Illustrative Math Alignment: Grade 7 Unit 8

Probability and Sampling

Lesson 19: Comparing Populations With Friends

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Definition--Statistics and Probability Concepts--Correlation 1	Correlation 1 Topic Statistics and Probability Definition Correlation measures the strength and direction of a linear relationship between two variables. Description Correlation is widely used in statistics to assess the relationship between variables, such as height and weight, and is applicable in fields like economics, psychology, and biology. A positive correlation indicates that as one variable increases, the other also increases. Understanding correlation helps students make predictions and understand data trends.	Data Analysis
Definition--Statistics and Probability Concepts--Correlation 2	Correlation 2 Topic Statistics and Probability Definition Correlation measures the strength and direction of a linear relationship between two variables. Description Correlation is widely used in statistics to assess the relationship between variables, such as height and weight, and is applicable in fields like economics, psychology, and biology. A positive correlation indicates that as one variable increases, the other also increases. Understanding correlation helps students make predictions and understand data trends.	Data Analysis
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--Dependent Event	Dependent Event Topic Statistics and Probability Definition A dependent event is an event whose outcome is influenced by the outcome of a preceding event.	Probability
Definition--Statistics and Probability Concepts--Histogram	Histogram Topic Statistics and Probability Definition A histogram is a graphical representation of data distribution using bars of different heights. Description Histograms are a fundamental tool in statistics for visualizing the frequency distribution of a dataset. They are used across various fields, including economics, biology, and engineering, to analyze data patterns and trends. By displaying data in intervals, histograms help identify the shape, central tendency, and variability of data. For students, understanding histograms is crucial for interpreting data visually and making informed decisions based on statistical evidence.	Data Analysis
Definition--Statistics and Probability Concepts--Independent Event	Independent Event Topic Statistics and Probability Definition An independent event is an event whose outcome is not affected by the outcome of another event. Description Independent events are a key concept in probability, where the occurrence of one event does not influence another. This principle is applied in various fields, such as quality control, where the failure of one product does not affect others. Understanding independent events is essential for students to accurately calculate probabilities and analyze situations where events occur without influencing each other.	Probability
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	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
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--Mutually Exclusive Events	Mutually Exclusive Events Topic Statistics and Probability Definition Mutually exclusive events are events that cannot occur simultaneously. Description In probability, mutually exclusive events are crucial for understanding scenarios where the occurrence of one event precludes the occurrence of another. This concept is applied in decision-making processes, such as project management, where choosing one option excludes others. For students, grasping mutually exclusive events is important for accurately calculating probabilities and understanding the structure of probability spaces.	Probability
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--Permutation 2	Permutation 2 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	Probability
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
Definition--Statistics and Probability Concepts--Probability	Probability Topic Statistics and Probability Definition Probability quantifies the likelihood of an event occurring. Description Probability is a key concept in statistics that assesses the chance that a specific event will occur out of all possible outcomes. This concept is widely used in various fields such as gambling, insurance, and any scenario involving uncertainty.	Probability
Definition--Statistics and Probability Concepts--Probability Model	Probability Model Topic Statistics and Probability Definition A probability model is a mathematical representation of a random phenomenon. Description Probability models are essential in understanding how to quantify uncertainty in various scenarios. They can be as simple as a coin toss or as complex as predicting stock market trends. These models usually incorporate the outcomes of an event and their associated probabilities.	Probability
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--Random Sample	Random Sample Topic Statistics and Probability Definition A random sample is a subset of individuals chosen from a larger population, selected in such a way that every individual has an equal chance of being chosen. Description Random sampling is a critical technique in statistics that helps ensure the representativeness of a sample by minimizing bias. It is widely used in survey research to ensure that the data collected reflects the diversity and characteristics of the entire population.	Data Gathering
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--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
Definition--Statistics and Probability Concepts--Sample Space	Sample Space Topic Statistics and Probability Definition A sample space is the set of all possible outcomes in a probability experiment. Description The sample space is a foundational concept in probability, providing the framework within which probabilities are assigned to events. It is used in various fields, such as finance, to model different investment outcomes, or in engineering to predict system failures. Understanding the sample space is crucial for students to accurately calculate probabilities and analyze different scenarios. It helps them develop a comprehensive understanding of how different events relate to each other within a probability model.	Probability
Definition--Statistics and Probability Concepts--Scatterplot	Scatterplot Topic Statistics and Probability Definition A scatterplot is a graphical representation of the relationship between two numerical variables. Description Scatterplots are essential tools in statistics for visualizing the correlation between two variables. They are widely used in fields like economics and biology to identify trends and relationships in data. For students, understanding scatterplots is important for interpreting data visually and analyzing the strength and direction of relationships between variables. This skill is crucial for developing their ability to conduct statistical analyses and draw meaningful conclusions from data.	Data Analysis
Definition--Statistics and Probability Concepts--Statistic	Statistic Topic Statistics and Probability Definition A statistic is a numerical measure that describes a characteristic of a sample. Description Statistics are vital in summarizing and analyzing data, providing insights into trends and patterns. They are used in various fields, including healthcare, to determine the effectiveness of treatments, or in business to assess consumer preferences. Understanding statistics is essential for students to interpret data accurately and make informed decisions based on statistical evidence. This knowledge forms the basis for more advanced statistical studies and applications.	Data Gathering
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--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
Definition--Statistics and Probability Concepts--Stem-and-Leaf Plot	Stem-and-Leaf Plot Topic Statistics and Probability Definition A stem-and-leaf plot is a graphical representation that organizes data points based on their place value. Description Stem-and-leaf plots are useful for displaying the distribution of a dataset in a concise format, preserving the original data while showing its shape. They are particularly helpful in exploratory data analysis to identify patterns and outliers. In educational settings, stem-and-leaf plots are used to teach students about data organization and visualization. Understanding this concept helps students develop skills in data interpretation and enhances their ability to summarize data effectively.	Data Analysis
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
Formulas--Mean	Formulas--Mean The formula for the Mean. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Formulas--Median	Formulas--Median The formula for the Median. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Formulas--Sum of Consecutive Integers	Formulas--Sum of Consecutive Integers The formula for the Sum of Consecutive Integers. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Sequences and Series
Formulas--Sum of Consecutive Odd Integers	Formulas--Sum of Consecutive Odd Integers The formula for the Sum of Consecutive Integers. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Sequences and Series
HTML5 Interactive: Data Displays	HTML5 Interactive: Data Displays In this interactive, review seven commonly used data displays. Provides a quck review tool for a unit on data analysis. Note: the download is the Teacher's Guide. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Data Gathering and Data Analysis
Instructional Resource--Fibonacci Sequence, Lesson 1	Instructional Resource \| Fibonacci Sequence, Lesson 1 The year 2023 is the Year of the Rabbit in the Chinese Zodiac. Media4Math would also like to make this the Year of Fibonacci. If you recall, Fibonacci investigated his famous number pattern by looking at the number pattern generated by the increase in the number of rabbits from month to month. The Fibonacci Sequence is one of the most important number patterns found in nature. —PRESS PREVIEW TO VIEW THE LESSON— To see the other lessons in this series, click on the link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Sequences
Instructional Resource--Fibonacci Sequence, Lesson 2	Instructional Resource \| Fibonacci Sequence, Lesson 2 This is a continuation of our exploration of the Fibonacci Sequence. In this lesson we look at the sequence as an example of a recursive function. —PRESS PREVIEW TO VIEW THE LESSON— To see the other lessons in this series, click on the link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Sequences
Instructional Resource--Segmented Bar Graphs	Instructional Resource \| Constructing a Segmented Bar Graph This tutorial goes over the construction of a segmented bar graph, along with how it differs from other chart types. —PRESS PREVIEW TO VIEW THE ACTIVITY— To see the complete collection of Instructional Resources, click on this link. Note: The download is a PDF file. Related Resources To see resources related to this topic click on the Related Resources tab above.	Data Analysis
Interactive Math Game--DragNDrop--Measures of Central Tendency--Mean	Interactive Math Game--DragNDrop Math--Measures of Central Tendency--Mean In this drag-and-drop game, have students practice their skills at calculating the mean of a data set. This game generates thousands of different combinations, offering an ideal opportunity for skill review in a game format. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Data Analysis
Interactive Math Game--DragNDrop--Measures of Central Tendency--Median	Description In this drag-and-drop game, have students practice their skills at calculating the median of a data set. This game generates thousands of different combinations, offering an ideal opportunity for skill review in a game format. Note: The download is the Teacher's Guide.	Data Analysis
Interactive Math Game--Memory Game: Number Cubes	Interactive Math Game--Memory Game: Number Cubes Use this math game to match different arrangements of dice. This is a Memory-style game in which students must remember the location of pairs of identical images. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	3-Dimensional Figures
Interactive Word Search Puzzle--Data Analysis, Puzzle 1	Interactive Word Search Puzzle--Data Analysis, Puzzle 1 Solve an interactive word search puzzle on the topic of Data Analysis. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Data Analysis
Interactive Word Search Puzzle--Data Analysis, Puzzle 2	Interactive Word Search Puzzle--Data Analysis, Puzzle 2 Solve an interactive word search puzzle on the topic of Data Analysis. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Data Analysis
Interactive Word Search Puzzle--Data Analysis, Puzzle 3	Interactive Word Search Puzzle--Data Analysis, Puzzle 3 Solve an interactive word search puzzle on the topic of Data Analysis. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Data Analysis
Interactive Word Search Puzzle--Data Analysis, Puzzle 4	Interactive Word Search Puzzle--Data Analysis, Puzzle 4 Solve an interactive word search puzzle on the topic of Data Analysis. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Data Analysis
Interactive Word Search Puzzle--Data Analysis, Puzzle 5	Interactive Word Search Puzzle--Data Analysis, Puzzle 5 Solve an interactive word search puzzle on the topic of Data Analysis. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Data Analysis
Math Clip Art--Statistics and Probability-- Inferences and Sample Size--10	Math Clip Art--Statistics and Probability-- Inferences and Sample Size--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
Math Clip Art--Statistics and Probability-- Inferences and Sample Size--11	Math Clip Art--Statistics and Probability-- Inferences and Sample Size--11 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-- Inferences and Sample Size--12	Math Clip Art--Statistics and Probability-- Inferences and Sample Size--12 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-- Inferences and Sample Size--9	Math Clip Art--Statistics and Probability-- Inferences and Sample Size--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--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--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--Inferences and Sample Size--01	Math Clip Art--Statistics--Inferences and Sample Size--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
Math Clip Art--Statistics--Inferences and Sample Size--02	Math Clip Art--Statistics--Inferences and Sample Size--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