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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 8

Data Sets and Distributions

Lesson 8: Describing Distributions on Histograms

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 1 Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, 1 Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 1

In this Investigation we explore uncertainty and randomness. This video is Segment 1 of a 4 segment series related to Data Analysis and Probability. Segments 1 and 2 are grouped together.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability

What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis.

Data Analysis and Data Gathering
Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 2: Honey Production Closed Captioned Video: Algebra Applications: Variables and Equations, 2 Closed Captioned Video: Algebra Applications: Variables and Equations, Segment 2: Honey Production

Honey bees not only produce a tasty treat, they also help pollinate flowering plants that provide much of the food throughout the world. So, when in 2006 bee colonies started dying out, scientists recognized a serious problem. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder.

Applications of Equations and Inequalities, Variables and Unknowns and Variable Expressions
Definition--Statistics and Probability Concepts--Relative Frequency Table Definition--Statistics and Probability Concepts--Relative Frequency Table Relative Frequency Table

Topic

Statistics and Probability

Definition

A relative frequency table displays the proportion of total occurrences for each category of data.

Description

Relative frequency tables are important in statistics as they summarize data in a way that makes it easy to analyze proportions and patterns within datasets. These tables allow for quick comparisons of different categories based on their frequency relative to the total.

Data Analysis
Definition--Statistics and Probability Concepts--Conditional Relative Frequency Definition--Statistics and Probability Concepts--Conditional Relative Frequency Conditional Relative Frequency

Topic

Statistics and Probability

Definition

Conditional relative frequency is the ratio of the frequency of a subset of data to the frequency of a condition.

Description

Conditional relative frequency is crucial in analyzing categorical data, helping to understand the distribution of data under specific conditions.

For example, the frequency of students who pass a test given they have attended all classes is a conditional relative frequency.

Understanding this concept helps students interpret data in surveys and experiments more accurately.

Data Analysis
Definition--Statistics and Probability Concepts--Joint Frequencies Definition--Statistics and Probability Concepts--Joint Frequencies Joint Frequencies

Topic

Statistics and Probability

Definition

Joint frequencies refer to the counts of occurrences for combinations of two categorical variables.

Description

In statistics, joint frequencies are used to analyze the relationship between two categorical variables, often displayed in a contingency table. This analysis is vital in fields such as market research, where understanding the joint distribution of consumer preferences can inform product development. For students, learning about joint frequencies is important for interpreting data from surveys and experiments, allowing them to explore relationships between variables effectively.

Data Analysis
Definition--Statistics and Probability Concepts--Marginal Frequencies Definition--Statistics and Probability Concepts--Marginal Frequencies Marginal Frequencies

Topic

Statistics and Probability

Definition

Marginal frequencies are the totals of rows or columns in a contingency table, representing the sum of joint frequencies for each category.

Description

Marginal frequencies provide insight into the overall distribution of each variable in a dataset. They are crucial in fields like epidemiology, where understanding the marginal distribution of diseases can inform public health strategies. For students, comprehending marginal frequencies is essential for summarizing data and drawing conclusions about the prevalence of certain characteristics within a population.

Data Analysis
Math Clip Art--Statistics and Probability-- Statistical Variability--Image 5 Math Clip Art--Statistics and Probability-- Statistical Variability--5 Math Clip Art--Statistics and Probability-- Statistical Variability--5

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics and Probability-- Statistical Variability--Image 6 Math Clip Art--Statistics and Probability-- Statistical Variability--6 Math Clip Art--Statistics and Probability-- Statistical Variability--6

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics and Probability-- Statistical Variability--Image 7 Math Clip Art--Statistics and Probability-- Statistical Variability--7 Math Clip Art--Statistics and Probability-- Statistical Variability--7

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics and Probability-- Statistical Variability--Image 8 Math Clip Art--Statistics and Probability-- Statistical Variability--8 Math Clip Art--Statistics and Probability-- Statistical Variability--8

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics and Probability-- Statistical Variability--Image 9 Math Clip Art--Statistics and Probability-- Statistical Variability--9 Math Clip Art--Statistics and Probability-- Statistical Variability--9

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics and Probability-- Statistical Variability--Image 10 Math Clip Art--Statistics and Probability-- Statistical Variability--10 Math Clip Art--Statistics and Probability-- Statistical Variability--10

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Definition--Measures of Central Tendency--Outlier Definition--Measures of Central Tendency--Outlier Outlier

Topic

Statistics

Definition

The outlier is is an extreme value for a data set.

Description

The Outlier is an important concept in statistics. While it doesn't represent the average data set, it does set the range of extreme values in the data set. An outlier can be extremely large or small. 

In mathematics education, understanding outlier is crucial as it lays the foundation for more advanced statistical concepts. It allows students to grasp the significance of data analysis and interpretation. In classes, students often perform exercises calculating the mean of sets, which enhances their understanding of averaging techniques.

Data Analysis
Definition--Statistics and Probability Concepts--Causation Definition--Statistics and Probability Concepts--Causation Causation

Topic

Statistics and Probability

Definition

Causation refers to the relationship between two events where one event is affected by the other.

Description

Causation is a fundamental concept in statistics that distinguishes between correlation and causation. Understanding causation is vital in fields like medicine and social sciences to establish cause-effect relationships.

For example, clinical trials are designed to establish causation between treatments and outcomes.

Grasping causation is important for students to critically evaluate research findings and understand the implications of statistical analyses.

Data Analysis
Definition--Measures of Central Tendency--Normal Distribution Definition--Measures of Central Tendency--Normal Distribution Normal Distribution

Topic

Statistics

Definition

The normal distribution is a measure of central tendency that provides an average representation of a set of data.

Description

The Normal Distribution is an important concept in statistics, used to summarize data effectively. In real-world applications, the Normal Distribution helps to interpret data distributions and is widely used in areas such as economics, social sciences, and research.

Data Analysis
Definition--Statistics and Probability Concepts--Bivariate Data Definition--Statistics and Probability Concepts--Bivariate Data Bivariate Data

Topic

Statistics and Probability

Definition

Bivariate data involves the analysis of two variables to determine relationships between them.

Description

Bivariate data is essential in statistics as it allows for the exploration of relationships between two variables, such as height and weight. This analysis is used in various fields, including economics, biology, and social sciences, to understand correlations and causations.

For example, a scatter plot can be used to visually represent bivariate data, helping to identify trends or patterns.

Data Analysis
Definition--Measures of Central Tendency--Categorical Data Definition--Measures of Central Tendency--Categorical Data Categorical Data

Topic

Statistics

Definition

Categorical data refers to data that can be divided into specific categories or groups.

Description

Categorical data is essential for organizing and analyzing information that falls into distinct categories, such as gender, race, or product type. This type of data is often used in market research, social sciences, and public health studies to identify patterns and relationships between groups. In mathematics, understanding categorical data is crucial for interpreting bar charts, pie charts, and frequency tables.

Data Analysis
Definition--Statistics and Probability Concepts--Probability Notation Definition--Statistics and Probability Concepts--Probability Notation Probability Notation

Topic

Statistics and Probability

Definition

Probability notation is a standardized way of expressing probabilities.

Description

Probability notation provides a concise language for defining and communicating probabilities in mathematics. It helps in avoiding confusion in statistical communication. Common symbols include P(A) for the probability of event A occurring.

Data Analysis
Definition--Statistics and Probability Concepts--Addition Rule of Probability Definition--Statistics and Probability Concepts--Addition Rule of Probability Addition Rule of Probability

Topic

Statistics and Probability

Definition

The Addition Rule of Probability is a key concept in statistics that helps in understanding the interaction between different events.

Description

The Addition Rule of Probability is crucial in the field of statistics because it allows us to make informed decisions based on the relationships between variables. For instance, in real-world applications, this concept is essential in various fields such as economics, social sciences, and health studies. Understanding how events affect each other can lead to better predictions and strategies.

Data Analysis
Definition--Statistics and Probability Concepts--Multiplication Rule of Probability Definition--Statistics and Probability Concepts--Multiplication Rule of Probability Multiplication Rule of Probability

Topic

Statistics and Probability

Definition

The multiplication rule of probability is used to find the probability of two independent events both occurring.

Description

The multiplication rule is essential in probability for calculating the likelihood of multiple independent events occurring together. This rule is applied in fields such as genetics, where the probability of inheriting multiple traits is determined. For students, understanding the multiplication rule is crucial for solving problems involving the probability of compound events and for developing a deeper understanding of probability theory.

Data Analysis
Definition--Statistics and Probability Concepts--Permutation 1 Definition--Statistics and Probability Concepts--Permutation 1 Permutation 1

Topic

Statistics and Probability

Definition

A permutation is an arrangement of items in a specific order.

Description

Permutations are used in probability and combinatorics to determine the number of ways to arrange a set of items, which is crucial in fields like cryptography, where secure codes are generated. The formula for permutations is 

Data Analysis
Definition--Statistics and Probability Concepts--Combination 1 Definition--Statistics and Probability Concepts--Combination 1 Combination 1

Topic

Statistics and Probability

Definition

A combination is a selection of items from a larger pool where order does not matter.

Description

Combinations are used in probability to determine the number of ways to select items from a set, which is crucial in fields like cryptography and game theory.

The formula for combinations is 

 

where n is the total number of items, and r is the number of items to choose.

Data Analysis
Definition--Measures of Central Tendency--Probability Distribution Definition--Measures of Central Tendency--Probability Distribution Probability Distribution

Topic

Statistics

Definition

A probability distribution describes how the values of a random variable are distributed.

Description

Probability distributions are fundamental in statistics, providing a mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. They are used in various fields such as finance, science, and engineering to model uncertainty and variability. For instance, the normal distribution is a common probability distribution that describes many natural phenomena.

Data Analysis
Definition--Statistics and Probability Concepts--Two-Way Frequency Table Definition--Statistics and Probability Concepts--Two-Way Frequency Table Two-Way Frequency Table

Topic

Statistics and Probability

Definition

A two-way frequency table displays the frequency of data points across two categorical variables.

Description

Two-way frequency tables are essential for analyzing the relationship between two categorical variables, often used in survey analysis to explore associations between different demographic factors. They help in identifying patterns and correlations within datasets.

Data Analysis
Definition--Statistics and Probability Concepts--Correlation Coefficient Definition--Statistics and Probability Concepts--Correlation Coefficient Correlation Coefficient

Topic

Statistics and Probability

Definition

The correlation coefficient is a measure that quantifies the degree to which two variables are related.

Data Analysis
Definition--Statistics and Probability Concepts--Residuals Definition--Statistics and Probability Concepts--Residuals Residuals

Topic

Statistics and Probability

Definition

Residuals are the differences between observed and predicted values in a dataset.

Description

In statistics, residuals are crucial for assessing the accuracy of predictions generated by statistical models. They represent the errors in prediction, providing insight into the model's performance and areas for potential improvement.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Data Plot--Example 4 Math Example--Charts, Graphs, and Plots--Data Plot--Example 4 Math Example--Charts, Graphs, and Plots-- Data Plot--Example 4

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Math Example--Charts, Graphs, and Plots-- Data Plot--Example 2 Math Example--Charts, Graphs, and Plots--Data Plot--Example 2 Math Example--Charts, Graphs, and Plots-- Data Plot--Example 2

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

Data Analysis
Definition--Measures of Central Tendency Definition--Measures of Central Tendency Measures of Central Tendency

Topic

Statistics

Definition

The measures of central tendency is a measure of central tendency that provides an average representation of a set of data.

Description

The Measures of Central Tendency is an important concept in statistics, used to summarize data effectively.

In real-world applications, the Measures of Central Tendency helps to interpret data distributions and is widely used in areas such as economics, social sciences, and research.

For example, if a data set consists of the values 2, 3, and 10, the mean is calculated as (2 + 3 + 10)/3 = 5.

Data Analysis
Definition--Statistics and Probability Concepts--Population Definition--Statistics and Probability Concepts--Population Population

Topic

Statistics and Probability

Definition

A population is the entire group under consideration in a statistical study.

Description

Population is a fundamental concept in statistics, representing the complete set of individuals or items that share a common characteristic. Understanding a population is crucial for statistical analysis as it serves as the basis for sampling and inferential statistics.

Data Gathering
Math Clip Art--Statistics--Comparative Statistics, Image 3 Math Clip Art--Statistics--Comparative Statistics--03 Math Clip Art--Statistics--Comparative Statistics--03

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Analysis
Math Clip Art--Statistics--Comparative Statistics, Image 2 Math Clip Art--Statistics--Comparative Statistic--02 Math Clip Art--Statistics--Comparative Statistic--02

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Analysis
Math Clip Art--Statistics--Comparative Statistics, Image 1 Math Clip Art--Statistics--Comparative Statistics--01 Math Clip Art--Statistics--Comparative Statistics--01

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Analysis
Math Clip Art--Statistics--Statistical Variability, Image 3 Math Clip Art--Statistics--Statistical Variability--03 Math Clip Art--Statistics--Statistical Variability--03

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics--Statistical Variability, Image 4 Math Clip Art--Statistics--Statistical Variability--04 Math Clip Art--Statistics--Statistical Variability--04

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics--Statistical Variability, Image 2 Math Clip Art--Statistics--Statistical Variability--02 Math Clip Art--Statistics--Statistical Variability--02

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Math Clip Art--Statistics--Statistical Variability, Image 1 Math Clip Art--Statistics--Statistical Variability--01 Math Clip Art--Statistics--Statistical Variability--01

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Gathering
Definition--Statistics and Probability Concepts--Statistical Distribution Definition--Statistics and Probability Concepts--Statistical Distribution Statistical Distribution

Topic

Statistics and Probability

Definition

A statistical distribution describes how values of a variable are distributed.

Description

Statistical distributions are fundamental in understanding data behavior and variability. They are used in various fields, such as finance, to model asset returns, or in biology, to understand population dynamics. Common distributions include normal, binomial, and Poisson distributions, each with its own properties and applications.

Data Gathering
Definition--Statistics and Probability Concepts--Statistic Variability Definition--Statistics and Probability Concepts--Statistical Variability Statistical Variability

Topic

Statistics and Probability

Definition

Statistical variability refers to the extent to which data points in a dataset differ from each other and from the central value.

Description

Understanding variability is essential in statistics as it provides insights into the consistency and reliability of data. Measures of variability, such as range, variance, and standard deviation, help in assessing the spread of data points around a central value.

Data Gathering
Worksheet: TI-Nspire Mini-Tutorial: A Probability Simulation of Rolling Two Dice Multiple Times (with Histogram) Worksheet: TI-Nspire Mini-Tutorial: A Probability Simulation of Rolling Two Dice Multiple Times (with Histogram) Worksheet: TI-Nspire Mini-Tutorial: A Probability Simulation of Rolling Two Dice Multiple Times (with Histogram)

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
Probability
Worksheet: TI-Nspire Mini-Tutorial: Creating a Histogram Worksheet: TI-Nspire Mini-Tutorial: Creating a Histogram Worksheet: TI-Nspire Mini-Tutorial: Creating a Histogram

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
Data Analysis
Video Transcript: Algebra Applications: Variables and Equations, Segment 2: Honey Production Video Transcript: Algebra Applications: Variables and Equations, Segment 2: Honey Production Video Transcript: Algebra Applications: Variables and Equations, Segment 2: Honey Production

This is the transcript for the video of same title. Video contents: Honey bees not only produce a tasty treat, they also help pollinate flowering plants that provide much of the food throughout the world. So, when in 2006 bee colonies started dying out, scientists recognized a serious problem. Analyzing statistics from honey bee production allows for a mathematical analysis of the so-called Colony Collapse Disorder.

Applications of Equations and Inequalities
Video Transcript: Algebra Nspirations: Data Analysis and Probability Video Transcript: Algebra Nspirations: Data Analysis and Probability Video Transcript: Algebra Nspirations: Data Analysis and Probability

This is the transcript for the video of same title. Video contents: What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different TI-Nspire iPad Applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis

Data Analysis
Video Transcript: Algebra Nspirations: Data Analysis and Probability, Part 1 Video Transcript: Algebra Nspirations: Data Analysis and Probability, 1 Video Transcript: Algebra Nspirations: Data Analysis and Probability, Part 1

This is the transcript for the video of same title. Video contents: In this Investigation we explore uncertainty and randomness.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Data Analysis
Video Transcript: Algebra Nspirations: Data Analysis and Probability, Part 2 Video Transcript: Algebra Nspirations: Data Analysis and Probability, 2 Video Transcript: Algebra Nspirations: Data Analysis and Probability, Part 2

This is the transcript for the video of same title. Video contents: In this Math Lab a hands-on probability activity involving coins is explored.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Data Analysis
Math Clip Art: Spinner, 10 Sections--Result 1 Math Clip Art: Spinner, 10 Sections--Result 1 Math Clip Art: Spinner, 10 Sections--Result 1

Topic

Probability and Statistics

Description

This image depicts a spinner divided into ten equal sections, which are colored red, yellow, green, light blue, orange, grey, brown, purple, yellow-green, and white. The spinner's arrow points to the red section, demonstrating one of the possible outcomes.

In the context of Probability and Statistics, this spinner represents a probability experiment with ten equally likely outcomes. It visually demonstrates the concepts of sample space and individual events within that space, each with a 1/10 probability of occurrence.

Probability
Math Clip Art: Spinner, 10 Sections--Result 10 Math Clip Art: Spinner, 10 Sections--Result 10 Math Clip Art: Spinner, 10 Sections--Result 10

Topic

Probability and Statistics

Description

This image depicts a spinner divided into ten equal sections, which are colored red, yellow, green, light blue, orange, grey, brown, purple, yellow-green, and white. The spinner's arrow points to the white section, demonstrating the final possible outcome in this probability model.

In the field of Probability and Statistics, this spinner exemplifies a uniform probability distribution with ten equally likely outcomes. Each spin has a 1/10 probability of landing on any given color, illustrating the concept of equiprobable events in a complex scenario.

Probability
Math Clip Art: Spinner, 10 Sections--Result 2 Math Clip Art: Spinner, 10 Sections--Result 2 Math Clip Art: Spinner, 10 Sections--Result 2

Topic

Probability and Statistics

Description

This image depicts a spinner divided into ten equal sections, which are colored red, yellow, green, light blue, orange, grey, brown, purple, yellow-green, and white. The spinner's arrow points to the yellow section, demonstrating one of the possible outcomes.

In the context of Probability and Statistics, this spinner represents a probability experiment with ten equally likely outcomes. It visually demonstrates the concepts of sample space and individual events within that space, each with a 1/10 probability of occurrence.

Probability
Math Clip Art: Spinner, 10 Sections--Result 3 Math Clip Art: Spinner, 10 Sections--Result 3 Math Clip Art: Spinner, 10 Sections--Result 3

Topic

Probability and Statistics

Description

This image depicts a spinner divided into ten equal sections, which are colored red, yellow, green, light blue, orange, grey, brown, purple, yellow-green, and white. The spinner's arrow points to the green section, demonstrating one of the possible outcomes.

In the context of Probability and Statistics, this spinner represents a probability experiment with ten equally likely outcomes. It visually demonstrates the concepts of sample space and individual events within that space, each with a 1/10 probability of occurrence.

Probability