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This lesson teaches students about relationships between variables using the distance, rate, time formula. Students will conduct an experiment to measure how long it takes group members to walk, jog, skip and run 20 yards. They will use the formula to calculate rates from the collected data. The lesson aims to help students understand how changing one value affects others in an equation.
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Lecture 03.
Taking of a measurement and the process of counting yield numbers that contain information. The objective of a person applying the tools of statistics to these numbers is to determine the nature of this information.
This task is made much easier if the numbers are organized and summarized.
Even quite small data sets are difficult to understand without some summarization. Statistical quantities such as the mean and variance can be extremely helpful in summarizing data but first we discuss tabular and graphical summaries.
There are several ways to present a statistical data like;
Frequency table
Simple bar diagrams
Multiple Bar Diagrams
Histogram
Frequency Polygon etc.
Steam and Leaf plots
Pie Charts
A frequency distribution is a tabular arrangement of data in which various items are arranged into classes or groups and the number of items falling in each class is stated.
The number of observations falling in a particular class is referred to as class frequency and is denoted by "f".
In frequency distribution all the values falling in a class are assumed to be equal to the midpoint of that class.
Data presented in the form of a frequency distribution is also called grouped data. A frequency distribution table contains a condensed summary of the original data.
There are two types of frequency distribution i) Simple Frequency distribution ) ii) Grouped Frequency distribution.
permutation and combination
- A sequence is an ordered list of objects where order matters and elements can repeat. A series is the sum of a sequence's terms.
- Sequences whose terms follow patterns are called progressions, including arithmetic and geometric progressions.
- An arithmetic progression has a constant difference between consecutive terms, and the nth term can be calculated using a formula involving the first term and common difference.
- A geometric progression multiplies the previous term by a fixed ratio, and the nth term can be calculated using a formula involving the first term and common ratio.
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This lesson plan is for an 8th grade mathematics class on inverse proportion. The teacher will introduce the concept of inverse proportion by having students analyze how the length and breadth of rectangles must change to maintain a constant area. Students will work in groups on worksheet problems, such as calculating the length and breadth of rectangles with given areas, to understand that as one dimension increases the other must decrease. The lesson aims to help students recognize and provide examples of inverse proportion, as well as solve related problems.
Measures of Central Tendency
This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data
Statistics and probability lesson5
The document discusses different methods for presenting data, including textual or narrative presentation, tabular presentation, and graphical presentation. It provides details on constructing frequency distribution tables, including identifying the range and number of classes, calculating class size, and tallying data. Frequency distribution tables show the distribution of data values and can include additional details like class marks, relative frequencies, and cumulative frequencies. Bar graphs are also discussed as a way to visually present the data in a frequency distribution table.
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(2) It outlines the content, learning outcomes, prerequisites, and teaching procedures for teaching students how to construct the circumcircle of a triangle.
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This document discusses strategies for differentiated instruction in mathematics. It defines differentiation as modifying tasks to fit students' ability levels, interests, and learning styles. The goals are to provide engaging math activities for all students and define several differentiation strategies with examples aligned to Common Core standards. Teachers will work in groups to create mathematical tasks with at least two modifications to differentiate instruction and consider strategies for differentiating assessment.
Measures of Dispersion
This document discusses various measures of dispersion used in statistics, including range, standard deviation, and mean deviation. It provides examples of calculating each measure using both individual data series and grouped data series. For range, it calculates the difference between the highest and lowest values. For standard deviation, it shows how to calculate it using the actual mean method and assumed mean method for both individual and grouped data. The key measures discussed are range, which is the difference between the maximum and minimum values, and standard deviation, which measures how far data points are from the mean.
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Lecture 03.
Taking of a measurement and the process of counting yield numbers that contain information. The objective of a person applying the tools of statistics to these numbers is to determine the nature of this information.
This task is made much easier if the numbers are organized and summarized.
Even quite small data sets are difficult to understand without some summarization. Statistical quantities such as the mean and variance can be extremely helpful in summarizing data but first we discuss tabular and graphical summaries.
There are several ways to present a statistical data like;
Frequency table
Simple bar diagrams
Multiple Bar Diagrams
Histogram
Frequency Polygon etc.
Steam and Leaf plots
Pie Charts
A frequency distribution is a tabular arrangement of data in which various items are arranged into classes or groups and the number of items falling in each class is stated.
The number of observations falling in a particular class is referred to as class frequency and is denoted by "f".
In frequency distribution all the values falling in a class are assumed to be equal to the midpoint of that class.
Data presented in the form of a frequency distribution is also called grouped data. A frequency distribution table contains a condensed summary of the original data.
There are two types of frequency distribution i) Simple Frequency distribution ) ii) Grouped Frequency distribution.
permutation and combination
- A sequence is an ordered list of objects where order matters and elements can repeat. A series is the sum of a sequence's terms.
- Sequences whose terms follow patterns are called progressions, including arithmetic and geometric progressions.
- An arithmetic progression has a constant difference between consecutive terms, and the nth term can be calculated using a formula involving the first term and common difference.
- A geometric progression multiplies the previous term by a fixed ratio, and the nth term can be calculated using a formula involving the first term and common ratio.
Lesson plan 15
This lesson plan is for an 8th grade mathematics class on inverse proportion. The teacher will introduce the concept of inverse proportion by having students analyze how the length and breadth of rectangles must change to maintain a constant area. Students will work in groups on worksheet problems, such as calculating the length and breadth of rectangles with given areas, to understand that as one dimension increases the other must decrease. The lesson aims to help students recognize and provide examples of inverse proportion, as well as solve related problems.
Measures of Central Tendency
This document discusses various measures of central tendency including arithmetic mean, median, and mode. It provides definitions and formulas for calculating each measure along with examples using raw data and grouped data. The three main points covered are:
1. Measures of central tendency (mean, median, mode) calculate the central or typical value in a data set and are used to describe data distributions.
2. The arithmetic mean is the sum of all values divided by the number of values, the median is the middle number when values are arranged in order, and the mode is the most frequent value.
3. Formulas and methods are provided for calculating each measure using both raw ungrouped data as well as grouped frequency distribution data
Statistics and probability lesson5
The document discusses different methods for presenting data, including textual or narrative presentation, tabular presentation, and graphical presentation. It provides details on constructing frequency distribution tables, including identifying the range and number of classes, calculating class size, and tallying data. Frequency distribution tables show the distribution of data values and can include additional details like class marks, relative frequencies, and cumulative frequencies. Bar graphs are also discussed as a way to visually present the data in a frequency distribution table.
Innovative lesson plan
(1) The document is a teaching manual for a mathematics lesson on circumcircles for 9th standard students.
(2) It outlines the content, learning outcomes, prerequisites, and teaching procedures for teaching students how to construct the circumcircle of a triangle.
(3) The teaching procedure involves drawing a triangle, constructing perpendicular bisectors of sides, finding their point of intersection which is the circumcenter, and using a compass to draw the circle passing through the three vertices.
Differentiated instruction
This document discusses strategies for differentiated instruction in mathematics. It defines differentiation as modifying tasks to fit students' ability levels, interests, and learning styles. The goals are to provide engaging math activities for all students and define several differentiation strategies with examples aligned to Common Core standards. Teachers will work in groups to create mathematical tasks with at least two modifications to differentiate instruction and consider strategies for differentiating assessment.
Measures of Dispersion
This document discusses various measures of dispersion used in statistics, including range, standard deviation, and mean deviation. It provides examples of calculating each measure using both individual data series and grouped data series. For range, it calculates the difference between the highest and lowest values. For standard deviation, it shows how to calculate it using the actual mean method and assumed mean method for both individual and grouped data. The key measures discussed are range, which is the difference between the maximum and minimum values, and standard deviation, which measures how far data points are from the mean.
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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.
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This document discusses the different levels of measurement in data: nominal, ordinal, interval, and ratio.
Nominal measurement assigns numbers or labels to categories but the numbers have no inherent order or magnitude. Ordinal measurement assigns numbers to rank categories in order but the differences between numbers are unknown. Interval measurement has equal distances between numbers like a Celsius thermometer. Ratio measurement has all the properties of interval plus a true zero point where the absence of a value can be measured.
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The document outlines the learning objectives, assessments, and exam structure for a Year 8 mathematics class taught by Ms. Asiya, including shapes, algebra, numbers, and data topics to be covered in the term, with 3 assessments worth 100 marks each and a 1.5 hour end of term exam. Students are provided with study materials and advice to ensure they understand the topics in preparation for their exams.
Mod mean quartile
1. The document discusses various measures of central tendency including mode, median, and quartiles.
2. Mode is the most frequent value in a data set. Median divides the data set into two equal halves. Quartiles divide the data set into four equal groups.
3. The document provides formulas and examples for calculating mode, median, and quartiles for both grouped and ungrouped data sets. Advantages and disadvantages of each measure are also discussed.
2.1 Part 1 - Frequency Distributions
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
Report frequency distribution table
This document discusses frequency distribution, which is a tabular arrangement that shows the frequency of different variable values. It organizes disorganized data into classes or intervals and summarizes the distribution. A frequency distribution specifies the class intervals or boundaries, class marks or midpoints, and class frequencies or number of observations in each interval. It is used to rank and organize data. The document then provides an example problem of constructing a frequency distribution table for the weights of 50 boys using 8 equal class intervals, and calculating the class boundaries and midpoints.
Jes al1 report
1. The document discusses organizing test scores into a single value frequency distribution by arranging scores in descending order, tallying each score, adding tally marks, and summing the totals.
2. It also discusses setting class boundaries for a grouped frequency distribution, which involves determining class limits, both apparent and real. Real limits extend from half a unit below and above the class values.
3. The document also defines class marks as the midpoint of a class, which is calculated by taking the average of the lower and upper class limits.
Percentile For Grouped Data
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.
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This document summarizes Chapter 2 of a statistics textbook. It covers descriptive statistics including frequency distributions, graphs of distributions, measures of central tendency, variation, and position. Section 2.1 discusses constructing frequency distributions and graphs including histograms, polygons, relative histograms, and ogives. Examples are provided to demonstrate how to construct these graphs from sample data on internet usage times. Key steps include determining class widths, limits, frequencies, midpoints, boundaries, and plotting the graphs.
DISPERSION
This document discusses various statistical methods for measuring central tendency and dispersion in data sets. It defines average or mean as representing the central part of a group. Dispersion is defined as the extent to which individual data points vary within a distribution. Methods for measuring dispersion described include range, quartile deviation, average deviation, and standard deviation. Standard deviation is specifically defined as a measure of how widely values are dispersed from the average value.
Quartile Deviation
This document discusses the calculation of quartile deviation from both ungrouped and grouped data. It defines quartiles as values that divide a data distribution into four equal parts (Q1, Q2, Q3). The quartile deviation is half the difference between the first (Q1) and third (Q3) quartiles. It provides the steps to find Q1, Q3, and quartile deviation from ungrouped data by ranking scores and using quartile locators. For grouped data, it uses formulas involving class limits and cumulative frequencies to determine Q1 and Q3, then takes half their difference. An example calculation is shown.
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The document provides instructions for organizing raw data into a frequency distribution table and describes different ways to represent the distribution graphically, including histograms, frequency polygons, and cumulative frequency curves. It explains how to calculate class intervals and frequencies from raw data and construct tables showing the distribution. It also discusses representing the same data through vertical bar graphs, line graphs connecting class points, and curves showing cumulative frequencies below given values.
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Assessment of Learning 2 (Overview)
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.
Level of-measurement
This document discusses the different levels of measurement in data: nominal, ordinal, interval, and ratio.
Nominal measurement assigns numbers or labels to categories but the numbers have no inherent order or magnitude. Ordinal measurement assigns numbers to rank categories in order but the differences between numbers are unknown. Interval measurement has equal distances between numbers like a Celsius thermometer. Ratio measurement has all the properties of interval plus a true zero point where the absence of a value can be measured.
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The document outlines the learning objectives, assessments, and exam structure for a Year 8 mathematics class taught by Ms. Asiya, including shapes, algebra, numbers, and data topics to be covered in the term, with 3 assessments worth 100 marks each and a 1.5 hour end of term exam. Students are provided with study materials and advice to ensure they understand the topics in preparation for their exams.
Mod mean quartile
1. The document discusses various measures of central tendency including mode, median, and quartiles.
2. Mode is the most frequent value in a data set. Median divides the data set into two equal halves. Quartiles divide the data set into four equal groups.
3. The document provides formulas and examples for calculating mode, median, and quartiles for both grouped and ungrouped data sets. Advantages and disadvantages of each measure are also discussed.
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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
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This document discusses frequency distribution, which is a tabular arrangement that shows the frequency of different variable values. It organizes disorganized data into classes or intervals and summarizes the distribution. A frequency distribution specifies the class intervals or boundaries, class marks or midpoints, and class frequencies or number of observations in each interval. It is used to rank and organize data. The document then provides an example problem of constructing a frequency distribution table for the weights of 50 boys using 8 equal class intervals, and calculating the class boundaries and midpoints.
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1. The document discusses organizing test scores into a single value frequency distribution by arranging scores in descending order, tallying each score, adding tally marks, and summing the totals.
2. It also discusses setting class boundaries for a grouped frequency distribution, which involves determining class limits, both apparent and real. Real limits extend from half a unit below and above the class values.
3. The document also defines class marks as the midpoint of a class, which is calculated by taking the average of the lower and upper class limits.
Percentile For Grouped Data
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%
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This document summarizes Chapter 2 of a statistics textbook. It covers descriptive statistics including frequency distributions, graphs of distributions, measures of central tendency, variation, and position. Section 2.1 discusses constructing frequency distributions and graphs including histograms, polygons, relative histograms, and ogives. Examples are provided to demonstrate how to construct these graphs from sample data on internet usage times. Key steps include determining class widths, limits, frequencies, midpoints, boundaries, and plotting the graphs.
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This document discusses various statistical methods for measuring central tendency and dispersion in data sets. It defines average or mean as representing the central part of a group. Dispersion is defined as the extent to which individual data points vary within a distribution. Methods for measuring dispersion described include range, quartile deviation, average deviation, and standard deviation. Standard deviation is specifically defined as a measure of how widely values are dispersed from the average value.
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This document discusses the calculation of quartile deviation from both ungrouped and grouped data. It defines quartiles as values that divide a data distribution into four equal parts (Q1, Q2, Q3). The quartile deviation is half the difference between the first (Q1) and third (Q3) quartiles. It provides the steps to find Q1, Q3, and quartile deviation from ungrouped data by ranking scores and using quartile locators. For grouped data, it uses formulas involving class limits and cumulative frequencies to determine Q1 and Q3, then takes half their difference. An example calculation is shown.
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This document provides definitions and examples for various math terms from A to Z. It summarizes each term with a definition and example. Many of the terms are related to other math concepts taught, such as using variables in algebra and geometry, exponents in equations, and fractions in various subjects. The document aims to explain foundational math terms and how they connect across topics.
Frequency Distributions and Graphs
The document provides instructions for organizing raw data into a frequency distribution table and describes different ways to represent the distribution graphically, including histograms, frequency polygons, and cumulative frequency curves. It explains how to calculate class intervals and frequencies from raw data and construct tables showing the distribution. It also discusses representing the same data through vertical bar graphs, line graphs connecting class points, and curves showing cumulative frequencies below given values.
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This document defines and explains how to calculate quartile deviation (QD). It begins by defining quartiles as the three points that divide a data set into four equal parts. The median acts as the base for calculating quartiles. Quartile deviation is then defined as half the difference between the first quartile (Q1) and third quartile (Q3). The document provides the formula for calculating QD as QD=(Q3-Q1)/2. It then explains how to calculate Q1, Q2, and Q3 for both odd-numbered and even-numbered data sets by arranging the data in ascending order and determining the values that divide the data into four equal parts. Sample calculations are shown for both odd
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The document presents a multi-step related rates problem involving finding the radius of a decreasing 10ft ice column when the height is 5ft. It also reflects on choosing this related rates problem to present, noting initial confusion with these type of problems, and issues with the logic of the decreasing radius as the height decreases. A second proposed problem involving Riemann sums and finding an integral is also mentioned.
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Voki
- 1. Voki Lesson Plan Teacher’s Name: Ms. Sunday Solomon Lesson Title: The Discovery Lab/ values that vary Description of Lesson: Students have been introduced to the distance equation d=rt where d=distance, r= rate, and t= time. The focus of this lesson is for students to be able to understand the relationships between two variables, as well as gain a deeper understanding of why values vary. This lesson is an extension of rates that change. A power point will be used to introduce key terms and concepts. A graphic organizer goes along with the power point notes. Included in the power point are the three different ways in which the formula can be used and interchanged (d=r/t, t= d/r and r = d/t). After the power point, I will use a Voki to explain give the students their next task, the Discovery Lab. The Discovery lab is the assessment for this lesson. Students will be split into 4 even teams, each team is responsible for recording how long it takes each member to walk, jog, skip, and run, 60 feet or 20 yards. The distance will always be 60 feet, which is known as the constant variable since it does not change. The times will vary according to each individual, and the rate(r) will be the unknown variable, because it is the one variable that they do not know. Students will use the formula d=rt to solve for the (r) rate. This activity provides students with a more tangible way to use the formula, instead of using practice problems out of the book. Students are recording and interpreting data, and understanding how one value affects another value in an equation. Standard(s): GA-GPS. M7A3: Students will understand relations and functions. M7A3 (b): Represent, describe and analyze a functional relation from a table, graph, and/or formula. M7A3 (c): Describe the variation of two quantities.
- 2. Objectives: Students will be able to represent tables, graphs, and formulas. Students will be able to describe tables, graphs, and formulas. Students will be able to interpret and explain how one variable affects the other. Materials: Data table Stop Watch Power Point and graphic organizer Brain Pop video: http://www.brainpop.com/science/motionsforceandtime/distancerateandtime/ Activities: The assessment for this lesson is the Discovery Lab. Students will use the formula d=rt to complete the lab. The class will be split into groups and each group will be responsible for recording the time it takes each team member to walk, jog, skip, and run 20 yards. The lab will take place outside where 20 yards will be sectioned off. Each group will receive a stop watch and a data table. Once all group members have completed each task, the students will return to the class to finish up the lab/assessment. The formula d=rt will now be manipulated to find the new equation; we are now looking for rate and not distance. The new formula will be r= d/t. Students will have to use some algebra skills to solve for r, in order to complete the data table. Individually students will calculate the rate for each group member using the new formula. There are 6 discussion and analyses questions. These questions will help the students to organize and interpret the results of their data in more depth. Students are given multiple ways to express their understanding of values that vary through the interpretation of collected data.