IndianaIndiana Probability and Statistics Curriculum
Video lessons and practice for every Probability and Statistics topic. Aligned to Indiana Academic Standards for Math so Indiana students stay on track.
Indiana Probability and 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). |
Indiana Probability and Statistics: Course Overview
Indiana high school students taking Probability and Statistics learn to collect, display, and interpret data while building a strong foundation in probability theory. The course aligns to Indiana Academic Standards for Math and prepares students for college-level statistics and data-driven reasoning in any field.
Data Analysis and Statistics
Students begin by representing data on dot plots, histograms, and box plots. They compare data sets using measures of center — mean and median — and spread, including interquartile range and standard deviation. The course covers normal distributions, two-way frequency tables, scatter plots, and correlation so students can describe relationships between variables and interpret real-world data sets.
- Represent data with dot plots, histograms, and box plots
- Compare center and spread across two or more data sets
- Fit data to a normal distribution and estimate population percentages
- Interpret two-way frequency tables using joint, marginal, and conditional relative frequencies
- Analyze scatter plots and compute correlation coefficients
- Distinguish between correlation and causation
Statistical Inference and Sampling
The course introduces statistics as a process for making inferences about populations from random samples. Students learn the differences among sample surveys, experiments, and observational studies, and they explore how randomization reduces bias. They use simulation to estimate margins of error and evaluate whether differences between treatments are statistically significant.
- Understand sampling and population inference
- Recognize differences among surveys, experiments, and observational studies
- Use simulation to develop margins of error
- Evaluate reports based on data quality and methodology
Probability Rules and Conditional Probability
Students apply the Addition Rule and the general Multiplication Rule to calculate probabilities of compound events. They define independence formally and use two-way tables to approximate conditional probabilities. Everyday examples help students recognize conditional probability and independence in real situations.
- Apply P(A or B) = P(A) + P(B) − P(A and B)
- Apply P(A and B) = P(A)P(B|A) using the Multiplication Rule
- Interpret conditional probability using two-way frequency tables
- Use permutations and combinations to count outcomes and find probabilities
Random Variables and Expected Value
The course closes with random variables and probability distributions. Students define random variables, graph probability distributions, and calculate expected values. They develop distributions from both theoretical models and empirical data, then use expected value to weigh outcomes and analyze decisions — from product testing to medical testing scenarios.
- Define random variables and graph probability distributions
- Calculate expected value from theoretical and empirical distributions
- Use expected value to evaluate decisions and strategies
- Apply probability to analyze real-world decisions fairly and accurately