Prob & Stats

Probability and Statistics is a college preparatory course where students learn to make decisions and predictions based on data. Pathfinder Tech follows the Massachusetts Mathematics Curriculum Frameworks which emphasizes that Probability and Statistics focus on the following 4 areas:

(1)  interpreting categorical and quantitative data;

(2)  making inferences and justifying conclusions;

(3)  conditional probability and rules of probability;

(4)  using probability to make decisions.

(Click here to read more about the Massachusetts Mathematics Curriculum Frameworks.)

Learning Objectives: Students will be able to...

• Identify the individuals and variables in a set of data.

• Classify variables as categorical or quantitative.

• Organize data in tables and graphs.

• Choose a table or graph to display data.

• Create stem-and-leaf plots.

• Create frequency tables and histograms.

• Describe the central tendency of a data set.

• Create box-and-whisker plots.

• Recognize misleading graphs.

• Recognize misleading statistics.

• Determine the experimental probability of an event.

• Use experimental probability to make predictions.

• Determine the theoretical probability of an event.

• Convert between probabilities and odds.

• Find the probability of independent events.

• Find the probability of dependent events.

• Solve problems involving permutations.

• Solve problems involving combinations.

Learning Objectives: Students will be able to...

• Identify the individuals and variables in a set of data.

• Classify variables as categorical or quantitative.

• Display categorical data with a bar graph. Decide whether it would be appropriate to make a pie chart.

• Identify what makes some graphs of categorical data deceptive.

• Calculate and display the marginal distribution of a categorical variable from a two-way table.

• Calculate and display the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table.

• Describe the association between two categorical variables by comparing appropriate conditional distributions.

• Make and interpret dotplots and stemplots.

• Describe a distribution (SOCS).

• Identify the shape of a distribution from a graph as roughly symmetric or skewed.

• Make and interpret histograms.

• Compare distributions of quantitative data using dotplots, stemplots, or histograms.

• Calculate measures of center (mean, median).

• Calculate and interpret measures of spread (range, IQR, standard deviation).

• Choose the most appropriate measure of center and spread in a given setting.

• Identify outliers using the 1.5 × IQR rule.

• Make and interpret boxplots.

• Use appropriate graphs and numerical summaries to compare distributions of quantitative variables.

Learning Objectives: Students will be able to...

• Find and interpret the percentile of an individual value within a distribution of data.

• Estimate percentiles and individual values using a cumulative relative frequency graph.

• Find and interpret the standardized score (z-score) of an individual within a distribution of data.

• Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and spread of a distribution of data.

• Estimate the relative locations of the median and mean on a density curve.

• Estimate areas (proportions of values) in a Normal distribution.

• Find the proportion of z-values in a specified interval, or a z-score from a percentile in the standard Normal distribution.

• Find the proportion of values in a specified interval, or the value that corresponds to a given percentile in any Normal distribution.

• Determine whether a distribution of data is approximately Normal from graphical and numerical evidence.

Learning Objectives: Students will be able to...

• Identify explanatory and response variables in situations where one variable helps to explain or influence the other.

• Make a scatterplot to display the relationship between two quantitative variables.

• Describe the direction, form, and strength of a relationship displayed in a scatterplot and identify outliers in a scatterplot.

• Interpret the correlation.

• Understand the basic properties of a correlation, including how the correlation is influenced by outliers.

• Use technology to calculate correlation.

• Explain why association does not imply causation.

• Interpret the slope and y-intercept of a least-squares regression line (LSRL).

• Use the LSRL to predict y given x.

• Calculate and interpret residuals and their standard deviation.

• Explain the concept of least squares.

• Determine the equation of a LSRL using a variety of methods.

• Construct and interpret residual plots to assess whether a linear model is appropriate.

• Assess how well the LSRL models the relationship between two variables.

• Describe how the slope, y-intercept, standard deviation of the residuals, and r2 are influenced by outliers. 

Learning Objectives: Students will be able to...

• Identify the population and sample in a statistical study.

• Identify voluntary response samples and convenience samples. Explain how these sampling methods can lead to bias.

• Describe how to obtain a random sample using slips of paper, technology, or a table of random digits.

• Distinguish a simple random sample from a stratified random sample or cluster sample. Give the advantages and disadvantages of each sampling method.

• Explain how undercoverage, nonresponse, question wording, and other aspects of a sample survey can lead to bias.

• Distinguish between an observational study and an experiment.

• Explain the concept of confounding.

• Identify the experimental units, explanatory and response variables, and treatments in an experiment.

• Describe a completely randomized design for an experiment.

• Describe the placebo effect and the purpose of blinding in an experiment.

• Interpret the meaning of statistically significant in the context of an experiment.

• Explain the purpose of blocking in an experiment. Describe a randomized block design or a matched pairs design for an experiment.

• Describe the scope of inference that is appropriate.

• Evaluate whether a statistical study has been carried out in an ethical way.

Learning Objectives: Students will be able to...

• Interpret probability as a long-run relative frequency.

• Use simulation to model chance behavior.

• Determine a probability model for a chance process.

• Use basic probability rules, including the complement rule and the addition rule for mutually exclusive events.

• Use a two-way table or Venn diagram to model a chance process and calculate probabilities involving two events.

• Use the general addition rule to calculate probabilities.

• Calculate and interpret conditional probabilities.

• Use the general multiplication rule to calculate probabilities.

• Use tree diagrams to model a chance process and calculate probabilities involving two or more events.

• Determine whether two events are independent.

• When appropriate, use the multiplication rule for independent events to compute probabilities.