Illustrative Math Alignment: Grade 7 Unit 8

Topic

Statistics

Definition

The upper quartile (Q3) is the median of the upper half of a data set, representing the 75th percentile.

Description

The upper quartile is a measure of position that indicates the value below which 75% of the data falls. It is used in conjunction with other quartiles to understand the distribution and spread of data. In real-world applications, the upper quartile is used in finance to assess investment performance and in education to evaluate student achievement levels.

Topic

Statistics

Definition

Variance is a measure of the dispersion of a set of values, calculated as the average of the squared deviations from the mean.

Description

Variance quantifies the degree of spread in a data set, providing insight into the variability of data points around the mean. It is a fundamental concept in statistics, used in fields such as finance, research, and engineering to assess risk and variability. A high variance indicates greater dispersion, while a low variance suggests that data points are closer to the mean.

Topic

Statistics

Definition

A weighted average is an average that takes into account the relative importance of each value, calculated by multiplying each value by its weight and summing the results.

Description

The weighted average is used when different data points contribute unequally to the final average. It is commonly applied in finance to calculate portfolio returns, in education to compute weighted grades, and in various fields where data points have different levels of significance. The weighted average provides a more accurate representation of data by considering the relative importance of each value.

Topic

Statistics

Definition

The weighted mean is the average of a data set where each value is multiplied by a weight reflecting its importance.

Description

The weighted mean is used when different data points contribute unequally to the final average. It is commonly applied in finance to calculate portfolio returns, in education to compute weighted grades, and in various fields where data points have different levels of significance. The weighted mean provides a more accurate representation of data by considering the relative importance of each value.

The formula for the Mean.

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The formula for the Median.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

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.

Related Resources

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.

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 math example demonstrates the calculation of the mean for a data set that includes negative numbers: 0, 8, 5, -5, 3, -8, 8, 4, 9, -4. The example emphasizes the step-by-step process of finding the mean, showing how to handle both positive and negative values in the calculation.

Topic

Measures of Central Tendency

Description

The image shows Example 10, demonstrating how to calculate the mean for a different set of numbers. This example illustrates finding the mean of the data set: -6, 5, -5, -5, -7, -7, -4, -1, 3. The calculation is presented step-by-step: Mean = Sum / Count. The sum of all numbers (-6 + 5 + (-5) + (-5) + (-7) + (-7) + (-4) + (-1) + 3) is divided by the count of numbers (10), resulting in -34 / 10 = -3.4.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for a dataset containing both positive and negative numbers: 7, 4, 1, 1, -1, -2, 9, 4, -9, -4. The step-by-step process shows how to sum all values, including negative ones, and divide by the total number of data points to find the mean.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for a dataset that includes negative numbers and zeros: 4, -1, 0, -2, -9, 0, -6, 5, 0, -1. The step-by-step process illustrates how to sum all values, including negatives and zeros, and divide by the total number of data points to determine the mean.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for a dataset containing both positive and negative numbers: -3, 8, 2, 1, 3, -6, -9, 3, -4. The step-by-step process demonstrates how to sum all values, including negative ones, and divide by the total number of data points to find the mean.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for a dataset that includes both positive and negative numbers: -1, 9, 3, 3, 6, -8, 8, 1, 4, 5. The step-by-step process shows how to sum all values, including negative ones, and divide by the total number of data points to determine the mean.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for a dataset containing both positive and negative numbers: -4, -5, 6, 2, 5, 7, 9, 9, -9, 5. The step-by-step process demonstrates how to sum all values, including negative ones, and divide by the total number of data points to find the mean.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for a dataset that includes negative numbers and zero: -4, 0, 2, 9, -2, -3, -5, 10, -7, 5. The step-by-step process illustrates how to sum all values, including negatives and zero, and divide by the total number of data points to determine the mean.

Topic

Measures of Central Tendency

Description

This image shows a math example calculating the mean of a data set. The numbers are: 4, 8, -6, -6, 6, -3, 4, -8, -6, -8. The solution uses the mean formula. Example 8 demonstrates finding the mean of the data set. The mean is calculated by summing all numbers and dividing by the count of numbers, resulting in (-15) / (10) = -1.5.

Topic

Measures of Central Tendency

Description

The image shows Example 9, illustrating how to find the mean of a data set using the mean formula. This example demonstrates finding the mean of the data set: -8, -9, 10, -2, 3, -2, -8, -3, 2, 5. The calculation is shown step-by-step: Mean = Sum / Count. The sum of all numbers (-8 + (-9) + 10 + (-2) + 3 + (-2) + (-8) + (-3) + 2 + 5) is divided by the count of numbers (10), resulting in -12 / 10 = -1.2.

Topic

Measures of Central Tendency

Description

This example demonstrates how to calculate the mean of a dataset, a fundamental concept in statistics. The mean, often referred to as the average, is a measure of central tendency that provides insight into the typical value of a dataset. By visually presenting the calculation process, students can better grasp the concept and its application in real-world scenarios.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for the numbers 16, 18, 0, 19, 12, 10, 7, and 20. The process involves summing all values (102) and dividing by the count of numbers (8), resulting in a mean of 12.75. This example highlights how the mean can provide a representative value for a dataset that includes both high and low numbers, including zero.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for the numbers 9, 3, 19, 9, 15, 15, 20, 7, and 2. The process involves summing all values (99) and dividing by the count of numbers (9), resulting in a mean of 11. This example demonstrates how the mean can provide a central value that represents a dataset with repeated numbers and a wide range of values.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for the numbers 17, 3, 10, 12, 4, 17, 7, 17, and 19. The process involves summing all values (106) and dividing by the count of numbers (9), resulting in a mean of approximately 11.78. This example showcases how the mean can provide a representative value for a dataset that includes repeated numbers and a wide range of values.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for the numbers 13, 7, 6, 19, 12, 7, 20, 9, 12, and 15. The process involves summing all values (120) and dividing by the count of numbers (10), resulting in a mean of 12. This example demonstrates how the mean can provide a central value that represents a dataset with repeated numbers and a wide range of values.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for the numbers 10, 2, 7, 16, 16, 17, 3, 10, 18, and 15. The process involves summing all values (114) and dividing by the count of numbers (10), resulting in a mean of 11.4. This example showcases how the mean can provide a representative value for a dataset that includes repeated numbers and a wide range of values.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for the numbers -11, 2, 5, and -16. The process involves summing all values (-20) and dividing by the count of numbers (4), resulting in a mean of -5. This example is particularly important as it demonstrates how to handle negative numbers when calculating the mean, a concept that often challenges students.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for the numbers -4, 18, -19, and 6. The process involves summing all values (1) and dividing by the count of numbers (4), resulting in a mean of 0.25. This example is particularly interesting as it shows how positive and negative numbers can nearly balance each other out, resulting in a mean close to zero.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for the numbers 15, 17, -20, -5, and 18. The process involves summing all values (25) and dividing by the count of numbers (5), resulting in a mean of 5. This example is particularly instructive as it demonstrates how to handle a mix of positive and negative numbers, including some relatively large values in both directions.

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the mean for the numbers -13, 9, 4, 14, and 8. The process involves summing all values (22) and dividing by the count of numbers (5), resulting in a mean of 4.4. This example is particularly instructive as it shows how a single negative number can significantly impact the mean, even when most of the numbers are positive.

Topic

Measures of Central Tendency

Description

This example illustrates the calculation of the mean for the numbers 14, -7, 5, 11, -5, and 0. The process involves summing all values (18) and dividing by the count of numbers (6), resulting in a mean of 3. This example is particularly instructive as it demonstrates how to handle a mix of positive and negative numbers, including zero, in the calculation of the mean.