Illustrative Math Alignment: Grade 7 Unit 8

Overview

Overview

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 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.

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.

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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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.

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

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 Mode of a Data Set."

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: Sample Mean."

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: The Mean and Normally Distributed Data."

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: Weighted Mean."

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

Topic

Measures of Central Tendency

Description

This video introduces the mean as a measure of central tendency, explaining it as the sum of values divided by their count. Examples include calculating test scores, flamingo wingspans, and football punt lengths, demonstrating how the mean is applied to summarize data. Key terms include mean, average, sum, and ratio.

Topic

Measures of Central Tendency

Description

The video explores calculating the mean with data sets including negative numbers, like temperatures in Fairbanks and Fargo, and tide heights in Gloucester. It emphasizes the mean's robustness across varying data types and scenarios. Key terms include negative numbers, sum, and ratio.

Topic

Measures of Central Tendency

Description

This segment discusses the median, another measure of central tendency, focusing on its calculation by ordering data and finding the middle value. Examples include test scores, basketball player heights, and family ages, highlighting scenarios where the median differs from the mean. Key terms include median, middle value, and ordering.

Topic

Measures of Central Tendency

Description

This section focuses on the mode, the most frequent value in a data set, and its applications in dice rolls, beverage ratings, and color preferences. It compares mode with mean and median, highlighting its utility in categorical data. Key terms include mode, frequency, and categorical data.

Topic

Measures of Central Tendency

Description

This section introduces the mean of probability distributions, also known as expected value, showing its calculation and interpretation in scenarios like dice rolls and coin flips. Key terms include mean, probability distribution, expected value, and weighted mean.

Topic

Measures of Central Tendency

Description

The video explains the sample mean and standard error, illustrating how they estimate population characteristics. Examples include trout lengths, macaw wingspans, and elephant weights. Key terms include sample mean, standard error, population mean, and summation.

Topic

Measures of Central Tendency

Description

This video examines the mean in normally distributed data, linking it to standard deviation and probabilities. Examples include batting averages, heights, and shoe sizes, emphasizing normal distribution properties. Key terms include mean, normal distribution, standard deviation, and probabilities.

Topic

Measures of Central Tendency

Description

The video introduces the weighted mean for data sets with different item frequencies, using examples like cylinder heights, kettlebell weights, and daycare ages. It compares weighted means to medians to show their practical applications. Key terms include weighted mean, weights, and frequency.