VirginiaVirginia Probability & Statistics Curriculum
Video lessons and practice for every Probability & Statistics topic. Aligned to Virginia Mathematics Standards of Learning for high school students.
Virginia Probability & Statistics Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
CC.HSS.ID.A.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). |
CC.HSS.ID.A.2 | 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. |
CC.HSS.ID.A.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). |
CC.HSS.ID.A.4 | 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. |
CC.HSS.ID.B.5 | 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. |
CC.HSS.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. |
CC.HSS.IC.A.1 | Understand statistics as a process for making inferences about population parameters based on a random sample from that population. |
CC.HSS.IC.A.2 | Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. |
CC.HSS.IC.B.3 | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. |
CC.HSS.IC.B.4 | 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. |
CC.HSS.IC.B.5 | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. |
CC.HSS.IC.B.6 | Evaluate reports based on data. |
CC.HSS.CP.A.2 | 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. |
CC.HSS.CP.A.3 | 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. |
CC.HSS.CP.A.5 | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. |
CC.HSS.CP.B.7 | 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. |
CC.HSS.CP.B.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. |
CC.HSS.MD.A.1 | 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. |
CC.HSS.MD.A.2 | Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. |
CC.HSS.MD.A.3 | Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. |
CC.HSS.MD.B.7 | Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). |
Virginia Probability & Statistics: What Students Learn
Virginia high school students in Probability & Statistics build skills across two major areas: statistics and probability. The course is aligned to Virginia Mathematics Standards of Learning (SOL) and prepares students to reason with data, interpret results, and apply probability to real decisions.
Data Analysis and Distributions
Students begin by representing data using dot plots, histograms, and box plots. They compare data sets using measures of center (mean and median) and spread (interquartile range and standard deviation). A key focus is understanding how shape, center, and spread change — and how outliers affect those measures.
- Fitting data to a normal distribution using mean and standard deviation
- Estimating population percentages using the normal curve
- Summarizing categorical data in two-way frequency tables
- Interpreting joint, marginal, and conditional relative frequencies
Scatter Plots, Correlation, and Causation
Students represent two quantitative variables on scatter plots and describe relationships. They compute and interpret the correlation coefficient using technology, and — critically — learn to distinguish between correlation and causation.
Statistical Inference and Sampling
This section covers how statistics is used to make inferences about populations from random samples. Topics include:
- Sample surveys, experiments, and observational studies
- Margin of error through simulation models
- Comparing two treatments using randomized experiments
- Evaluating data-based reports for validity
Probability Rules and Conditional Probability
Students study independence, conditional probability, the Addition Rule, and the general Multiplication Rule. They use two-way tables as sample spaces and apply probability concepts to everyday situations.
- P(A and B) = P(A) × P(B) for independent events
- Conditional probability: P(A|B) = P(A and B)/P(B)
- Addition Rule: P(A or B) = P(A) + P(B) − P(A and B)
- Permutations and combinations for compound event probabilities
Random Variables and Expected Value
Students define random variables, graph probability distributions, and calculate expected values. They develop distributions using both theoretical probabilities and empirical data, then apply expected value to weigh decisions and analyze real-world strategies such as medical testing or game theory.