Illustrative Math Alignment: Grade 6 Unit 8

Topic

Statistics

Definition

The mode of categorical data is the most frequent item in a categorical data set.

Description

The Mode of Categorical Data is useful for finding the most frequent data item used with non-numerical data. For example, preferences for discrete characteristics can result in a mode.

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

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Description

Standard deviation quantifies the degree of variation in a data set, indicating how much individual data points deviate from the mean. It is a crucial statistic for understanding the spread of data and is widely used in fields such as finance, research, and quality control to assess variability and risk. A low standard deviation indicates that data points are close to the mean, while a high standard deviation suggests greater variability.

Topic

Statistics

Definition

A histogram is a graphical representation of data distribution using bars of different heights.

Description

Histograms are used to visualize the frequency distribution of continuous data, making it easier to identify patterns and trends. They are widely used in fields such as economics, biology, and engineering to analyze data distributions and detect anomalies. In mathematics, histograms are essential for understanding probability distributions and statistical inference.

Topic

Statistics

Definition

A skewed distribution is a probability distribution that is not symmetric, with data tending to cluster more on one side.

Description

Skewed distributions occur when data is not evenly distributed around the mean, resulting in a longer tail on one side. Skewness can be positive (right-skewed) or negative (left-skewed), affecting the interpretation of data and statistical measures such as the mean and median. Skewed distributions are common in real-world data, such as income levels and test scores, where extreme values can influence the overall distribution.

Topic

Statistics

Definition

A symmetric distribution is a probability distribution where the left and right sides are mirror images of each other.

Description

Symmetric distributions are characterized by data that is evenly distributed around the mean, resulting in a balanced, mirror-image shape. The most common symmetric distribution is the normal distribution, which is widely used in statistics for modeling natural phenomena. Symmetric distributions are important for statistical inference, as many statistical tests assume data is symmetrically distributed.

Topic

Statistics

Definition

Continuous data is numerical data that can take any value within a range.

Description

Continuous data is vital for representing measurements such as height, weight, and temperature, which can assume an infinite number of values within a given range. In real-world applications, continuous data is used in fields like engineering, physics, and economics to model and predict outcomes. Understanding continuous data is essential for performing calculations involving integrals and derivatives in calculus.

Topic

Statistics

Definition

Discrete data consists of countable values, often represented by whole numbers.

Description

Discrete data is commonly used in situations where data points are distinct and separate, such as the number of students in a class or the number of cars in a parking lot. It is crucial for fields like computer science, where discrete structures and algorithms are fundamental. In mathematics, discrete data is used in probability theory and combinatorics, helping to solve problems involving permutations and combinations.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

In this set of math examples, analyze the behavior of different scatterplots. This includes linear and quadratic models.

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

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

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.

In this TI Nspire tutorial, the Spreadsheet and Calculator windows are used to find the mean of a data list. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

In this TI Nspire tutorial, the Spreadsheet and Calculator windows are used to find the median of a data list. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Finding the Mean of a Data List.

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

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Finding the Median of a Data List.

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

In this Investigation we look at real-world data involving endangered wolf populations. This video is Segment 3 of a 4 segment series related to Data Analysis and Probability. Segments 3 and 4 are grouped together.

In this Investigation we explore uncertainty and randomness. This video is Segment 1 of a 4 segment series related to Data Analysis and Probability. Segments 1 and 2 are grouped together.

What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis.

Linear Expressions, Equations, and Functions

Another factor in the mortgage crisis was the use of adjustable rate mortgages. Students run a number of scenarios to test adjustable rate mortgages, while also taking into account the state of the housing market during the time of the mortgage crisis.

Having learned the general features of a mortgage, students learn the specifics of a subprime mortgage. With this comes the notion of a credit score, and with credit scores come the probabilities for a loan default. Students use the amortization table to run probability simulations to determine possible loan defaults on subprime mortgages.

The time value of money is at the basis of all loans. Students learn about the key factors that determine monthly mortgage payments and use the TI-Nspire to create an amortization table. This table is used throughout the rest of the program to explore different scenarios.

In this introductory segment students learn about the mortage crisis of 2008. In the process they get a brief introduction to what a mortgage is.

In this episode of Algebra Applications, students explore the dramatic events of 2008 related to the mortgage crisis. Brought about principally through mortgage defaults, the effect on the overall economy was severe. Yet, this situation offers an ideal case study for the exploration of key concepts in data analysis and probability. By exploring these questions students get a front row seat to the historical events of the world's largest economy.

Video Tutorial: Ratios and Rates: Rates from Data. In this video, we look at linear data sets that can be used to find the rate of change.

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 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 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 tutorial, students arrange decimal data using place value techniques.

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.