- Course type: Self-paced
- Available Lessons: 66
- Average Lesson Length: 8 min
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Watch a preview:chapter 1 / lesson 1What is Quantitative Data? - Definition & Examples
Course SummaryRefresh your lesson plans and utilize technology in your classroom with this engaging course on statistics and probability. Our video lessons, quizzes and chapter tests can be used to supplement your teaching and ensure it meets to Common Core State Standards.
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6 chapters in Common Core Math - Statistics & Probability: High School Standards
Course Practice TestCheck your knowledge of this course with a 50-question practice test.
- Comprehensive test covering all topics
- Detailed video explanations for wrong answers
About the Course
The collective teamwork of parents, educators and community leaders established the Common Core State Standards, which gauges the appropriate benchmark of students' subject-level comprehension at every grade level. The common core math standards measure the ability to perform specific mathematical functions as well as understand the principles and theories that support them. www.heiqigong.com's collection on statistics and probability breaks down the elements of these branches of math, making the concepts, theories and calculations clear and easy to comprehend. Each lesson offers a short quiz that can be used to preview your students' current knowledge level as well as test their understanding after the material has been covered. Video lessons introduce the following topics with examples, sample problems and engaging graphics:
- Quantitative data, data sets, and dot plots
- Categorical data, bar graphs, pie charts, and frequency
- Bivariate data, scatter plots, residuals and linear regression
- Random sampling, modeling, simulation, and randomized experiments
- Conditional probability, permutation, and types of events
- Random variables, expected values, and probability concepts in problem solving
Students proficient in mathematical statistics and probability will be able to apply the rules, theories and calculations to real-life situations that use data modeling and prediction. Often, math subjects require a significant amount of memorization, and the video lessons in this collection use repetition and overlapping to help students fully understand and retain the concepts discussed.
Data Sets and Dot Plots on the Real Number Line (CCSS.Math.Content.HSS-ID.A.1)
Standard: Represent data with plots on the real number line (dot plots, histograms, and box plots).
After defining quantitative data, the chapter offers lessons on creating and interpreting histograms, and plotting on the real number line using dot plots and box plots.
Mean, Median, Mode & Range (CCSS.Math.Content.HSS-ID.A.2)
Standard: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Lessons cover finding the center in data sets, and how to calculate for the mean, median, mode and range. Students learn the difference between average and median as well as quartiles and the interquartile range.
Shape, Center, Spread and Outliers (CCSS.Math.Content.HSS-ID.A.3)
Standard: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Help students find the shape, symmetry, spread and skewness in data sets. Lessons also cover maximums, minimums and outliers.
Normal Distribution: (CCSS.Math.Content.HSS-ID.A.4)
Standard: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Lessons introduce students to normal distribution and z-scores. Students can also learn how to estimate areas under the normal curve or estimate population percentages using normal distribution. Use the lessons for additional practice using the normal distribution.
Categorical Data (CCSS.Math.Content.HSS-ID.B.5)
Standard: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
Teach students about frequency and relative frequency tables, as well as how to calculate percent increase with relative and cumulative frequency tables.
Bivariate Data and Scatter Plots (CCSS.Math.Content.HSS-ID.B.6)
Standard: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Lessons define bivariate data and explain a two-way table. Students learn about joint, marginal, and conditional frequencies, as well as how to create and interpret scatter plots.
Linear Regression (CCSS.Math.Content.HSS-ID.B.6a)
Standard: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
Use simple linear regression to fit data to a line, and show students how to solve problems using linear regression.
Analyzing Residuals (CCSS.Math.Content.HSS-ID.B.6b)
Standard: Informally assess the fit of a function by plotting and analyzing residuals.
This lesson explains and simplifies the process for analyzing residuals.
Correlation Coefficient (CCSS.Math.Content.HSS-ID.B.6c)
Standard: Fit a linear function for a scatter plot that suggests a linear association.
This lesson teaches students how to interpret the slope and intercept of a linear model.
Linear Data Modeling (CCSS.Math.Content.HSS-ID.C.7)
Standard: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Use these lessons to practice interpreting linear relationships using data.
Correlation Coefficient (CCSS.Math.Content.HSS-ID.C.8)
Standard: Compute (using technology) and interpret the correlation coefficient of a linear fit.
Explain how the correlation coefficient is used to illustrate the linear dependence of variables or data sets.
Correlation and Causation (CCSS.Math.Content.HSS-ID.C.9)
Standard: Distinguish between correlation and causation.
Show the interrelationship of variable quantities and how it differs from the relationship of cause and effect.
Populations and Random Sampling (CCSS.Math.Content.HSS-IC.A.1)
Standard: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
These lessons explain the difference between statistics and parameters as well as populations and samples, then show students how to use random sampling to make inferences with data.
Standard: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
Use this lesson to explain the evidence for strength of a model through data gathering.
Experiments and Observational Studies (CCSS.Math.Content.HSS-IC.B.3)
Standard: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
This lesson teaches students how controlled experiments differ from observational studies.
Random Sampling (CCSS.Math.Content.HSS-IC.B.4)
Standard: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
This lesson describes random selection and random allocation, as well as estimating a parameter from sample data.
Randomized Experiments (CCSS.Math.Content.HSS-IC.B.5)
Standard: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Use these lessons to explain how to develop a margin of error using simulation models, design a randomized experiment, and use simulations to determine if differences between groups are significant.
Evaluating Reports (CCSS.Math.Content.HSS-IC.B.6)
Standard: Evaluate reports based on data.
This lesson shows students how to evaluate and interpret reports using data.
Sample Space (CCSS.Math.Content.HSS-CP.A.1)
Standard: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or,' 'and,' 'not').
These lessons introduce elements, intersections and unions as mathematical sets, define evens as subsets of a sample space, and identify the probability of simple, compound and complementary events.
Independent and Dependent Events (CCSS.Math.Content.HSS-CP.A.2)
Standard: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
Determine the probability of independent and dependent events, and explain the 'At Least One' Rule in the probability of independent events.
Conditional Properties and Independence (CCSS.Math.Content.HSS-CP.A.3)
Standard: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
Lessons for this standard include instruction on how to calculate simple conditional properties, and explain conditional properties and independence.
Two-Way Frequency Tables (CCSS.Math.Content.HSS-CP.A.4)
Standard: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
Use two-way frequency tables to decide if events are independent and to estimate conditional probabilities.
Conditional Properties & Independence in Real Life (CCSS.Math.Content.HSS-CP.A.5)
Standard: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
Review the uses of conditional properties and independence, and learn how to apply them to real-life situations.
Conditional Probability Model (CCSS.Math.Content.HSS-CP.B.6)
Standard: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
Lessons cover finding the conditional probability of an event and interpreting the data.
Addition Rule (CCSS.Math.Content.HSS-CP.B.7)
Standard: Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
Provide an explanation of the Addition Rule and apply it to problems in probability.
Multiplication Rule (CCSS.Math.Content.HSS-CP.B.8)
Standard: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Teach the Multiplication Rule in probability, and provide combinations of formula and example problems.
Standard: (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
These lessons show how to calculate a permutation and the probability of permutations.
Random Variables (CCSS.Math.Content.HSS-MD.A.1)
Standard: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
Provide an overview of random variables and graph probability distributions associated with random variables.
Standard: (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
Use the lessons on finding and interpreting the expected value of a random variable.
Theoretical Probabilities (CCSS.Math.Content.HSS-MD.A.3)
Standard: (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
Lessons teach how to develop probability distributions theoretically and find expected values.
Empirical Distributions (CCSS.Math.Content.HSS-MD.A.4)
Standard: (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
Use these lessons to teach students how to develop the probability of distributions empirically and find the expected values.
Payoff Values (CCSS.Math.Content.HSS-MD.B.5)
Standard: (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
Lessons show students how to compare game strategies based on expected values.
Games of Chance (CCSS.Math.Content.HSS-MD.B.5a)
Standard: Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.
Use the lesson on finding the expected values in games of chance to illustrate this standard.
Random Numbers (CCSS.Math.Content.HSS-MD.B.6)
Standard: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
This collection includes a lesson that explains how to generate random numbers.
Probability Concepts (CCSS.Math.Content.HSS-MD.B.7)
Standard: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Show students how to apply probability concepts to problem solving.
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