html#!/lecture/DSSML24-041a/rate
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Timothy Spann
https://www.youtube.com/@FLaNK-Stack
https://medium.com/@tspann
https://www.datainmotion.dev/
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2. Presentation of Data
Objectives: At the end of the lesson,
the students should be able to:
1. Prepare a stem-and-leaf plot
2. Describe data in textual form
3. Construct frequency distribution table
4. Create graphs
5. Read and interpret graphs and tables
MCPegollo/Basic Statistics/SRSTHS
3. Ungrouped vs. Grouped Data
Data can be classified as grouped or
ungrouped.
Ungrouped data are data that are not
organized, or if arranged, could only be
from highest to lowest or lowest to
highest.
Grouped data are data that are
organized and arranged into different
classes or categories.
MCPegollo/Basic Statistics/SRSTHS
4. Presentation of Data
Textual
Method
• Rearrangem
ent from
lowest to
highest
• Stem-and-leaf
plot
Tabular
Method
• Frequency
distribution
table (FDT)
• Relative
FDT
• Cumulative
FDT
• Contingency
Table
Graphical
Method
• Bar Chart
• Histogram
• Frequency
Polygon
• Pie Chart
• Less than,
greater than
Ogive
MCPegollo/Basic Statistics/SRSTHS
5. Textual Presentation of Data
Data can be presented using
paragraphs or sentences. It involves
enumerating important characteristics,
emphasizing significant figures and
identifying important features of data.
MCPegollo/Basic Statistics/SRSTHS
6. Textual Presentation of Data
Example. You are asked to present the
performance of your section in the
Statistics test. The following are the
test scores of your class:
34 42 20 50 17 9 34 43
50 18 35 43 50 23 23 35
37 38 38 39 39 38 38 39
24 29 25 26 28 27 44 44
49 48 46 45 45 46 45 46
MCPegollo/Basic Statistics/SRSTHS
7. Solution
First, arrange the data in order for you to
identify the important characteristics. This
can be done in two ways: rearranging from
lowest to highest or using the stem-and-leaf
plot.
Below is the rearrangement of data from lowest
to highest:
9 23 28 35 38 43 45 48
17 24 29 37 39 43 45 49
18 25 34 38 39 44 46 50
20 26 34 38 39 44 46 50
23 27 35 38 42 45 46 50
MCPegollo/Basic Statistics/SRSTHS
8. With the rearranged data, pertinent data
worth mentioning can be easily
recognized. The following is one way
of presenting data in textual form.
In the Statistics class of 40 students, 3 obtained
the perfect score of 50. Sixteen students got a score
of 40 and above, while only 3 got 19 and below.
Generally, the students performed well in the test
with 23 or 70% getting a passing score of 38 and
above.
MCPegollo/Basic Statistics/SRSTHS
9. Another way of rearranging data is by
making use of the stem-and-leaf plot.
What is a stem-and-leaf plot?
Stem-and-leaf Plot is a table which
sorts data according to a certain pattern. It
involves separating a number into two parts.
In a two-digit number, the stem consists of
the first digit, and the leaf consists of the
second digit. While in a three-digit number,
the stem consists of the first two digits, and
the leaf consists of the last digit. In a one-digit
number, the stem is zero.
MCPegollo/Basic Statistics/SRSTHS
10. Below is the stem-and-leaf plot of the
ungrouped data given in the example.
Stem Leaves
0 9
1 7,8
2 0,3,3,4,5,6,7,8,9
3 4,4,5,5,7,8,8,8,8,9,9,9
4 2,3,3,4,4,5,5,5,6,6,6,8,9
5 0,0,0
Utilizing the stem-and-leaf plot, we can readily see the
order of the data. Thus, we can say that the top ten
got scores 50, 50, 50, 49, 48, 46, 46, 46,45, and 45
and the ten lowest scores are 9, 17, 18, 20,
23,23,24,25,26, and 27. MCPegollo/Basic Statistics/SRSTHS
11. Exercise:
Prepare a stem-and-leaf plot and
present in textual form.
The ages of 40 teachers in a public
school
23 27 28 36 35 38 39 40
32 42 44 54 56 48 55 48
30 31 35 36 47 48 43 38
34 26 28 29 45 34 45 44
36 38 39 38 36 35 40 40
MCPegollo/Basic Statistics/SRSTHS
Stem Leaf
2 3,6,7,8,8,9
3 0,1,2,4,4,5,5,5,6,6,6,6,8,8,8,8,9,9
4 0,0,0,2,3,4,4,5,5,7,8,8,8
5 4,5,6
12. Tabular Presentation of Data
Below is a sample of a table with all of its parts
indicated:
MCPegollo/Basic Statistics/SRSTHS
http://www.sws.org.ph/youth.htm
Table Number
Table Title
Column Header
Row Classifier
Body
Source Note
13. Frequency Distribution Table
A frequency distribution table is a table
which shows the data arranged into
different classes(or categories) and
the number of cases(or frequencies)
which fall into each class.
The following is an illustration of a
frequency distribution table for
ungrouped data:
MCPegollo/Basic Statistics/SRSTHS
14. Sample of a Frequency Distribution
Table for Ungrouped Data
Table 1.1
Frequency Distribution for the Ages of 50
Students Enrolled in Statistics
Age Frequency
12 2
13 13
14 27
15 4
16 3
17 1
N = 50
MCPegollo/Basic Statistics/SRSTHS
15. Sample of a Frequency
Distribution Table for Grouped
Data Table 1.2
Frequency Distribution Table for the Quiz Scores of
50 Students in Geometry
Scores Frequency
0 - 2 1
3 - 5 2
6 - 8 13
9 - 11 15
12 - 14 19
MCPegollo/Basic Statistics/SRSTHS
16. Lower Class Limits
are the smallest numbers that can actually belong
to different classes
Rating Frequency
0 - 2 1
3 - 5 2
6 - 8 13
9 - 11 15
12 - 14 19
17. Lower Class Limits
are the smallest numbers that can
actually belong to different classes
Lower Class
Limits
Rating Frequency
0 - 2 1
3 - 5 2
6 - 8 13
9 - 11 15
12 - 14 19
18. Upper Class Limits
are the largest numbers that can actually
belong to different classes
Rating Frequency
0 - 2 1
3 - 5 2
6 - 8 13
9 - 11 15
12 - 14 19
19. Upper Class Limits
are the largest numbers that can actually
belong to different classes
Upper Class
Limits
Rating Frequency
0 - 2 1
3 - 5 2
6 - 8 13
9 - 11 15
12 - 14 19
20. Class Boundaries
are the numbers used to separate classes,
but without the gaps created by class limits
22. Class Boundaries
number separating classes
Class
Boundaries
Rating Frequency
- 0.5
0 - 2 20
3 - 5 14
6 - 8 15
9 - 11 2
12 - 14 1
2.5
5.5
8.5
11.5
14.5
23. Class Midpoints
The Class Mark or Class Midpoint is the
respective average of each class limits
24. Class Midpoints
midpoints of the classes
Class
Midpoints
Rating Frequency
0 - 1 2 20
3 - 4 5 14
6 - 7 8 15
9 - 10 11 2
12 - 13 14 1
25. Class Width
is the difference between two consecutive lower class
limits or two consecutive class boundaries
Rating Frequency
0 - 2 20
3 - 5 14
6 - 8 15
9 - 11 2
12 - 14 1
26. Class Width
is the difference between two consecutive lower class
limits or two consecutive class boundaries
Class Width
Rating Frequency
3 0 - 2 20
3 3 - 5 14
3 6 - 8 15
3 9 - 11 2
3 12 - 14 1
27. Guidelines For Frequency Tables
1. Be sure that the classes are mutually exclusive.
2. Include all classes, even if the frequency is zero.
3. Try to use the same width for all classes.
4. Select convenient numbers for class limits.
5. Use between 5 and 20 classes.
6. The sum of the class frequencies must equal the
number of original data values.
28. Constructing A Frequency Table
1. Decide on the number of classes .
2. Determine the class width by dividing the range by the number of
classes (range = highest score - lowest score) and round
up.
class width round up of
range
number of classes
3. Select for the first lower limit either the lowest score or a
convenient value slightly less than the lowest score.
4. Add the class width to the starting point to get the second lower
class limit, add the width to the second lower limit to get the
third, and so on.
5. List the lower class limits in a vertical column and enter the
upper class limits.
6. Represent each score by a tally mark in the appropriate class.
Total tally marks to find the total frequency for each class.
29. Homework
Gather data on the ages of your
classmates’ fathers, include your own.
Construct a frequency distribution table for
the data gathered using grouped and
ungrouped data.
What are the advantages and
disadvantages of using ungrouped
frequency distribution table?
What are the advantages and
disadvantages of using grouped
frequency distribution table?
MCPegollo/Basic Statistics/SRSTHS
34. Complete FDT
A complete FDT has class mark or
midpoint (x), class boundaries (c.b),
relative frequency or percentage
frequency, and the less than
cumulative frequency (<cf) and the
greater than cumulative frequency
(>cf).
MCPegollo/Basic Statistics/SRSTHS
35. Complete Frequency Table
Grouped Frequency Distribution for the Test
Class
Intervals
(ci)
<cf
Table 2-6
>cf
Scores of 52 Students in Statistics
Frequency
(f)
Class
Mark (x)
Relative
Frequency
(rf)
Class
Boundary
(cb)
0 - 2 20 1 -0.5 – 2.5 38.5% 20 52
3 – 5 14 4 2.5 – 5.5 26.9% 34 32
6 – 8 15 7 5.5 – 8.5 28.8% 49 18
9 – 11 2 10 8.5 – 11.5 3.8% 51 3
12 – 14 1 13 11.5 – 14.5 1.9% 52 1
36. Exercise:
For each of the following class intervals, give
the class width(i), class mark (x), and class
boundary (cb)
Class interval (ci) Class Width Class Mark Class
Boundary
MCPegollo/Basic Statistics/SRSTHS
a. 4 – 8
b. 35 – 44
c. 17 – 21
d. 53 – 57
e. 8 – 11
f. 108 – 119
g. 10 – 19
h. 2.5 – 2. 9
i. 1. 75 – 2. 25
37. Construct a complete FDT with 7
classes
The following are the IQ scores of 60
student applicants in a certain high
school
128 106 96 94 85 75
113 103 96 91 94 70
109 113 109 100 81 81
103 113 91 88 78 75
106 103 100 88 81 81
113 106 100 96 88 78
96 109 94 96 88 70
103 102 88 78 95 90
99 89 87 96 95 104
89 99 101 105 103 125
MCPegollo/Basic Statistics/SRSTHS
38. Contingency Table
This is a table which shows the data
enumerated by cell. One type of such
table is the “r by c” (r x c) where the
columns refer to “c” samples and the
rows refer to “r” choices or
alternatives.
MCPegollo/Basic Statistics/SRSTHS
39. Example
Table 1
The Contingency Table for the Opinion of Viewers on
the TV program “Budoy”
Choice/Sample Men Women Children Total
Like the Program 50 56 45 151
Indifferent 23 16 12 51
Do not like the
43 55 40 138
program
Total 116 127 97 340
Give as many findings as you can, and draw as many conclusions
from your findings. The next table can help you identify significant
findings.
MCPegollo/Basic Statistics/SRSTHS
40. Example
Table 1
The Contingency Table for the Opinion of Viewers on
the TV program “Budoy”
MCPegollo/Basic Statistics/SRSTHS
Choice/Sampl
e
Men Women Children Total
Like the
Program
50 (33%)
(43%)
56(37%)
(44%)
45(30%)
(46%)
151
(44%)
Indifferent 23(45%)
(20%)
16(31%)
(13%)
12(24%)
(12%)
51
(15%)
Do not like the
program
43(53%)
(37%)
55(40%)
(43%)
40(29%)
(41%)
138(41%)
Total 116
(34%)
127
(37%)
97
(28%)
340
Do not use this table for presentation because the percentages might
confuse the readers. Can you explain the percentages in each cell?