This module discusses computing measures of central tendency (mean, median, mode) for grouped data using two methods: 1) class marks and 2) coded deviations. It provides examples and practice problems for finding the mean of grouped data using both formulas. Students are expected to learn how to calculate and interpret the mean, median, and mode of grouped data.
This document is the introduction section of a Grade 10 mathematics learner's module developed by the Department of Education of the Philippines. It was collaboratively developed by educators from various educational institutions and reviewed by experts. The module encourages teachers and stakeholders to provide feedback to help improve it. The introduction outlines that the module contains 8 lessons covering topics like sequences, polynomials, circles, coordinate geometry, permutations, combinations, and probability. It is intended to develop students' critical thinking and problem solving skills in support of the K-12 education program in the Philippines.
Measures of central tendency (ungrouped data)LilianneSoriano
This document defines and provides examples of the three measures of central tendency: mean, median, and mode. It explains that the mean is the average value found by summing all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the most frequently occurring value. The document provides examples of calculating and interpreting these measures. It then gives practice problems asking to find and analyze these values for different data sets.
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILESChuckry Maunes
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILES
Video Presentation Link: https://www.youtube.com/watch?v=bRYWBbvOMpo
Reference: Grade 10 Mathematics LM
This document defines and provides formulas for several statistical analysis methods: frequency and percentage distribution to calculate percentages for data profiles; mean to calculate the average value; t-test to determine if there are significant differences between the means of two variables; analysis of variance (ANOVA) to determine if frequencies differ significantly among multiple groups; Pearson product-moment correlation coefficient to measure the association between two variables; multiple correlation to test the relationship between independent and dependent variables; and multiple regression to predict dependent variables from independent variables.
Here are the answers to the pre-assessment questions:
1. B
2. A
3. B
4. D
5. B
6. C
7. C
8. A
9. B
10. C
11. B
12. A
13. B
14. B
For the mini-research question, here is a suggested outline:
Conduct a mini-research or survey among your classmates to determine the following:
1. Number of students interested to join the FUN RUN activity
2. Possible date preference for the activity
3. Suggested registration fee and minimum pledges
4. Prizes for top 3 runners
how to determine your sample size using Slovin's formula.
please click subscribe to get notifications when new materials are uploaded.
also kindly hit the like and share button so others may easily find this material.
thanks.
This course introduces students to the nature of mathematics by exploring how it describes patterns found in nature and its applications in daily life. Students will learn that mathematics is more than just formulas, but also a means of understanding aesthetics, logic, and science. The course will survey how mathematics provides tools for managing finances, making choices, appreciating designs, and dividing resources. Students will complete exercises applying mathematical concepts to gain a broader understanding of its dimensions and test their comprehension.
This document is the introduction section of a Grade 10 mathematics learner's module developed by the Department of Education of the Philippines. It was collaboratively developed by educators from various educational institutions and reviewed by experts. The module encourages teachers and stakeholders to provide feedback to help improve it. The introduction outlines that the module contains 8 lessons covering topics like sequences, polynomials, circles, coordinate geometry, permutations, combinations, and probability. It is intended to develop students' critical thinking and problem solving skills in support of the K-12 education program in the Philippines.
Measures of central tendency (ungrouped data)LilianneSoriano
This document defines and provides examples of the three measures of central tendency: mean, median, and mode. It explains that the mean is the average value found by summing all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the most frequently occurring value. The document provides examples of calculating and interpreting these measures. It then gives practice problems asking to find and analyze these values for different data sets.
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILESChuckry Maunes
MEASURES OF POSITION FOR UNGROUPED DATA : QUARTILES , DECILES , & PERCENTILES
Video Presentation Link: https://www.youtube.com/watch?v=bRYWBbvOMpo
Reference: Grade 10 Mathematics LM
This document defines and provides formulas for several statistical analysis methods: frequency and percentage distribution to calculate percentages for data profiles; mean to calculate the average value; t-test to determine if there are significant differences between the means of two variables; analysis of variance (ANOVA) to determine if frequencies differ significantly among multiple groups; Pearson product-moment correlation coefficient to measure the association between two variables; multiple correlation to test the relationship between independent and dependent variables; and multiple regression to predict dependent variables from independent variables.
Here are the answers to the pre-assessment questions:
1. B
2. A
3. B
4. D
5. B
6. C
7. C
8. A
9. B
10. C
11. B
12. A
13. B
14. B
For the mini-research question, here is a suggested outline:
Conduct a mini-research or survey among your classmates to determine the following:
1. Number of students interested to join the FUN RUN activity
2. Possible date preference for the activity
3. Suggested registration fee and minimum pledges
4. Prizes for top 3 runners
how to determine your sample size using Slovin's formula.
please click subscribe to get notifications when new materials are uploaded.
also kindly hit the like and share button so others may easily find this material.
thanks.
This course introduces students to the nature of mathematics by exploring how it describes patterns found in nature and its applications in daily life. Students will learn that mathematics is more than just formulas, but also a means of understanding aesthetics, logic, and science. The course will survey how mathematics provides tools for managing finances, making choices, appreciating designs, and dividing resources. Students will complete exercises applying mathematical concepts to gain a broader understanding of its dimensions and test their comprehension.
This document is the introduction section of a Grade 10 mathematics learner's module developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools, colleges, and universities. The introduction provides an overview of the material, noting that it is designed to support the K-12 Basic Education Program and ensure students meet expected standards. It describes the development and review process and lists the eight modules included in the material, which are aimed at developing students' critical thinking and problem-solving skills.
Chapter 6 the review of related literature and studiesMaria Theresa
Here are the steps to take to write a literature review:
1. Define your research topic. Your literature review should be focused on a specific area related to your research problem or question.
2. Search academic databases and other sources. Use keywords related to your topic to search databases like Google Scholar, ERIC, PsycINFO, and more.
3. Take detailed notes. As you find relevant sources, take thorough notes including the author, year, title, source, key findings and conclusions. Cite sources using APA or other required style.
4. Organize your sources. Group related sources together around important themes, theories, concepts or debates. This will help structure your review.
5
The document provides background information on factors that affect students' mathematics performance. It discusses how positive attitudes and understanding the real-world applications of math can improve performance. The conceptual framework outlines how student-related factors like interest and study habits, and teacher-related factors like personality, teaching skills, and instructional materials influence mathematics performance. The study aims to determine the extent of these factors and their relationship to performance among high school students.
Frequency and percentage distributions organize raw data by counting observations within each data point or group. Weighted means calculate averages where some data points contribute more weight than others. Statistical treatment of data through methods like these is essential to appropriately analyze data and draw valid conclusions from experiments.
1. The document discusses Value-Added Tax (VAT) in the Philippines, including what it is, who pays it, tax rates, and invoicing/receipt requirements for VAT-registered businesses.
2. VAT is imposed on the sale, barter, exchange or lease of goods/properties and services in the Philippines at 12% of the gross selling price or gross receipts. It is also imposed on imports.
3. Businesses whose gross sales/receipts exceed 1.9 million pesos per year must register for VAT and charge VAT on sales, issue VAT invoices/receipts, and file monthly VAT returns.
The document provides a literature review on import products in hardware establishments. It discusses foreign literature on international trade and how trade differs between domestic and international markets. Local literature examines issues like parallel imports in the pharmaceutical industry and import substitution strategies. The theoretical framework discusses the conditionally-free import theory. There are also definitions of key terms like importing problems and ownership knowledge.
This chapter outlines the research methodology used in the study. It describes the descriptive survey research design used to assess the socio-demographic profiles and career choices of senior high school students. It also describes the population and sample, which consisted of senior high school students from a particular school. A researcher-developed questionnaire was used to collect data on student profiles and career preferences. Data gathering procedures and the statistical analysis of the data collected, including frequencies, percentages, means, and correlations, are also described.
The document proposes a Speech Festival 2015 event for BSED-III English students at Surigao del Sur State University. The event aims to encourage students to participate and showcase their speaking skills through various individual and group literary events like oration, storytelling, declamation, and news casting. It will be held on October 14, 2015 in Room 205 and have a budget of 1,950 PHP to cover snacks, certificates, and other expenses. The event is expected to help students perform literary pieces and reflect on the role of language in teaching speaking.
Grade 10 Math - Second Quarter Summative Testrobengie monera
This document appears to be a summative test for a 10th grade mathematics class covering topics in polynomials and geometry. It contains 45 multiple choice questions testing students' understanding of polynomial functions, properties of circles, coordinate geometry, and solving geometric problems using coordinates. The test includes questions on identifying the degree and leading term of polynomials, graphing polynomial functions, properties of secants, tangents, and circles, finding distances and areas using coordinates, and identifying geometric shapes from their vertices.
This document provides an overview of sources for conducting a local related literature review and local studies. It discusses that a literature review analyzes published work in a specific topic area, while related studies examine previous research conducted on the topic. Sources of local literature and studies mentioned include books, journals, theses/dissertations from Philippine universities. Specific databases are also listed that provide access to Philippine periodicals and publications. Examples of a local literature and local study are then briefly described to illustrate the concepts.
This document provides an introduction to and overview of a learning module on sequences. It outlines two main lessons that will be covered:
1) Arithmetic Sequences - including finding the nth term, next terms, means, and sums of terms
2) Geometric and Other Sequences - including finding the nth term, means, and sums of terms for geometric sequences as well as exploring other types of sequences like harmonic and Fibonacci sequences.
The module will help students learn about different types of sequences, how to analyze and calculate their properties, and apply these concepts to solve real-world problems. A pre-assessment is also included to gauge students' prior knowledge on topics related to sequences.
This is the first chapter of the course Readings in Philippine History as per the course guide from Commission on Higher Education.
Course sub-topics:
1. Meaning and Relevance of History
2. Distinction of Primary and Secondary source; External and Internal Criticism
This chapter discusses the presentation, analysis, and interpretation of data in a research paper. It explains that data should be presented in chronological order through statistical tables and graphs, textual presentation, and interpretation or inferences. The chapter focuses on guidelines for tabular presentation, including constructing tables with titles, numbers, headings, bodies, and notes. It also discusses graphical presentation of data through common graphs like bar graphs, line graphs, circle graphs, pictograms, and map graphs. The chapter notes that textual presentation involves using statements with numbers to describe data and supplement tables and graphs. It concludes that interpretation should follow each table and include conditions, possible causes, possible effects, and comparisons to previous studies.
There are over a hundred indigenous groups in the Philippines with varying populations, living primarily in Luzon, Visayas, and Mindanao. In Luzon, the main groups are the Igorots of the Cordillera Mountains, the Negritos including the Agta and Aeta, and the Caraballo tribes. In Visayas, the Mangyans inhabit Mindoro island. In Mindanao, the Lumad are non-Muslim hill tribes while the Moro practice Islam and include groups like the Maranao and Maguindanao. These indigenous communities have maintained distinct cultures and traditions but have also been influenced by colonialism and migration over the centuries.
This document is the learner's material for precalculus developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools. The document contains the copyright notice and details that it is the property of the Department of Education and may not be reproduced without their permission. It provides the table of contents that outlines the units and lessons covered in the material.
This module discusses measures of central tendency for grouped data. It introduces computing the mean, median, and mode for grouped data using class marks and frequencies. It provides formulas and examples for finding the mean using class marks and the coded deviation method. Students are given practice problems to calculate the mean of various grouped data sets involving test scores, heights, ages, incomes, and more using both methods.
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 contains titles for potential research projects. The research titles cover a wide range of topics related to the impacts of COVID-19, such as the pandemic's effect on small businesses, students' self-learning skills, and family relationships during community quarantine. Other topics include the influence of packaging and branding on consumer behavior, the relationship between chess and math skills, and feasibility studies for various sustainable energy and agriculture projects.
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.
This module discusses measures of variability such as range and standard deviation. It provides examples of computing the range of various data sets as the difference between the highest and lowest values. Standard deviation is introduced as a more reliable measure that considers how far all values are from the mean. Students learn to calculate standard deviation by finding the deviation of each value from the mean, squaring the deviations, taking the average of the squared deviations, and extracting the square root. They practice computing and interpreting the range and standard deviation of sample data sets.
This document is the introduction section of a Grade 10 mathematics learner's module developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools, colleges, and universities. The introduction provides an overview of the material, noting that it is designed to support the K-12 Basic Education Program and ensure students meet expected standards. It describes the development and review process and lists the eight modules included in the material, which are aimed at developing students' critical thinking and problem-solving skills.
Chapter 6 the review of related literature and studiesMaria Theresa
Here are the steps to take to write a literature review:
1. Define your research topic. Your literature review should be focused on a specific area related to your research problem or question.
2. Search academic databases and other sources. Use keywords related to your topic to search databases like Google Scholar, ERIC, PsycINFO, and more.
3. Take detailed notes. As you find relevant sources, take thorough notes including the author, year, title, source, key findings and conclusions. Cite sources using APA or other required style.
4. Organize your sources. Group related sources together around important themes, theories, concepts or debates. This will help structure your review.
5
The document provides background information on factors that affect students' mathematics performance. It discusses how positive attitudes and understanding the real-world applications of math can improve performance. The conceptual framework outlines how student-related factors like interest and study habits, and teacher-related factors like personality, teaching skills, and instructional materials influence mathematics performance. The study aims to determine the extent of these factors and their relationship to performance among high school students.
Frequency and percentage distributions organize raw data by counting observations within each data point or group. Weighted means calculate averages where some data points contribute more weight than others. Statistical treatment of data through methods like these is essential to appropriately analyze data and draw valid conclusions from experiments.
1. The document discusses Value-Added Tax (VAT) in the Philippines, including what it is, who pays it, tax rates, and invoicing/receipt requirements for VAT-registered businesses.
2. VAT is imposed on the sale, barter, exchange or lease of goods/properties and services in the Philippines at 12% of the gross selling price or gross receipts. It is also imposed on imports.
3. Businesses whose gross sales/receipts exceed 1.9 million pesos per year must register for VAT and charge VAT on sales, issue VAT invoices/receipts, and file monthly VAT returns.
The document provides a literature review on import products in hardware establishments. It discusses foreign literature on international trade and how trade differs between domestic and international markets. Local literature examines issues like parallel imports in the pharmaceutical industry and import substitution strategies. The theoretical framework discusses the conditionally-free import theory. There are also definitions of key terms like importing problems and ownership knowledge.
This chapter outlines the research methodology used in the study. It describes the descriptive survey research design used to assess the socio-demographic profiles and career choices of senior high school students. It also describes the population and sample, which consisted of senior high school students from a particular school. A researcher-developed questionnaire was used to collect data on student profiles and career preferences. Data gathering procedures and the statistical analysis of the data collected, including frequencies, percentages, means, and correlations, are also described.
The document proposes a Speech Festival 2015 event for BSED-III English students at Surigao del Sur State University. The event aims to encourage students to participate and showcase their speaking skills through various individual and group literary events like oration, storytelling, declamation, and news casting. It will be held on October 14, 2015 in Room 205 and have a budget of 1,950 PHP to cover snacks, certificates, and other expenses. The event is expected to help students perform literary pieces and reflect on the role of language in teaching speaking.
Grade 10 Math - Second Quarter Summative Testrobengie monera
This document appears to be a summative test for a 10th grade mathematics class covering topics in polynomials and geometry. It contains 45 multiple choice questions testing students' understanding of polynomial functions, properties of circles, coordinate geometry, and solving geometric problems using coordinates. The test includes questions on identifying the degree and leading term of polynomials, graphing polynomial functions, properties of secants, tangents, and circles, finding distances and areas using coordinates, and identifying geometric shapes from their vertices.
This document provides an overview of sources for conducting a local related literature review and local studies. It discusses that a literature review analyzes published work in a specific topic area, while related studies examine previous research conducted on the topic. Sources of local literature and studies mentioned include books, journals, theses/dissertations from Philippine universities. Specific databases are also listed that provide access to Philippine periodicals and publications. Examples of a local literature and local study are then briefly described to illustrate the concepts.
This document provides an introduction to and overview of a learning module on sequences. It outlines two main lessons that will be covered:
1) Arithmetic Sequences - including finding the nth term, next terms, means, and sums of terms
2) Geometric and Other Sequences - including finding the nth term, means, and sums of terms for geometric sequences as well as exploring other types of sequences like harmonic and Fibonacci sequences.
The module will help students learn about different types of sequences, how to analyze and calculate their properties, and apply these concepts to solve real-world problems. A pre-assessment is also included to gauge students' prior knowledge on topics related to sequences.
This is the first chapter of the course Readings in Philippine History as per the course guide from Commission on Higher Education.
Course sub-topics:
1. Meaning and Relevance of History
2. Distinction of Primary and Secondary source; External and Internal Criticism
This chapter discusses the presentation, analysis, and interpretation of data in a research paper. It explains that data should be presented in chronological order through statistical tables and graphs, textual presentation, and interpretation or inferences. The chapter focuses on guidelines for tabular presentation, including constructing tables with titles, numbers, headings, bodies, and notes. It also discusses graphical presentation of data through common graphs like bar graphs, line graphs, circle graphs, pictograms, and map graphs. The chapter notes that textual presentation involves using statements with numbers to describe data and supplement tables and graphs. It concludes that interpretation should follow each table and include conditions, possible causes, possible effects, and comparisons to previous studies.
There are over a hundred indigenous groups in the Philippines with varying populations, living primarily in Luzon, Visayas, and Mindanao. In Luzon, the main groups are the Igorots of the Cordillera Mountains, the Negritos including the Agta and Aeta, and the Caraballo tribes. In Visayas, the Mangyans inhabit Mindoro island. In Mindanao, the Lumad are non-Muslim hill tribes while the Moro practice Islam and include groups like the Maranao and Maguindanao. These indigenous communities have maintained distinct cultures and traditions but have also been influenced by colonialism and migration over the centuries.
This document is the learner's material for precalculus developed by the Department of Education of the Philippines. It was collaboratively developed by educators from public and private schools. The document contains the copyright notice and details that it is the property of the Department of Education and may not be reproduced without their permission. It provides the table of contents that outlines the units and lessons covered in the material.
This module discusses measures of central tendency for grouped data. It introduces computing the mean, median, and mode for grouped data using class marks and frequencies. It provides formulas and examples for finding the mean using class marks and the coded deviation method. Students are given practice problems to calculate the mean of various grouped data sets involving test scores, heights, ages, incomes, and more using both methods.
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 contains titles for potential research projects. The research titles cover a wide range of topics related to the impacts of COVID-19, such as the pandemic's effect on small businesses, students' self-learning skills, and family relationships during community quarantine. Other topics include the influence of packaging and branding on consumer behavior, the relationship between chess and math skills, and feasibility studies for various sustainable energy and agriculture projects.
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.
This module discusses measures of variability such as range and standard deviation. It provides examples of computing the range of various data sets as the difference between the highest and lowest values. Standard deviation is introduced as a more reliable measure that considers how far all values are from the mean. Students learn to calculate standard deviation by finding the deviation of each value from the mean, squaring the deviations, taking the average of the squared deviations, and extracting the square root. They practice computing and interpreting the range and standard deviation of sample data sets.
Mean, Median, Mode: Measures of Central Tendency Jan Nah
There are three common measures of central tendency: mean, median, and mode. The mean is the average value found 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 value that occurs most frequently. Each measure provides a single number to represent the central or typical value in a data set.
A coffee shop conducted a two-day survey to determine the average number of cappuccinos made per hour. A histogram showed the frequency of cappuccinos made within various hourly intervals. To calculate the average, interval midpoints were determined and multiplied by the frequencies. The total of these products was divided by the total frequency, determining that the average number of cappuccinos made per hour was 10.
This document introduces special products and factors of polynomials. It discusses how patterns can be used to simplify algebraic expressions and solve geometric problems. Students will learn to identify special products through pattern recognition, find special products of polynomials, and apply these concepts to real-world problems. The goals are to demonstrate understanding of key concepts and solve practice problems accurately using different strategies.
Here are the steps to find the measures of central tendency for this data set:
1. Find the mean (average) by adding all the values and dividing by the total number of values:
34 + 35 + 40 + 40 + 48 + 21 + 20 + 19 + 34 + 45 + 19 + 17 + 18 + 15 + 16 = 400
Total number of values is 15
So, mean = 400/15 = 26.67
2. Find the mode by determining the most frequent value:
The most frequent values are 40 and 19, both appearing twice. Therefore, the modes are 40 and 19.
3. Find the median by ordering the values from lowest to highest and picking the middle value:
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.
The document provides instructions for organizing and presenting statistical data using frequency tables and histograms. It discusses how to construct a frequency table by grouping raw data into intervals and tallying the frequencies. It then explains how to create a histogram by using the frequency table to draw rectangles whose widths represent intervals and heights represent frequencies. The lesson emphasizes that frequency tables and histograms are useful tools for organizing large data sets and communicating patterns in the data visually.
This document provides a teaching guide for a Statistics and Probability course for senior high school students. It begins with an introduction that discusses the importance of statistics and data analysis. It then outlines the structure and goals of the teaching guide, which includes sections on introduction, instruction, practice, enrichment, and evaluation. The guide is meant to help teachers facilitate student understanding, mastery of concepts, and a sense of ownership over their learning. It also discusses aligning the guide with DepEd and CHED standards to prepare students for college. The preface provides additional context on statistics as a discipline and its growing importance.
This document defines and provides examples for calculating the mean, median, mode, and range of a data set. It explains that the mean is calculated by adding all values and dividing by the number of values, the median involves ordering values and selecting the middle one, the mode is the most frequent value, and the range is the difference between the highest and lowest values. Examples are given for each statistical measure.
K to 12 - Grade 8 Math Learners Module Quarter 2Nico Granada
Here are the completed statements based on the conclusions:
1. n(A × B) = n(B × A).
2. A × B ≠ B × A.
The key conclusions are:
1. The cardinalities of the Cartesian products A × B and B × A are equal, since n(A × B) = n(B × A).
2. However, the sets A × B and B × A are not equal, since the ordered pairs will be arranged differently, so A × B ≠ B × A.
This document is a mathematics module on statistics II from the Malaysian Ministry of Education. It contains instructions for a 35 question multiple choice test covering statistical concepts like mean, median, mode, and data representation through tables, charts, and graphs. The questions test students' understanding of English language terms and apply statistical techniques to analyze sets of data.
This Mathematics Learner's module discusses about the basic concepts of Probability and its strategies. It also teaches includes some examples about Probability.
This learner modules talks about the Triangle Inequality. It also talks about the theorems & postulates that supports triangle inequalities in one or two triangles.
The document discusses various measures of central tendency used in statistics. The three most common measures are the mean, median, and mode. The mean is the sum of all values divided by the number of values and is affected by outliers. The median is the middle value when data is arranged from lowest to highest. The mode is the most frequently occurring value in a data set. Each measure has advantages and disadvantages depending on the type of data distribution. The mean is the most reliable while the mode can be undefined. In symmetrical distributions, the mean, median and mode are equal, but the mean is higher than the median for positively skewed data and lower for negatively skewed data.
Here are the answers:
(a) A B is shown in Set 2. It contains all elements that belong to A or B or both.
(b) A B is shown in Set 3. It contains elements that belong to both A and B.
2. Given sets P = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8}, find P Q and P Q.
3. Draw a Venn diagram to represent the following sets:
A = {x | x is a prime number less than 10}
B = {x | x is an even number less than 10}
Statistik praktis: 3 kesalahan dalam menggunakan angka rata rataGede Manggala
Dokumen tersebut memberikan tiga kesalahan umum dalam menggunakan rata-rata untuk mengambil keputusan, yaitu (1) membandingkan rata-rata beberapa kelompok tanpa melihat distribusi datanya, (2) menilai kinerja berdasarkan pencapaian rata-rata target tanpa melihat variasi aktual, (3) menghitung kapasitas operasi berdasarkan rata-rata tanpa melihat sebaran dan pola datanya. Dokumen ini men
This summary provides an overview of the document in 3 sentences:
This honors project examines how food functions symbolically in various versions of popular Western fairy tales such as "Hansel and Gretel," "Little Red Riding Hood," "Rapunzel," and "Snow White." The project begins by introducing the topic, providing definitions of key terms, and outlining the methodology. The author analyzes different versions of tales in relation to tale types and motifs related to food, consumption, gender, and social relationships to uncover new meanings and cultural insights. Tables were created as part of the research process to map and analyze how food is portrayed across versions of the selected fairy tales.
This summary provides a high-level overview of the document in 3 sentences:
The document is an excerpt from Rudyard Kipling's classic novel "The Jungle Book". It describes how Mowgli, a human child raised by wolves, is presented to the wolf pack at the monthly pack meeting. During the meeting, Shere Khan the tiger disputes the wolves' acceptance of Mowgli, but Mother Wolf defends Mowgli and he is allowed to stay with the pack.
1. This module covers quadratic functions and how to graph them. Students will learn to identify the vertex, axis of symmetry, and direction of opening of quadratic graphs.
2. Key aspects covered include how changing coefficients a, h, and k affect the width, translation, and vertical shift of the graph. When a increases, the graph narrows; changing h translates the graph left or right; and changing k shifts the graph up or down.
3. The steps for graphing a quadratic function are finding the vertex, axis of symmetry, direction of opening, and making a table of values to plot points.
This document discusses measures of central tendency, specifically how to calculate the mean of grouped data. It provides the formula for calculating the mean of grouped data and walks through an example of finding the mean test scores of students. The document demonstrates how to find the midpoint of each score group, multiply by the frequency, sum the results, and divide by the total frequency to determine the mean.
lesson 3 presentation of data and frequency distributionNerz Baldres
This document provides an overview of key concepts for presenting data and constructing frequency distributions. It defines different methods for presenting data including textual, tabular, and graphical forms. Tabular methods include components like table headings and stubs. Graphical methods are shown like bar graphs, line graphs, and pie charts. Frequency distributions arrange data by class intervals and calculate frequencies. Terms are defined for range, class interval, and cumulative and relative frequency. Examples demonstrate how to construct frequency distributions and calculate cumulative and relative frequencies.
Analysis and interpretation of Assessment.pptxAeonneFlux
The document provides information on statistics, frequency distributions, measures of central tendency (mean, median, mode), and how to calculate and interpret them. It defines statistics, descriptive and inferential statistics, and frequency distributions. It outlines the steps to construct a frequency distribution and calculate the mean, median, and mode for both ungrouped and grouped data. Examples are provided to demonstrate calculating each measure of central tendency.
Group 3 measures of central tendency and variation - (mean, median, mode, ra...reymartyvette_0611
This document discusses various measures of central tendency and variation. It defines central tendency as indicating where the center of a distribution tends to be, and mentions that measures of central tendency answer whether scores are generally high or low. It then discusses specific measures of central tendency - the mean, median, and mode - and how to calculate each one for both ungrouped and grouped data. It also discusses other measures of variation like range and standard deviation, and how to compute standard deviation for ungrouped and grouped data.
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.
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.
The steps in computing the median are similar to that of Q1 and Q3
. In finding the median,
we need first to determine the median class. The Q1 class is the class interval where
the 𝑁
4
th score is contained, while the class interval that contains the 3𝑁
4
𝑡ℎ
score is the Q3 class.
Formula :𝑄𝑘 = LB +
𝑘𝑁
4
−𝑐𝑓𝑏
𝑓𝑄𝑘
𝑖
LB = lower boundary of the of the 𝑄𝑘 class
N = total frequency
𝑐𝑓𝑏= cumulative frequency of the class before the 𝑄𝑘 class
𝑓𝑄𝑘
= frequency of the 𝑄𝑘 class
i = size of the class interval
k = the value of quartile being asked
The interquartile range describes the middle 50% of values when
ordered from lowest to highest. To find the interquartile range (IQR),
first find the median (middle value) of the upper and the lower half of
the data. These values are Q1 and Q3
. The IQR is the difference
between Q3 and Q1
.
Interquartile Range (IQR) = Q3 – Q1
The quartile deviation or semi-interquartile range is one-half the
difference between the third and the first quartile.
Quartile Deviation (QD) =
𝑄3−𝑄1
2
The formula in finding the kth decile of a distribution is
𝐷𝑘 = 𝑙𝑏𝑑𝑘 +
(
𝑘
10)𝑁 − 𝑐𝑓
𝑓𝐷𝑘
𝑖
𝐿𝐵𝑑𝑘 − 𝐿𝑜𝑤𝑒𝑟 𝐵𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑁 − 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑖𝑒𝑠
𝑐𝑓 − 𝑐𝑢𝑚𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑏𝑒𝑓𝑜𝑟𝑒 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝐹𝑑𝑘 − 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑘𝑡ℎ 𝑑𝑒𝑐𝑖𝑙𝑒
𝑖 − 𝑐𝑙𝑎𝑠𝑠 𝑠𝑖𝑧𝑒
The document discusses statistical concepts used in analyzing assessment data. It defines statistics as the science of collecting, organizing, summarizing, and interpreting data. Descriptive statistics are used to describe data through measures of central tendency like the mean, median, and mode, while inferential statistics make predictions about a larger data set based on a sample. The document outlines steps for constructing frequency distributions and calculating the mean, including determining class limits and sizes. Graphs like histograms and frequency polygons can be used to visually represent grouped assessment data.
The document provides information about descriptive statistics including how they are used to summarize and organize data from samples and populations. Descriptive statistics include measures of central tendency like the mean, median, and mode as well as measures of variability like range, interquartile range, variance and standard deviation. Examples are given showing how to calculate and present these statistics including frequency distributions, histograms, bar graphs and measures of central tendency and variability.
Mode of Grouped Data - Math 7 (4th Quarter)Carlo Luna
This document discusses the concept of mode in grouped data. It provides examples of calculating the mode of different data sets. The mode is the value that occurs most frequently in a data set. For grouped data, the mode is calculated using a formula that considers the lower boundary of the modal class, the frequency of the modal class, and the frequencies of neighboring classes. Worked examples demonstrate applying this formula to frequency distributions to determine the modal value.
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 contains data and analysis on the level of aspiration and readiness of senior high school students in pursuing tertiary education. It includes distribution tables and charts showing respondents by gender, academic strand, age, and family income. Measures of central tendency and variation are calculated on the data sets, including range, midrange, mean, median, mode, variance and standard deviation. Results are summarized on the levels of aspiration and readiness based on the analysis.
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.
Frequency Distribution (Class-interval- Tally).pptxAlwinCAsuncion
The document defines various measures of central tendency including mean, median, and mode for both ungrouped and grouped data. It also defines key terms related to frequency distributions such as lower class limit, upper class limit, class boundaries, class marks, class width, and cumulative frequency. An example is provided to illustrate the construction of a grouped frequency distribution table involving 7 classes with a class width of 7 using data on exam scores of 40 students.
Here are the steps to solve this problem:
1. Prepare the frequency distribution table with the class intervals, frequencies, and calculate fX.
2. Find the mean (x) using the formula x = fX/f.
3. Calculate the deviations (X - x).
4. Square the deviations to get (X - x)2.
5. Multiply the frequencies and squared deviations to get f(X - x)2.
6. Calculate the variance using the formula σ2 = f(X - x)2 / (f - 1).
7. Take the square root of the variance to get the standard deviation.
8. The range is the difference between the upper
Basic Statistics for Class 11, B.COm, BSW, B.A, BBA, MBAGaurav Rana
The document provides an overview of key concepts in statistics for social work. It discusses topics such as data collection methods, organization and presentation of data, measures of central tendency including mean, median and mode, and measures of dispersion. For example, it explains how to calculate the arithmetic mean for both grouped and ungrouped data using direct, assumed mean and step deviation methods. It also discusses how to calculate the median and mode for discrete and continuous data series.
This document defines and provides examples of frequency distributions and measures of central tendency. It discusses array, frequency distribution, class intervals, class boundaries, class marks, relative frequency distributions, and cumulative frequency distributions. It also covers calculating the mean, median, and mode of both ungrouped and grouped data. Formulas are provided for determining the mean, median, and mode of grouped data using class marks, frequencies, and boundaries.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
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at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
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How to Make a Field Mandatory in Odoo 17Celine George
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This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
Azure Interview Questions and Answers PDF By ScholarHat
Module 2 statistics
1. Module 2
Statistics
What this module is about
This module is about finding the measures of central tendency of grouped
data. As you go over this material, you will develop the skills in computing the
mean, median and mode of grouped data.
What you are expected to learn
This module is designed for you to find the measures of central tendency
using grouped data. Specifically, you are to find the mean, median and mode of
grouped data.
How much do you know
Use the frequency distribution table below to answer the questions.
Scores of Students in a Mathematics Test
Class Frequency
46 – 50
1
41 – 45
2
36 – 40
2
31 – 35
3
26 – 30
7
21 – 25
10
16 – 20
13
11 – 15
6
6 – 10
4
1–5
2
1. What is the class size?
2. What is the class mark of the class with the highest frequency?
3. What is ∑ fX ?
2. 4. Find the mean score.
5. What is the median class?
6. Determine the cumulative frequency of the median class.
7. Solve for the median score.
8. What is the modal class?
9. Determine the lower boundary of the modal class
10. Compute for the modal score.
What you will do
Lesson 1
The Mean of Grouped Data Using the Class Marks
When the number of items in a set of data is too big, items are grouped for
convenience. The manner of computing for the mean of grouped data is given by
the formula:
Mean =
∑(fX)
∑f
where: f is the frequency of each class
X is the class mark of class
The Greek symbol ∑ (sigma) is the mathematical symbol for summation. This
means that all items having this symbol are to be added. Thus, the symbol ∑f
means the sum of all frequencies, and ∑fX means the sum of all the products of
the frequency and the corresponding class mark.
Examples:
Compute the mean of the scores of the students in a Mathematics IV test.
Class Frequency
46 – 50
1
41 – 45
5
36 – 40
11
31 – 35
12
26 – 30
11
21 – 25
5
16 – 20
2
11 – 15
1
2
3. The frequency distribution for the data is given below. The columns X and
fX are added.
Class
46 – 50
f
1
41 – 45
5
36 – 40
21 – 25
1
1
1
2
1
1
5
16 – 20
2
11 – 15
1
31 – 35
26 – 30
X
4
8
4
3
3
8
3
3
2
8
2
3
1
8
1
3
fX
48
215
418
396
308
115
36
13
∑f = 48
∑fX = 1,549
∑(fX)
Mean =
∑f
1,549
Mean =
48
Mean =32.27
The mean score is 32.27.
Solve for the mean gross sale of Aling Mely’s Sari-sari Store for one
month.
Sales in Pesos Frequency
4,501 – 5,000
3
4,001 – 4,500
4
3,501 – 4,000
6
3,001 – 3,500
5
2,501 – 3,000
7
2,001 – 2,500
3
1,501 – 2,000
1
1,001 – 1,500
1
The frequency distribution for the data is given below. The columns X and
fX are added.
3
4. Sales in Pesos f
X
1,001 – 1,500 1 1,250
1,501 – 2,000 1 1,750
2,001 – 2,500 3 2,250
2,501 – 3,000 7 2,750
3,001 – 3,500 5 3,250
3,501 – 4,000 6 3,750
4,001 – 4,500 4 4,250
4,501 – 5,000 3 4,750
∑f = 30
∑fX = 99,000
∑(fX)
Mean =
∑f
99, 000
Mean =
30
Mean = 3,300
The mean gross sale is P3, 300.
fX
1,250
1,750
6,750
19,250
16,250
22,500
17,000
14,250
Try this out
Solve for the mean of each grouped data using the class marks.
Set A
1. Scores of Diagnostic Test of IV-Narra Students
Score Frequency
36 – 40
1
31 – 35
10
26 – 20
10
21 – 25
16
16 – 20
9
11 – 15
4
2. Height of IV-1 and IV-2 Students
Height in
cm
175 – 179
170 – 174
165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
Frequency
2
5
8
11
21
14
17
2
4
5. 3. Midyear Test Scores of IV-Newton
Score Frequency
41 – 45
1
36 – 40
8
31 – 35
8
26 – 30
14
21 – 25
7
16 – 20
2
4. Ages of San Lorenzo High School Teachers
Age
Frequency
21 – 25
5
26 – 30
8
31 – 35
8
36 – 40
11
41 – 45
15
46 – 50
14
51 – 55
12
56 – 60
5
61 – 65
2
5. Pledges to the Victims of Typhoon Mulawin
Pledges in Pesos Frequency
9,000 – 9,999
4
8,000 – 8,999
12
7,000 – 7,999
13
6,000 – 6,999
15
5,000 – 5,999
19
4,000 – 4,999
30
3,000 – 3,999
21
2,000 – 2,999
41
1,000 – 1,999
31
0 – 999
14
Set B
1. Scores of Periodic Test of IV-Molave Students
5
6. Score Frequency
46 – 50
2
41 – 45
9
36 – 40
13
31 – 35
11
26 – 30
10
21 – 25
5
2. Height of IV-2 Students
Height in
cm
175 – 179
170 – 174
165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
Frequency
3
4
10
9
24
11
13
6
3. Midyear Test Scores of Students in English
Class Frequency
91 – 95
1
86 – 90
6
81 – 85
7
76 – 80
4
71 – 75
7
66 – 70
12
61 – 65
5
56 – 80
5
51 – 55
1
46 – 50
2
4. Ages of Sta. Barbara High School Teachers
6
7. Class Frequency
21 – 25
4
26 – 30
14
31 – 35
15
36 – 40
11
41 – 45
12
46 – 50
10
51 – 55
9
56 – 60
3
61 – 65
3
5. Monthly Income of the Families of Fourth Year Students
Income in Pesos Frequency
9,000 – 9,999
18
8,000 – 8,999
22
7,000 – 7,999
33
6,000 – 6,999
56
5,000 – 5,999
50
4,000 – 4,999
31
Set C
1. Scores of Achievement Test in Filipino of IV-Kamagong Students
Score Frequency
86 – 90
2
81 – 85
9
76 – 80
8
71 – 75
13
66 – 60
12
61 – 65
6
2. Weight of First Year Students
Weight in kg Frequency
75 – 79
1
70 – 74
4
65 – 69
10
60 – 64
14
55 – 59
21
50 – 54
15
45 – 69
14
40 – 44
1
7
8. 3. Final Test Scores of IV-Rizal
Score Frequency
91 – 95
1
86 – 90
5
81 – 85
9
76 – 80
16
71 – 75
6
66 – 70
3
4. Ages of Seniro Factory Employees
Age
Frequency
21 – 25
8
26 – 30
18
31 – 35
11
36 – 40
16
41 – 45
12
46 – 50
10
51 – 55
2
56 – 60
2
61 – 65
1
5. Average Grades of Students of Engineering Block in the First
Semester
Average Grade Frequency
1.01 – 1.50
4
1.51 – 2.00
10
2.01 – 2.50
18
2.51 – 3.00
26
3.01 – 3.50
24
3.51 – 4.00
16
4.01 – 4.50
7
4.51 – 5.00
5
Lesson 2
The Mean of Grouped Data Using the Coded Deviation
8
9. An alternative formula for computing the mean of grouped data makes use
of coded deviation:
∑(fd)
Mean = A.M. +
i
∑f
where: A.M. is the assumed mean
f is the frequency of each class
d is the coded deviation from A.M.
i is the class interval
Any class mark can be considered as assumed mean. But it is convenient
to choose the class mark with the highest frequency. The class chosen to contain
A.M. is given a 0 deviation.
Subsequently, consecutive positive integers are assigned to the classes
upward and negative integers to the classes downward.
This is illustrated in the next examples using the same data in lesson 1.
Examples:
Compute the mean of the scores of the students in a Mathematics IV test.
Class Frequency
46 – 50
1
41 – 45
5
36 – 40
11
31 – 35
12
26 – 30
11
21 – 25
5
16 – 20
2
11 – 15
1
The frequency distribution for the data is given below. The columns X, d
and fd are added.
Class
46 – 50
f
1
41 – 45
5
36 – 40
X
4
8
4
3
3
8
1
1
9
d
3
fd
3
2
10
1
11
10. 31 – 35
21 – 25
1
2
1
1
5
16 – 20
2
11 – 15
1
26 – 30
3
3
2
8
2
3
1
8
1
3
0
0
-1 -11
-2 -10
-3
-6
-4
-4
A.M. = 33
∑f = 48
∑fd = -7
i=5
∑(fd)
Mean = A.M. +
i
∑f
−7
Mean = 33 + (5)
48
Mean = 33 + (-0.73)
Mean = 32.27
The mean score is 32.27.
Solve for the mean gross sale of Aling Mely’s Sari-sari Store for one
month.
Sales in Pesos Frequency
1,001 – 1,500
1
1,501 – 2,000
1
2,001 – 2,500
3
2,501 – 3,000
7
3,001 – 3,500
5
3,501 – 4,000
6
4,001 – 4,500
4
4,501 – 5,000
3
The frequency distribution for the data is given below. The columns X, d
and fd are added.
Sales in Pesos f
X
d
1,001 – 1,500 1 1,250 -3
1,501 – 2,000 1 1,750 -2
2,001 – 2,500 3 2,250 -1
10
fd
-3
-2
-3
11. 2,501 – 3,000
3,001 – 3,500
3,501 – 4,000
4,001 – 4,500
4,501 – 5,000
7
5
6
4
3
2,750
3,250
3,750
4,250
4,750
0
1
2
3
4
0
5
12
12
12
A.M. = 2,750
∑f = 30
∑fd = 33
i = 500
∑(fd)
Mean = A.M. +
i
∑f
33
Mean = 2, 750 + (500)
30
Mean = 2,750 + 550
Mean = 3,300
The mean gross sale is P3,300.
Try this out
Solve for the mean of each grouped data using coded deviation.
Set A
1.
Scores of Diagnostic Test of IV-Narra Students
Score Frequency
36 – 40
1
31 – 35
10
26 – 20
10
21 – 25
16
16 – 20
9
11 – 15
4
2.
Height of IV-1 and IV-2 Students
Height in
cm
175 – 179
170 – 174
Frequency
2
5
11
12. 165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
3.
8
11
21
14
17
2
Midyear Test Scores of IV-Newton
Score Frequency
41 – 45
1
36 – 40
8
31 – 35
8
26 – 30
14
21 – 25
7
16 – 20
2
4.
Ages of San Lorenzo High School Teachers
Age
Frequency
21 – 25
5
26 – 30
8
31 – 35
8
36 – 40
11
41 – 45
15
46 – 50
14
51 – 55
12
56 – 60
5
61 – 65
2
5.
Pledges to the Victims of Typhoon Mulawin
Pledges in Pesos Frequency
9,000 – 9,999
4
8,000 – 8,999
12
7,000 – 7,999
13
6,000 – 6,999
15
5,000 – 5,999
19
4,000 – 4,999
30
12
13. 3,000 – 3,999
2,000 – 2,999
1,000 – 1,999
0 – 999
21
41
31
14
Set B
0
1. Scores of Periodic Test of IV-Molave Students
Score Frequency
46 – 50
2
41 – 45
9
36 – 40
13
31 – 35
11
26 – 30
10
21 – 25
5
1
2
2. Height of IV-2 Students
Height in
cm
175 – 179
170 – 174
165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
3
Frequency
3
4
10
9
24
11
13
6
3. Midyear Test Scores of Students in English
Class Frequency
91 – 95
1
86 – 90
6
81 – 85
7
76 – 80
4
71 – 75
7
13
14. 66 – 70
61 – 65
56 – 80
51 – 55
46 – 50
4
12
5
5
1
2
4. Ages of Sta. Barbara High School Teachers
Class Frequency
21 – 25
4
26 – 30
14
31 – 35
15
36 – 40
11
41 – 45
12
46 – 50
10
51 – 55
9
56 – 60
3
61 – 65
2
5
6
5. Monthly Income of the Families of Fourth Year Students
Income in Pesos Frequency
9,000 – 9,999
18
8,000 – 8,999
22
7,000 – 7,999
33
6,000 – 6,999
56
5,000 – 5,999
50
4,000 – 4,999
31
Set C
0
1. Scores of Achievement Test in Filipino of IV-Kamagong Students
Score Frequency
86 – 90
2
81 – 85
9
76 – 80
8
71 – 75
13
66 – 60
12
61 – 65
6
1
2. Weight of First Year Students
14
15. Weight in kg Frequency
75 – 79
1
70 – 74
4
65 – 69
10
60 – 64
14
55 – 59
21
50 – 54
15
45 – 69
14
40 – 44
1
2
3. Final Test Scores of IV-Rizal
3
Score Frequency
91 – 95
1
86 – 90
5
81 – 85
9
76 – 80
16
71 – 75
6
66 – 70
3
4. Ages of Seniro Factory Employees
Age
Frequency
21 – 25
8
26 – 30
18
31 – 35
11
36 – 40
16
41 – 45
12
46 – 50
10
51 – 55
2
56 – 60
2
61 – 65
1
4
5. Average Grades of Students of Engineering Block in the First Semester
Average Grade Frequency
1.01 – 1.50
4
1.51 – 2.00
10
2.01 – 2.50
18
2.51 – 3.00
26
3.01 – 3.50
24
3.51 – 4.00
16
4.01 – 4.50
7
4.51 – 5.00
5
15
16. Lesson 3
The Median of Grouped Data
The median is the middle value in a set of quantities. It separates an ordered
set of data into two equal parts. Half of the quantities found above the median
and the other half is found below it.
In computing for the median of grouped data, the following formula is used:
∑ f − cf
Median = lb mc + 2
i
f mc
where: lbmc is the lower boundary of the median class
f is the frequency of each class
cf is the cumulative frequency of the lower class next to
the median class
fmc is the frequency of the median class
i is the class interval
The median class is the class that contains the
∑f
2
th
quantity. The
computed median must be within the median class.
Examples:
1. Compute the median of the scores of the students in a Mathematics IV
test.
Class Frequency
46 – 50
1
41 – 45
5
36 – 40
11
31 – 35
12
26 – 30
11
21 – 25
5
16 – 20
2
11 – 15
1
16
17. The frequency distribution for the data is given below. The columns for lb
and “less than” cumulative frequency are added.
Class
46 – 50
41 – 45
36 – 40
31 – 35
26 – 30
21 – 25
16 – 20
11 – 15
f
1
5
1
1
1
2
1
1
5
2
1
lb
“<” cf
45.5
48
40.5
47
35.5
42
30.5
31
25.5
19
20.5
15.5
10.5
8
3
1
∑f
48
=
= 24, the 24th quantity is in the class 31 – 35. Hence, the
2
2
median class is 31 – 35.
lbmc = 30.5
∑f = 48
cf = 19
fmc = 12
i=5
∑ f − cf
Median = lb mc + 2
i
f mc
48 − 19
Median = 30.5 + 2
(5)
12
Median = 30.5 + 2.08
Since
Median = 32.58
The median score is 32.58.
2. Solve for the median gross sale of Aling Mely’s Sari-sari Store for one
month.
Sales in Pesos Frequency
1,001 – 1,500
1
1,501 – 2,000
1
17
18. 2,001 – 2,500
2,501 – 3,000
3,001 – 3,500
3,501 – 4,000
4,001 – 4,500
4,501 – 5,000
3
7
5
6
4
3
The frequency distribution for the data is given below. The columns for lb
and “less than” cumulative frequency are added.
Sales in Pesos
1,001 – 1,500
1,501 – 2,000
2,001 – 2,500
2,501 – 3,000
3,001 – 3,500
3,501 – 4,000
4,001 – 4,500
4,501 – 5,000
Since
f
1
1
3
7
5
6
4
3
lb
“<” cf
1,000.5
1
1,500.5
2
2,000.5
5
2,500.5
12
3,000.5
17
3,500.5
23
4,000.5
27
4,500.5
30
∑f
30
=
= 15, the 15th quantity is in the class 3,001 – 3,500.
2
2
Hence, the median class is 3,001 – 3,500.
lbmc = 3,000.5
∑f = 30
cf = 12
fmc = 5
i = 500
Median = lb mc
∑ f − cf
+ 2
i
f mc
30 − 12
Median = 3, 000.5 + 2
(500)
5
Median = 3,000.5 + 300
18
19. Median = 3,300.5
The median score is 3,300.5.
Try this out
Solve for the median of each grouped data using coded deviation.
Set A
1.
Scores of Diagnostic Test of IV-Narra Students
Score Frequency
36 – 40
1
31 – 35
10
26 – 20
10
21 – 25
16
16 – 20
9
11 – 15
4
2.
Height of IV-1 and IV-2 Students
Height in
cm
175 – 179
170 – 174
165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
3.
Frequency
2
5
8
11
21
14
17
2
Midyear Test Scores of IV-Newton
Score Frequency
41 – 45
1
19
20. 36 – 40
31 – 35
26 – 30
21 – 25
16 – 20
4.
8
8
14
7
2
Ages of San Lorenzo High School Teachers
Age
Frequency
21 – 25
5
26 – 30
8
31 – 35
8
36 – 40
11
41 – 45
15
46 – 50
14
51 – 55
12
56 – 60
5
61 – 65
2
5.
Pledges to the Victims of Typhoon Mulawin
Pledges in Pesos Frequency
9,000 – 9,999
4
8,000 – 8,999
12
7,000 – 7,999
13
6,000 – 6,999
15
5,000 – 5,999
19
4,000 – 4,999
30
3,000 – 3,999
21
2,000 – 2,999
41
1,000 – 1,999
31
0 – 999
14
Set B
5. Scores of Periodic Test of IV-Molave Students
20
21. Score Frequency
46 – 50
2
41 – 45
9
36 – 40
13
31 – 35
11
26 – 30
10
21 – 25
5
0
2. Height of IV-2 Students
Height in
cm
175 – 179
170 – 174
165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
Frequency
3
4
10
9
24
11
13
6
1
3. Midyear Test Scores of Students in Filipino
Class Frequency
73 – 75
1
70 – 72
6
67 – 69
7
64 – 66
4
61 – 63
7
58 – 60
12
55 – 57
5
52 – 54
5
49 – 51
1
46 – 48
2
2
4. Ages of Tagkawayan High School Teachers
Class Frequency
25 – 28
4
29 – 33
14
33 – 36
15
37 – 40
11
21
22. 41 – 44
45 – 48
49 – 52
53 – 56
57 – 60
3
12
10
9
3
2
5. Monthly Income of the Families of Fourth Year Students
Income in Pesos Frequency
9,000 – 9,999
18
8,000 – 8,999
22
7,000 – 7,999
33
6,000 – 6,999
56
5,000 – 5,999
50
4,000 – 4,999
31
Set C
0
1. Final Grades in Filipino of IV-Kamagong Students
Score Frequency
89 – 91
2
86 – 88
9
83 – 85
8
80 – 82
13
77 – 79
12
74 – 76
6
1
2. Weight of First Year Students
Weight in kg Frequency
93 – 99
1
86 – 92
4
79 – 85
10
72 – 78
14
65 – 71
21
58 – 64
15
51 – 57
14
44 – 50
1
2
3. Final Grades of IV-Rizal Students in Mathematics
Score Frequency
93 – 95
1
90 – 92
5
87 – 89
9
84 – 86
16
22
23. 81 – 83
78 – 80
3
6
3
4. Ages of IRSO Foods Company Workers
Age
Frequency
27 – 22
8
33 – 28
18
39 – 34
11
45 – 40
16
51 – 46
12
57 – 52
10
63 – 58
2
4
5. Average Grades of Students of Engineering Block in the First Semester
Average Grade Frequency
1.01 – 1.50
4
1.51 – 2.00
10
2.01 – 2.50
18
2.51 – 3.00
26
3.01 – 3.50
24
3.51 – 4.00
16
4.01 – 4.50
7
4.51 – 5.00
5
Lesson 4
The Mode of Grouped Data
The mode of grouped data can be approximated using the following
formula:
D1
Mode = lb mo +
i
D1 + D 2
where: lbmo is the lower boundary of the modal class.
D1 is the difference between the frequencies of the modal class and
the next lower class.
23
24. D2 is the difference between the frequencies of the modalclass and
the next upper class.
i is the class interval.
The modal class is the class with the highest frequency. If binomial
classes exist, any of these classes may be considered as modal class.
Examples:
1. Compute the mode of the scores of the students in a Mathematics IV
test.
Class Frequency
46 – 50
1
41 – 45
5
36 – 40
11
31 – 35
12
26 – 30
11
21 – 25
5
16 – 20
2
11 – 15
1
he frequency distribution for the data is given below. The column for lb is
added.
Class
46 – 50
41 – 45
36 – 40
31 – 35
26 – 30
21 – 25
16 – 20
11 – 15
f
1
5
1
1
1
2
1
1
5
2
1
lb
45.5
40.5
35.5
30.5
25.5
20.5
15.5
10.5
Since class 31 – 35 has the highest frequency, the modal class is 31 – 35.
24
25. lbmo = 30.5
D1 = 12 – 11 = 1
D2 = 12 – 11 = 1
i=5
D1
Mode = lbmo +
i
D1 + D 2
1
Mode = 30.5 +
(5)
1 + 1
Mode = 30.5 + 2.5
Mode = 33
The mode score is 33.
2. Solve for the median gross sale of Aling Mely’s Sari-sari Store for one
month.
Sales in Pesos Frequency
1,001 – 1,500
1
1,501 – 2,000
1
2,001 – 2,500
3
2,501 – 3,000
7
3,001 – 3,500
5
3,501 – 4,000
6
4,001 – 4,500
4
4,501 – 5,000
3
The frequency distribution for the data is given below. The column for lb is
added.
Sales in Pesos
1,001 – 1,500
1,501 – 2,000
2,001 – 2,500
2,501 – 3,000
3,001 – 3,500
3,501 – 4,000
4,001 – 4,500
4,501 – 5,000
f
1
1
3
7
5
6
4
3
lb
1,000.5
1,500.5
2,000.5
2,500.5
3,000.5
3,500.5
4,000.5
4,500.5
Since the class 2,501 – 3,000 has the highest frequency, the modal class
is 2,501 – 3,000.
25
26. lbmo = 2,500.5
D1 = 7 – 3 = 4
D2 = 7 – 5 = 2
i = 500
D1
Mode = lbmo +
i
D1 + D 2
4
Mode = 2,500.5 +
(500)
4 + 2
Mode = 2,500.5 + 333.33
Mode = 2,833.83
The mode score is 2,833.83.
Try this out
Solve for the mode of each grouped data.
Set A
0
1. Scores of Diagnostic Test of IV-Narra Students
Score Frequency
36 – 40
1
31 – 35
10
26 – 20
10
21 – 25
16
16 – 10
9
1–5
4
1
2. Height of IV-2 Students
Height in
cm
175 – 179
170 – 174
165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
2
Frequency
2
5
8
11
21
14
17
2
3. Midyear Test Scores of IV-Newton
26
27. 3
Score Frequency
41 – 45
1
36 – 40
8
31 – 35
8
26 – 30
14
21 – 25
7
16 – 20
2
4
5
4. Ages of San Lorenzo High School Teachers
Age
Frequency
21 – 25
5
26 – 30
8
31 – 35
8
36 – 40
11
41 – 45
15
46 – 50
14
51 – 55
12
56 – 60
5
61 – 65
2
6
5. Pledges to the Victims of Typhoon Mulawin
Pledges in Pesos Frequency
9,000 – 9,999
4
8,000 – 8,999
12
7,000 – 7,999
13
6,000 – 6,999
15
5,000 – 5,999
19
4,000 – 4,999
30
3,000 – 3,999
21
2,000 – 2,999
41
1,000 – 1,999
31
0 – 999
14
27
28. Set B
0
1. Scores of Periodic Test of IV-Molave Students
Score Frequency
46 – 50
2
41 – 45
9
36 – 40
13
31 – 35
11
26 – 30
10
21 – 25
5
1
2
2. Height of IV-2 Students
Height in
cm
175 – 179
170 – 174
165 – 169
160 – 164
155 – 159
150 – 154
145 – 169
140 – 144
3
Frequency
3
4
10
9
24
11
13
6
3. Midyear Test Scores of Students in English
Class Frequency
91 – 95
1
86 – 90
6
81 – 85
7
76 – 80
4
71 – 75
7
66 – 70
12
61 – 65
5
56 – 80
5
51 – 55
1
46 – 50
2
28
29. 4
4. Ages of Sta. Barbara High School Teachers
Class Frequency
21 – 25
4
26 – 30
14
31 – 35
15
36 – 40
11
41 – 45
12
46 – 50
10
51 – 55
9
56 – 60
3
61 – 65
1
5
5. Monthly Income of the Families of Fourth Year Students
Income in Pesos Frequency
9,000 – 9,999
18
8,000 – 8,999
22
7,000 – 7,999
33
6,000 – 6,999
56
5,000 – 5,999
50
4,000 – 4,999
31
Set C
1.
Scores of Achievement Test in Filipino of IV-Kamagong Students
Score Frequency
86 – 90
2
81 – 85
9
76 – 80
8
71 – 75
13
66 – 60
12
61 – 65
6
2.
Weight of First Year Students
Weight in kg Frequency
75 – 79
1
29
30. 70 – 74
65 – 69
60 – 64
55 – 59
50 – 54
45 – 69
40 – 44
3.
4
10
14
21
15
14
1
Final Test Scores of IV-Rizal
Score Frequency
91 – 95
1
86 – 90
5
81 – 85
9
76 – 80
16
71 – 75
6
56 – 70
3
4.
Ages of Seniro Factory Employees
Age
Frequency
21 – 25
8
26 – 30
18
31 – 35
11
36 – 40
16
41 – 45
12
46 – 50
10
51 – 55
2
56 – 60
2
61 – 65
1
5.
Average Grades of Students of Engineering Block in the First
Semester
Average Grade Frequency
1.01 – 1.50
4
1.51 – 2.00
10
2.01 – 2.50
18
2.51 – 3.00
26
3.01 – 3.50
24
3.51 – 4.00
16
4.01 – 4.50
7
4.51 – 5.00
5
30
31. Let’s summarize
1. When the number of items in a set of data is too big, items are grouped for
convenience. The manner of computing for the mean of grouped data is given by
the formula:
∑(fX)
Mean =
∑f
where: f is the frequency of each class
X is the class mark of class
2. An alternative formula for computing the mean of grouped data makes
use of coded deviation:
∑(fd)
Mean = A.M. +
i
∑f
where: A.M. is the assumed mean
f is the frequency of each class
d is the coded deviation from A.M.
i is the class interval
Any class mark can be considered as assumed mean. But it is convenient
to choose the class mark with the highest frequency. The class chosen to contain
A.M. is given a 0 deviation. Subsequently, consecutive positive integers are
assigned to the classes upward and negative integers to the classes downward.
.
3.
used:
In computing for the median of grouped data, the following formula is
Median = lb mc
∑ f − cf
+ 2
i
f mc
where: lbmc is the lower boundary of the median class
f is the frequency of each class
cf is the cumulative frequency of the lower class next to
the median class
fmc is the frequency of the median class
31
32. i is the class interval
The median class is the class that contains the
∑f
2
th
quantity. The
computed median must be within the median class
4.
The mode of grouped data can be approximated using the following
formula:
D1
Mode = lb mo +
i
D1 + D 2
where: lbmo is the lower boundary of the modal class
D1 is the difference between the frequencies of the
modal class and the next upper class
D2 is the difference between the frequencies of the
modal class and the next lower class
i is the class interval
The modal class is the class with the highest frequency. If binomial
classes exist, any of these classes may be considered as modal class
What have you learned
Use the frequency distribution table below to answer the questions.
Scores of Students in a Mathematics IV Test
Class Frequency
46 – 50
1
41 – 45
2
36 – 40
3
31 – 35
10
26 – 30
6
21 – 25
9
32
33. 16 – 20
11 – 15
6 – 10
1–5
5
6
4
2
1. What is the class size?
2. What is the class mark of the class with the highest frequency?
3. What is ∑ fX ?
4. Find the mean score.
5. What is the median class?
6. Determine the cumulative frequency of the median class.
7. Solve for the median score.
8. What is the modal class?
9. Determine the lower boundary of the modal class
10. Compute for the modal score.
33
34. Answer Key
How much do you know
1. 50
2. 18
3. 1,085
4. 21.7
5. 16 – 20
6. 25
7. 20.5
8. 16 – 25
9. 15.5
10. 19
Try this out
Lesson 1
Set A
1.
2.
3.
4.
5.
24.6
156.75 cm
30
42.38 years
P4,019.50
Set B
1.
2.
3.
4.
5.
34.7
156.88 cm
71.9
39.63 years
P6,589.98
Set C
1.
2.
3.
4.
5.
73.8
57.5 kg
79.25
36.75 years
2.97
34.7
156.88 cm
71.9
39.63 years
P6,589.98
Set C
1.
2.
3.
4.
5.
73.8
57.5 kg
79.25
36.75 years
2.97
35.05
156.58 cm
60.5
39.05 years
P6,428.07
Set C
1.
2.
3.
4.
5.
81.12
67.83 kg
85.56
34.31 years
3.39
Lesson 2
Set A
1.
2.
3.
4.
5.
24.6
156.75 cm
30
42.38 years
P4,019.50
Set B
1.
2.
3.
4.
5.
Lesson 3
Set A
1.
2.
3.
4.
5.
24.25
156.17 cm
29.43
43.17 years
P3,666.17
Set B
1.
2.
3.
4.
5.
34
35. Lesson 4
Set A
1.
2.
3.
4.
5.
23.19
156.56 cm
28.19
44.5 years
P2,332.83
Set B
1.
2.
3.
4.
5.
37.17
156.82 cm
68.42
30.5 years
P6,206.40
What have you learned
1. 47
2. 33
3. 1,159
4. 24.15
5. 21 – 25
6. 26
7. 24.39
8. 31 – 35
9. 30.5
10. 32.32
35
Set C
1.
2.
3.
4.
5.
71.33
56.81 kg
78.44
28.44 years
2.905