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.
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Math Example--Measures of Central Tendency--Range: Example 25 | Math Example--Measures of Central Tendency--Range: Example 25TopicMeasures of Central Tendency DescriptionThis example demonstrates how to find the range of the following set of numbers: 42, 31, 16, 0, 35, 26, 30, 14, 6, 2, 13, 37, 33, 36, 19, 48, 3, 9, 45, 12. The solution involves arranging the numbers from least to greatest and finding the difference between the two extremes. The range is calculated to be 48. This example is valuable for understanding the concept of range, as it teaches students how to identify the maximum and minimum from a larger set of non-negative numbers and find their difference. |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 26 | Math Example--Measures of Central Tendency--Range: Example 26TopicMeasures of Central Tendency DescriptionThis example illustrates how to find the range of the following set of numbers: 28, 49, 1, -19, -37, 43, 27, 32, -10, 39, -19, -48, -49, 28, 36, 37, 44, 42, 29, -17. The solution involves arranging the numbers from least to greatest and finding the difference between the two extremes. The range is calculated to be 98. This example is particularly valuable as it includes a mix of positive and negative values, as well as repeated numbers, helping students understand how to handle diverse and complex datasets when calculating the range. |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 3 | Math Example--Measures of Central Tendency--Range: Example 3TopicMeasures of Central Tendency |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 4 | Math Example--Measures of Central Tendency--Range: Example 4TopicMeasures of Central Tendency |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 5 | Math Example--Measures of Central Tendency--Range: Example 5TopicMeasures of Central Tendency |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 6 | Math Example--Measures of Central Tendency--Range: Example 6TopicMeasures of Central Tendency |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 7 | Math Example--Measures of Central Tendency--Range: Example 7TopicMeasures of Central Tendency |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 8 | Math Example--Measures of Central Tendency--Range: Example 8TopicMeasures of Central Tendency |
Data Analysis |
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Math Example--Measures of Central Tendency--Range: Example 9 | Math Example--Measures of Central Tendency--Range: Example 9TopicMeasures of Central Tendency DescriptionThis example demonstrates how to find the range of a set of numbers: 22, 13, 15, 1, 16, 28, 3, 5, 18, 42, 8, 9. The solution involves arranging the numbers from least to greatest and finding the difference between the two extremes. The range is calculated to be 41. This example is valuable for understanding the concept of range, as it teaches students how to identify the maximum and minimum from a set of numbers and find their difference. The process encourages critical thinking and helps students visualize the relationship between numbers in a dataset. |
Data Analysis |
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Math Example--Measures of Central Tendency--Sample Mean--Example 1 | Math Example--Measures of Central Tendency--Sample Mean--Example 1TopicMeasures of Central Tendency DescriptionThis 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. |
Data Analysis |
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Math Example--Measures of Central Tendency--Sample Mean--Example 2 | Math Example--Measures of Central Tendency--Sample Mean--Example 2TopicMeasures of Central Tendency DescriptionThis 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. |
Data Analysis |
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Math Example--Measures of Central Tendency--Sample Mean--Example 3 | Math Example--Measures of Central Tendency--Sample Mean--Example 3TopicMeasures of Central Tendency DescriptionThis 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. |
Data Analysis |
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Math Example--Measures of Central Tendency--Sample Mean--Example 4 | Math Example--Measures of Central Tendency--Sample Mean--Example 4TopicMeasures of Central Tendency DescriptionThis 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. |
Data Analysis |
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Math Example--Measures of Central Tendency--Sample Mean--Example 5 | Math Example--Measures of Central Tendency--Sample Mean--Example 5TopicMeasures of Central Tendency DescriptionThis 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. |
Data Analysis |
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Math Example--Measures of Central Tendency--Sample Mean--Example 6 | Math Example--Measures of Central Tendency--Sample Mean--Example 6TopicMeasures of Central Tendency DescriptionThis 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. |
Data Analysis |
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Math Example--Measures of Central Tendency--Sample Mean--Example 7 | Math Example--Measures of Central Tendency--Sample Mean--Example 7TopicMeasures of Central Tendency DescriptionThis 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. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 1 | Math Example--Measures of Central Tendency--Weighted Mean--Example 1TopicMeasures of Central Tendency DescriptionThis example demonstrates the calculation of a weighted mean for a data set consisting of the values 6, 9, and 7, with weights of 4, 5, and 6 respectively. The weighted mean is computed using the formula: (4 * 6 + 5 * 9 + 6 * 7) / (4 + 5 + 6), resulting in a final answer of 7.4. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 2 | Math Example--Measures of Central Tendency--Weighted Mean--Example 2TopicMeasures of Central Tendency DescriptionThis example illustrates the calculation of a weighted mean for a data set containing the values 1, 10, and 5, with weights of 4, 5, and 6 respectively. The weighted mean is computed using the formula: (4 * 1 + 5 * 10 + 6 * 5) / (4 + 5 + 6), resulting in a final answer of 5.6. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 3 | Math Example--Measures of Central Tendency--Weighted Mean--Example 3TopicMeasures of Central Tendency DescriptionThis example demonstrates the calculation of a weighted mean for a data set containing negative and positive values: -5, 5, and 1, with weights of 4, 5, and 6 respectively. The weighted mean is computed using the formula: (4 * -5 + 5 * 5 + 6 * 1) / (4 + 5 + 6), resulting in a final answer of approximately 0.733. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 4 | Math Example--Measures of Central Tendency--Weighted Mean--Example 4TopicMeasures of Central Tendency DescriptionThis example illustrates the calculation of a weighted mean for a data set containing mostly negative values: -3, 2, and -5, with weights of 4, 3, and 5 respectively. The weighted mean is computed using the formula: (4 * -3 + 3 * 2 + 5 * -5) / (4 + 3 + 5), resulting in a final answer of approximately -2.133. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 5 | Math Example--Measures of Central Tendency--Weighted Mean--Example 5TopicMeasures of Central Tendency DescriptionThis example demonstrates the calculation of a weighted mean in a real-world context, using kettlebells of different weights: 32, 24, and 16 pounds, with quantities of 4, 6, and 3 respectively. The weighted mean is computed using the formula: (4 * 32 + 6 * 24 + 3 * 16) / (4 + 6 + 3), resulting in an average weight of 24.62 pounds. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 6 | Math Example--Measures of Central Tendency--Weighted Mean--Example 6TopicMeasures of Central Tendency DescriptionThis example illustrates another real-world application of weighted mean, using kettlebells of different weights: 32, 24, and 16 pounds, with quantities of 5, 7, and 4 respectively. The weighted mean is computed using the formula: (5 * 32 + 7 * 24 + 4 * 16) / (5 + 7 + 4), resulting in an average weight of 24.5 pounds. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 7 | Math Example--Measures of Central Tendency--Weighted Mean--Example 7TopicMeasures of Central Tendency DescriptionThis example demonstrates the calculation of a weighted mean using coins of different values: pennies (1 cent), nickels (5 cents), and dimes (10 cents), with quantities of 3, 2, and 4 respectively. The weighted mean is computed using the formula: (3 * 1 + 2 * 5 + 4 * 10) / (3 + 2 + 4), resulting in an average value of approximately 5.56 cents. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 8 | Math Example--Measures of Central Tendency--Weighted Mean--Example 8TopicMeasures of Central Tendency DescriptionThis example illustrates the calculation of a weighted mean using a collection of coins with different values. The image shows pennies, nickels, dimes, and quarters stacked in columns, representing quantities of 4, 3, 5, and 2 respectively. The weighted mean is computed using the formula: (4 * 1 + 3 * 5 + 5 * 10 + 2 * 25) / (4 + 3 + 5 + 2), resulting in an average value of 8.5 cents. |
Data Analysis |
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Math Example--Measures of Central Tendency--Weighted Mean--Example 9 | Math Example--Measures of Central Tendency--Weighted Mean--Example 9TopicMeasures of Central Tendency DescriptionThis example demonstrates the calculation of a weighted mean in the context of probability, specifically finding the average sum when rolling two fair dice. The image displays a grid showing all possible outcomes of rolling two dice, with sums ranging from 2 to 12. The frequencies of each sum are highlighted in red, serving as the weights in the weighted mean calculation. The weighted mean is computed using the formula: (2 * 1 + 3 * 2 + 4 * 3 + 5 * 4 + 6 * 5 + 7 * 6 + 8 * 5 + 9 * 4 + 10 * 3 + 11 * 2 + 12 * 1) / 36, resulting in an average sum of 7. |
Data Analysis |
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MATH EXAMPLES--The Mean | MATH EXAMPLES--The Mean
This set of tutorials provides 42 examples of calculating the mean. NOTE: The download is a PPT file. |
Data Analysis |
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MATH EXAMPLES--The Median | MATH EXAMPLES--The Median
This set of tutorials provides 40 examples of calculating the median. NOTE: The download is a PPT file. |
Data Analysis |
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MATH EXAMPLES--The Mode | MATH EXAMPLES--The Mode
This set of tutorials provides 78 examples of calculating the mode. NOTE: The download is a PPT file. |
Data Analysis |
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MATH EXAMPLES--The Range | MATH EXAMPLES--The Range
This set of tutorials provides 26 examples of calculating the range. NOTE: The download is a PPT file. |
Data Analysis |
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Math in the News: Issue 103--Gas Prices | Math in the News: Issue 103--Gas Prices: Why Are They Decreasing?
December 2014. In this issue of Math in the News we analyze data in tabular and graphic formats to investigate the changing price of gasoline. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 104--The Decline of Radio Shack | Math in the News: Issue 104--The Decline of Radio Shack
December 2014. In this issue of Math in the News we analyze the reasons why Radio Shack has struggled as a business. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 105--Movie Statistics: 2014 | Math in the News: Issue 105--Movie Statistics: 2014
January 2015. In this issue of Math in the News we review box office statistics for the previous year. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 106--A Box Office Monster! | Math in the News: Issue 106--A Box Office Monster!
July 2015. In this issue of Math in the News we analyze the amazing box office success of the recently released Jurassic World. This provides an excellent application of data analysis and linear equations. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Linear Functions, Standard Form and Data Analysis |
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Math in the News: Issue 109--Was Ali the Greatest? | Math in the News: Issue 109--Was Ali the Greatest?
July 2016. In this issue of Math in the News we look at Muhammad Ali's boxing record and compare his record to other boxers. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
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Math in the News: Issue 110--Summer Travel | Math in the News: Issue 110--Summer Travel
August 2016. In this issue of Math in the News calculate average speed to various vacation destinations when traveling by car. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
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Math in the News: Issue 111--Summer Blockbusters | Math in the News: Issue 111--Summer Blockbusters
August 2016. In this issue of Math in the News, look at real world box office data to analyze what makes a movie a blockbuster. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 113--Olympic Power | Math in the News: Issue 113--Olympic Power
November 2016. In this issue of Math in the News, we look at the history of the Olympics. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 114--Thanksgiving Dinner | Math in the News: Issue 114--Thanksgiving Dinner Grocery Shopping
November 2016. In this issue of Math in the News, we look at the history of Thanksgiving, as well as the cost of preparing the historically relevant meal. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
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Math in the News: Issue 116: The 2021 Olympics | Math in the News: Issue 116: The 2021 Olympics
August 2021. In this issue of Math in the News we look at various charts and statistics about the Tokyo Olympics. Students are shown a series of charts and are then asked questions to encourage them to analyze the data. This is an excellent back-to-school activity with the focus on real-world data. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 117--Box Office Hits and Misses | Math in the News: Issue 117 | Box Office Hits and Misses
December 2022. In this issue of Math in the News we look at box office hits and misses from Disney. The House of Blockbosters every now and then misfires. It's useful to analyze box office data to see what we can learn from the hits and misses. —PRESS PREVIEW TO SEE THE SLIDE SHOW— This is part of the Math in the News collection. To see the complete collection, click on this link.Note: The download is a PPT file. Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 52--The iPhone | Math in the News: Issue 52--Did the iPhone Doom the Blackberry?
April 2012. In this issue of Math in the News we look at the future of Research in Motion's Blackberry, in light of the rise of the iPhone and Android devices. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 59--The Butterfly Migration | Math in the News: Issue 59--The Butterfly Migration
September 2012. In this issue of Math in the News we look at the great Monarch butterfly migration. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 66--Data Analysis, Halloween Style | Math in the News: Issue 66--Data Analysis, Halloween Style
October 2012. In this issue of Math in the News, we look at Halloween-related data. In particular, we look at statistics related to pumpkins. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 79--The End of an Era? | Math in the News: Issue 79--The End of an Era?
September 2013. In this issue we take a second look at Blackberry's financial woes. This is a follow-up report from Issue 52, where we looked at the company's revenue problems. Here we examine its final fate. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 80--A Season for the Ages | Math in the News: Issue 80--A Season for the Ages
October 2013. In this issue we follow Peyton Manning's extraordinary season with the Denver Broncos. This is a follow-up from Issue 51. This is an excellent opportunity to look at different data graphs, including box-and-whisker plots, bar graphs, and tabular data. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 81--The Growth of America | Math in the News: Issue 81--The Growth of America
October 2013. In this issue we look at how America has grown from its formation as a country. We look at the increase in the number of states, the increase in the population, and the demographic factors that have become prominent in recent years. We look at data in tables and graphs. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 82--Halloween Stats | Math in the News: Issue 82--Halloween Stats
October 2013. In this issue we look at statistics related to Halloween 2013. We explore how the economy is affecting holiday spending. We also investigate why Halloween has grown in popularity over the years. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 83--Super Typhoon Haiyan | Math in the News: Issue 83--Super Typhoon Haiyan
November 2013. In this issue of Math in the News we look at Typhoon Haiyan to learn to distinguish between typhoons and hurricanes. This creates an opportunity to use Venn Diagrams as a means of classifying information. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 85--2013 Movies: A Year in Review | Math in the News: Issue 85--2013 Movies: A Year in Review
January 2014. In this issue of Math in the News we look at box office data from 2013. We look for patterns in the data and analyze the data using different data displays, including bar graphs, line graphs, scatterplot, and tables. This provides an excellent opportunity for data analysis. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
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Math in the News: Issue 89--Who Will Win Super Bowl XLVIII? | Math in the News: Issue 89--Who Will Win Super Bowl XLVIII?
January 2014. In this issue of Math in the News we look at football statistics to examine who stands the best chance of winning Super Bowl XLVIII. This is an excellent opportunity for data analysis. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Data Analysis |
