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
Math Example--Measures of Central Tendency--Median: Example 5	Math Example--Measures of Central Tendency--Median: Example 5 Topic Measures of Central Tendency Description This example demonstrates how to find the median of the following set of numbers: 49, 3, 27, 46, 7, 32, 21, 33, 33. The process involves arranging the numbers from least to greatest and then identifying the middle value. In this case, with an odd number of terms, the median is simply the middle number after sorting, which is 32.	Data Analysis
Math Example--Measures of Central Tendency--Median: Example 6	Math Example--Measures of Central Tendency--Median: Example 6 Topic Measures of Central Tendency Description This example illustrates the process of finding the median for the set of numbers: 15, 24, -6, -16, 50, 12, -50, 43, 35. The solution involves arranging the numbers from least to greatest and then identifying the middle value. With an odd number of terms, the median is simply the middle number after sorting, which in this case is 15.	Data Analysis
Math Example--Measures of Central Tendency--Median: Example 7	Math Example--Measures of Central Tendency--Median: Example 7 Topic Measures of Central Tendency Description This example demonstrates finding the median of the following set of numbers: 23, 30, 9, 34, 13, 40, 26, 30, 45, 36. The solution involves arranging the numbers from least to greatest and then identifying the middle value. With an even number of terms, the median is calculated as the average of the two middle terms, resulting in a median of 30.	Data Analysis
Math Example--Measures of Central Tendency--Median: Example 8	Math Example--Measures of Central Tendency--Median: Example 8 Topic Measures of Central Tendency Description This example demonstrates how to find the median of the following set of numbers: 50, 14, 47, 43, 25, 10, 18, 21, 20, 19. The process involves arranging the numbers in ascending order and then identifying the middle value. With an even number of terms, the median is calculated as the average of the two middle terms, resulting in a median of 20.5.	Data Analysis
Math Example--Measures of Central Tendency--Median: Example 9	Math Example--Measures of Central Tendency--Median: Example 9 Topic Measures of Central Tendency Description This example illustrates the process of finding the median for the set of numbers: 13, -3, 23, -20, -14, -32, -31, -21, 36, -14. The solution involves arranging the numbers from least to greatest and then identifying the middle value. With an even number of terms, the median is calculated as the average of the two middle terms, resulting in a median of -14.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 1	Math Example--Measures of Central Tendency--Mode: Example 1 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows a set of numbers with an example of finding the mode. The numbers are arranged from least to greatest, and it concludes that there is no mode. The example demonstrates that in some cases, a data set may not have a mode when no number appears more than once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 10	Math Example--Measures of Central Tendency--Mode: Example 10 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image presents an example where no mode is found in a set of numbers after sorting them from least to greatest. This demonstrates that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 11	Math Example--Measures of Central Tendency--Mode: Example 11 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image demonstrates finding the mode by arranging numbers in order and identifying the most frequent number. After sorting, it becomes clear that 48 appears twice, while all other numbers appear only once, making 48 the mode of this data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 12	Math Example--Measures of Central Tendency--Mode: Example 12 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows an example with multiple modes after sorting a list of numbers and highlighting those that appear most often. After arranging the numbers from least to greatest, it becomes evident that both 26 and 32 appear twice, while all other numbers appear only once. This demonstrates that a data set can have more than one mode.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 13	Math Example--Measures of Central Tendency--Mode: Example 13 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows a set of numbers with instructions to find the mode. The numbers are arranged from least to greatest, and "No Mode" is indicated. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 14	Math Example--Measures of Central Tendency--Mode: Example 14 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image presents a set of numbers with instructions to find the mode. The numbers are sorted, and the mode is highlighted as 25. This example demonstrates how to identify the mode when a number appears more frequently than others in a data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 15	Math Example--Measures of Central Tendency--Mode: Example 15 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image displays a set of numbers with instructions to find the mode. Numbers are arranged in order with modes highlighted as 19 and 24. This example illustrates that a data set can have more than one mode, which occurs when two or more numbers appear with the highest frequency.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 16	Math Example--Measures of Central Tendency--Mode: Example 16 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows a set of numbers with instructions to find the mode. The numbers are arranged in order and "No Mode" is indicated. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 17	Math Example--Measures of Central Tendency--Mode: Example 17 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows a math example finding the mode of a set of numbers. The numbers are arranged from least to greatest, and the mode is highlighted. This example demonstrates how to identify the mode when a number appears more frequently than others in a data set that includes both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 18	Math Example--Measures of Central Tendency--Mode: Example 18 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image illustrates finding the mode of a set. The numbers are sorted and two modes are identified and highlighted. This example demonstrates that a data set can have multiple modes, even when it contains both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 19	Math Example--Measures of Central Tendency--Mode: Example 19 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows a set of numbers with no mode. The numbers are arranged in ascending order to demonstrate that no number repeats. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 2	Math Example--Measures of Central Tendency--Mode: Example 2 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image presents a set of numbers with an example of finding the mode. The numbers are sorted, showing that the mode is 14. This example illustrates how to identify the mode when a number appears more frequently than others in a data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 20	Math Example--Measures of Central Tendency--Mode: Example 20 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image displays a math example where the mode is found by sorting the numbers and identifying the most frequent one. After arranging the numbers from least to greatest, it becomes clear that 0 appears twice, while all other numbers appear only once, making 0 the mode of this data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 21	Math Example--Measures of Central Tendency--Mode: Example 21 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image shows Example 21, focusing on finding the mode of a set of numbers. The numbers are listed in random order and then sorted from least to greatest. The mode is highlighted in red, demonstrating how to identify the mode when a number appears more frequently than others in a data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 22	Math Example--Measures of Central Tendency--Mode: Example 22 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image shows Example 22, which involves finding the mode of a set of numbers. The numbers are sorted from least to greatest, but no number repeats more than once, indicating no mode. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 23	Math Example--Measures of Central Tendency--Mode: Example 23 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image shows Example 23 with a set of numbers where the mode is determined by sorting and identifying the most frequent number. The mode is highlighted in red, demonstrating how to identify the mode when a number appears more frequently than others in a data set that includes both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 24	Math Example--Measures of Central Tendency--Mode: Example 24 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image shows Example 24 with a set of numbers where two modes are identified after sorting. Both modes are highlighted in red, demonstrating that a data set can have multiple modes, even when it contains both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 25	Math Example--Measures of Central Tendency--Mode: Example 25 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows a math example focused on finding the mode of a set of numbers. The numbers are arranged in ascending order, and it is highlighted that there is no mode in this data set. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 26	Math Example--Measures of Central Tendency--Mode: Example 26 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image provides a math example on finding the mode of a number set. The numbers are sorted in order with the mode (2) highlighted as it appears most frequently. This demonstrates how to identify the mode when a number appears more frequently than others in a data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 27	Math Example--Measures of Central Tendency--Mode: Example 27 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image illustrates a math problem about determining the mode from a list of numbers. The sorted list shows two modes (23 and 24) highlighted as they appear most frequently. This demonstrates that a data set can have more than one mode, which occurs when two or more numbers appear with the highest frequency.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 28	Math Example--Measures of Central Tendency--Mode: Example 28 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image depicts an example where students are tasked to find the mode in a number sequence. After sorting the numbers in order it is shown that there is no mode present in this set. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 29	Math Example--Measures of Central Tendency--Mode: Example 29 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The numbers are listed, and a solution is provided below. This example demonstrates how to identify the mode when a number appears more frequently than others in a data set that includes both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 3	Math Example--Measures of Central Tendency--Mode: Example 3 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. This image illustrates a set of numbers with an example to find the mode. After sorting, it identifies two modes: 38 and 50. This example demonstrates that a data set can have more than one mode, which occurs when two or more numbers appear with the highest frequency.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 30	Math Example--Measures of Central Tendency--Mode: Example 30 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows a math example labeled "Example 30" about finding the mode of a set of numbers. The numbers are listed, and a solution is provided below. This example demonstrates that a data set can have multiple modes, even when it contains both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 31	Math Example--Measures of Central Tendency--Mode: Example 31 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The numbers are listed, and a solution is provided below. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 32	Math Example--Measures of Central Tendency--Mode: Example 32 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The numbers are listed, and a solution is provided below. This example demonstrates how to identify the mode when a number appears more frequently than others in a data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 33	Math Example--Measures of Central Tendency--Mode: Example 33 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image shows an example problem asking to find the mode of a set of numbers. The numbers are listed and then rearranged from least to greatest. The mode is highlighted in red. This example demonstrates that a data set can have multiple modes, even when it contains both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 34	Math Example--Measures of Central Tendency--Mode: Example 34 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image presents a problem where the task is to find the mode of a given set of numbers. The numbers are arranged in order but no number appears more than once; hence there is no mode. This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 35	Math Example--Measures of Central Tendency--Mode: Example 35 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image displays a math example where a set of numbers is provided to find the mode. The numbers are sorted and the mode is highlighted in red as it appears multiple times in the list. This example demonstrates how to identify the mode when a number appears more frequently than others in a data set that includes both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 36	Math Example--Measures of Central Tendency--Mode: Example 36 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image features an example problem asking for the mode of a list of numbers. After sorting them in ascending order and identifying duplicates with highlights in red indicating multiple modes present in this example. This demonstrates that a data set can have multiple modes, even when it contains both positive and negative numbers.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 37	Math Example--Measures of Central Tendency--Mode: Example 37 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. An example of finding the mode in a set of numbers is presented. The numbers are listed, sorted, and analyzed to determine if there is a mode. The result is "No Mode." This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 38	Math Example--Measures of Central Tendency--Mode: Example 38 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. An example showing how to find the mode in a set of numbers is presented. The numbers are sorted and analyzed to find that "42" is the mode. This demonstrates how to identify the mode when a number appears more frequently than others in a data set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 39	Math Example--Measures of Central Tendency--Mode: Example 39 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. An example illustrating how to find the mode in a set of numbers is presented. The numbers are sorted and analyzed to reveal two modes: "43" and "44." This demonstrates that a data set can have multiple modes, which occurs when two or more numbers appear with the highest frequency.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 4	Math Example--Measures of Central Tendency--Mode: Example 4 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. The image displays a set of numbers with an example for finding the mode. After arranging them, it concludes that there is no mode. This example reinforces the concept that not all data sets have a mode, particularly when each number appears only once in the set.	Data Analysis
Math Example--Measures of Central Tendency--Mode: Example 40	Math Example--Measures of Central Tendency--Mode: Example 40 Topic Measures of Central Tendency Description This example showcases a situation of measures of central tendency, where the goal is to identify a key summary measure in a set of data. An example showing how to find the mode in a set of negative and positive numbers is presented. The analysis shows there is "No Mode." This example reinforces the concept that not all data sets have a mode, particularly when each number in the set appears only once.	Data Analysis

Illustrative Math Alignment: Grade 7 Unit 8

Probability and Sampling

Lesson 19: Comparing Populations With Friends

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