Making waves in STEM

Probability and Statistics

  • Date created

    June 30, 2020

  • Last updated

    June 17, 2021

Enroll in Probability and Statistics with Dolphin STEM Academy

Course Overview

Probability and Statistics is a mathematics course that teaches two related, but
distinguishable disciplines. Probability is the study of the likelihood that an event will
occur. For example, what is the likelihood that you will win a writing contest if there are
3,000 entries? What are the chances that you will land that lead role in the school play if
30 students audition? In statistics, you will practice the science of collecting and
analyzing numerical data in order to make decisions. The study of statistics upholds that
of probability. You’ve likely worked with both disciplines to varying degrees during your
math education.

In this course, you will represent and interpret data using dot plots, histograms, box
plots, two-way frequency tables, and scatter plots. You will study normal distributions
and distinguish between correlation and causation. You will also determine the
conditional probability of two events or whether the events are independent. Using
counting techniques and the rules of probability, you will calculate probabilities and use
the results to make educated and fair decisions. You will evaluate several data
collection techniques and statistical models, including simulations. The course closes
with information on how you can use probability models to represent situations arising in
everyday life that involve both payoff and risk.

Course Goals

By the end of this course, you will be able to do the following:
Summarize, represent, and interpret data on a single count or measurement variable.
Summarize, represent, and interpret data on two categorical and quantitative variables.
Interpret linear models.
Understand independence and conditional probability and use them to interpret data.
Use the rules of probability to compute probabilities of compound events in a uniform
probability model.
Use probability to evaluate outcomes of decisions.
Understand and evaluate random processes underlying statistical experiments.
Make inferences and justify conclusions from sample surveys, experiments, and
observational studies.
Calculate expected values and use them to solve problems.

Math Skills

Two semesters of Algebra 1 is a prerequisite for Probability and Statistics. Before
beginning this course, you should be able to do the following:

Represent linear relationships graphically and with equations.
Graph functions using basic calculator skills.
Understand that the probability of a chance event is a number between 0 and 1.

General Skills

To participate in this course, you should be able to do the following:

Complete basic operations with word processing software, such as Microsoft Word or Google Docs.
Understand the basics of spreadsheet software, such as Microsoft Excel or Google
Spreadsheets, but having prior computing experience is not necessary.
Perform online research using various search engines and library databases.
Communicate through email and participate in discussion boards.

For a complete list of general skills that are required for participation in online courses,
refer to the Prerequisites section of the Plato Student Orientation document, found at
the beginning of this course.

Credit Value

Probability and Statistics is a 0.5-credit course.

Course Materials

Notebook
Computer with Internet connection and speakers or headphones
Microsoft Word or equivalent
Microsoft Excel or equivalent

Course Pacing Guide

This course description and pacing guide is intended to help you keep on schedule with
your work. Note that your course instructor may modify the schedule to meet the
specific needs of your class.

Unit 1: Representing and Interpreting Data

Summary

In this unit, you will learn how to represent data using dot plots, histograms, and box
plots. You will also understand the importance of showing and interpreting the center
and spread of data as you compare two or more data sets. Finally, you’ll use the
concepts of center and spread to fit a data set to a normal distribution, also known as a
bell curve.

Unit 2: Relating Data Sets

Summary

In this unit, you will investigate the relationships between sets of data using graphing
techniques. For example, you will interpret the slope and intercept of a linear model and
fit an algebraic function to data in a scatter plot. You will also compute the dependence
or correlation of two variables in a linear plot and distinguish between correlation and
causation.

Unit 3: Independent and Conditional Probability

Summary

In this unit, you will apply the addition and multiplication rules of probability to calculate
probabilities using a uniform model. You will understand that an event is a set of
outcomes that can be related to other events or can be independent of them. You will
also use permutations and combinations to find the probabilities of compound events.

Unit 4: Applying Probability

Summary

In this unit, you will use probability models to assess situations that arise in the real
world. You will apply counting rules to determine probabilities and use them to make fair
decisions and analyze strategies. Finally, you will find and interpret the conditional
probability of an event as it relates to other events.

Unit 5: Making Inferences and Conclusions

Summary

In this unit, you will form conjectures about populations based on a random sample of
the population. You will work with simulations that imitate real-world data and judge their
validity. You will study the differences in data gathering techniques in surveys,
experiments, and observational studies, and you will analyze the data sets generated by
each. You will complete the unit by evaluating reports based on data.

Unit 6: Using Probability to Make Decisions

Summary

Probability can help you weigh possible outcomes when faced with a difficult decision.
In this unit, you will gain practical skills to use probabilities for decision making. You will
develop and graph probability distributions by assigning random variables to quantities
of interest. You will also make predictions using probability distributions and empirical
data. You will determine the probability of a payoff value which defines the risks and
rewards associated with a decision, and you will solve for probabilities that will help you
make fair choices in more complex situations.

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We are super proud of him and appreciate your support! Christopher has had some great positive things to say. It’s really cool that he is connecting with kids and teachers from all over – a great “virtual” way to open up his world and perspective. 

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Thank you for always being here for me! Big thanks to Mrs Debbie for all the support and encouragement! Mirabel from Malaysia Dolphin STEM Academy 5 2021-06-15T15:36:43+00:00 Mirabel from Malaysia Big thanks to Mrs Debbie for all the support and encouragement! https://dolphinstemacademy.com/testimonials/thank-you-for-always-being-here-for-me/

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Keenna H.

I believe his confidence in himself has grown! Mrs. Debbie and her team have been awesome through this entire school year and I appreciate your support and patience with me! Keenna H. Dolphin STEM Academy 5 2021-06-18T01:33:46+00:00 Keenna H. Mrs. Debbie and her team have 
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