Illustrative Math Alignment: Grade 7 Unit 8

Overview

Overview

Overview

This collection of math examples focuses on Measures of Central Tendency, specifically the Mean of a Probability Distribution. The set comprises 7 images that progressively increase in complexity, covering various skills related to calculating and understanding the mean in probability distributions.

Overview

This collection of math examples focuses on Measures of Central Tendency, specifically the Sample Mean. The set comprises 7 downloadable PNG images that progressively increase in complexity, covering various skills related to calculating and understanding sample means.

Overview

This is a collection of video tutorials, transcripts, and closed captioned videos on measures of central tendency.

In this video tutorial students learn how to calculate the mean when all of the data items are positive numbers. Includes three real-world examples.

In this video tutorial students learn how to calculate the mean when some of the data items are negative numbers. Includes three real-world examples.

In this video tutorial students learn how to find the median of a data set. The mean is also calculated so that students can learn similarities and differences between these two measures of central tendency. Includes three real-world examples.

In this video tutorial students learn how to calculate the mode of a data set, as well as how the mode differs from the mean and median.Includes three real-world examples.

In this video tutorial students learn about the mean of a probability distribution. Includes a brief discussion of expected value, plus a brief tie-in to weighted means. Includes three real-world examples.

In this video tutorial students learn about sample mean from a random sampling of data. All examples involve normally distributed data with a known population mean and standard deviation. Includes three real-world examples.

In this video tutorial students learn about normally distributed data and how to identify the population mean from the normal distribution. Standard deviation is briefly introduced. Includes three real-world examples.

In this video tutorial students extend their understanding of mean by looking at examples of weighted means (sometimes referred to as weighted averages). Includes three real-world examples.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for a probability distribution of a fair six-sided die. The probability of each outcome (1 to 6) is equally 1/6. The mean is calculated by multiplying each possible outcome by its probability and summing the results. For this fair die, the mean is determined to be 3.5.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for a probability distribution of an unfair six-sided die. Unlike a fair die, the probabilities are not equally distributed, with a higher probability (2/6) for rolling a 1. The mean is calculated using the same method as before, resulting in approximately 2.83.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for another unfair six-sided die. In this case, the probability of rolling a 1 is even higher (3/6), while some numbers have a probability of 0. The mean is calculated using the same method, resulting in 2.5.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for an unfair six-sided die where the number 5 has a significantly higher probability (3/6) than other numbers. The mean is calculated using the same method as previous examples, resulting in 4.5.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for the probability distribution of the sum when rolling two fair dice. There are 11 possible outcomes (2 to 12), each with its own probability. The mean is calculated using the same method as previous examples, resulting in 7.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for the probability distribution of the number of heads when flipping three fair coins. The possible outcomes are 0, 1, 2, or 3 heads, each with its own probability. The mean is calculated using the same method as previous examples, resulting in 1.5.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for the probability distribution of the number of heads when flipping three coins, one of which is unfair. The possible outcomes are 0, 1, 2, or 3 heads, but the probabilities are skewed due to the unfair coin. The mean is calculated using the same method as previous examples, resulting in 1.9.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the sample mean for a group of 30 trout. The image displays a table showing the lengths of these trout, along with the formula for calculating the sample mean. The population of adult trout has a mean length of 15 inches with a standard deviation of 2. The sample mean is calculated by summing all the lengths (472.22 inches) and dividing by the number of trout (30), resulting in a sample mean of 15.74 inches.

Topic

Measures of Central Tendency

Description

This example presents another calculation of the sample mean for a group of 30 trout. The image shows a table with the lengths of these trout and the formula for the sample mean. The population of adult trout has a mean length of 15 inches with a standard deviation of 2. The sample mean is computed by adding all the lengths (436.73 inches) and dividing by the number of trout (30), yielding a sample mean of 14.56 inches.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the sample mean for a group of 40 trout. The image displays a table showing the lengths of these trout, along with the formula for calculating the sample mean. The population of adult trout has a mean length of 15 inches with a standard deviation of 2. The sample mean is calculated by summing all the lengths (615.86 inches) and dividing by the number of trout (40), resulting in a sample mean of 15.39 inches.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the sample mean for a group of 30 macaws. The image shows a table with the wingspans of these macaws and the formula for calculating the sample mean. The population of adult macaws has an average wingspan of 48 inches with a standard deviation of 6. The sample mean is computed by summing all the wingspans (1432.28 inches) and dividing by the number of macaws (30), yielding a sample mean of 47.74 inches.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the sample mean for another group of 30 macaws. The image displays a table showing the wingspans of these macaws, along with the formula for calculating the sample mean. The population of adult macaws has an average wingspan of 48 inches with a standard deviation of 6. The sample mean is calculated by summing all the wingspans (1398.02 inches) and dividing by the number of macaws (30), resulting in a sample mean of 46.6 inches.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the sample mean for a group of 30 adult male elephants. The image shows a table with the weights of these elephants and the formula for calculating the sample mean. The population of adult male elephants has an average weight of 12,000 pounds with a standard deviation of 1,500 pounds. The sample mean is computed by summing all the weights (370,924.22 pounds) and dividing by the number of elephants (30), yielding a sample mean of 12,364.14 pounds.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the sample mean for a group of 30 mature sequoia trees. The image presents a table showing the heights of these trees, along with the formula for computing the sample mean. The population of mature sequoia trees has an average height of 220 feet with a standard deviation of 25 feet. By summing all the heights (6,844.64 feet) and dividing by the number of trees (30), we obtain a sample mean of 228.15 feet.

July 2014. In this issue of Math in the News we look at the mathematics of the Nielsen Ratings. This provides an excellent application of ratios, proportions, and percents.

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November 2016. In this issue of Math in the News, we look at the history of the Olympics.

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February 2012. In this issue we look at unemployment statistics from the Bureau of Labor Statistics.

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5/2/11. In this issue we explore the wildfires in Texas. In particular, we conduct random walk simulations as a tool for predicting the path of a wildfire.

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March 2014. In this issue of Math in the News we look at the Iditarod Race in Alaska. This gives us an opportunity to analyze data on average speed. We look at data in tables and line graphs and analyze the winning speeds over the history of the race.

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This is the transcript for the video entitled, "Video Tutorial: Measures of Central Tendency: Finding the Mean of a Data Set I."

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

This is the transcript for the video entitled, "Video Tutorial: Measures of Central Tendency: Finding the Mean of a Data Set II."

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