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Introduction

Before we can begin to easily identify opportunities to implement probability and statistics into our other mathematics course, we need to have a basic understanding of what these two branches of math entail. In this first unit, you will develop a basic understanding of statistics, probability, where their real-life applications occur in the world around us, and possible career paths that we can spark interest in our students to pursue.

Lesson 1: Intro to Probability and Statistics

We hear the terms “probability” and “statistics” thrown around all the time, but do we know what they mean and how the two are different from one another? By the end of this lesson, you will be able to explain the difference between probability and statistics and what each branch is responsible for studying.

Probability

Probability is best defined as measuring the likelihood that an event will occur. It is often represented as a fraction or a percentage and ranges from zero to one. Where the number lands on the scale between zero and one determines the likelihood of the event.

Click here to watch a short video overviewing an introduction to probability.

Statistics

Statistics is best defined as the science of collecting, organizing, analyzing, and interpreting data. This data is often collected through a survey or an experiment and is organized in a table or a dot plot. Once the data is organized, it becomes a lot easier to recognize trends, outliers, and clusters, which allows statisticians to make interpretations.

Click here to watch a short video overviewing an introduction to statistics.

One of the most common ways to analyze and interpret data is by determining the mean, median, mode, range, and standard deviation of the data set. Students are taught how to calculate these five in 7^th grade math and again in Algebra I. They already have a basic understanding of statistics without even knowing it. Click here to watch a short video on calculating mean, median, mode, range and standard deviation.

The Difference Between the Two

A common misconception is the thinking that probability and statistics are the same thing. This stems from constantly hearing the two stemmed together in a sentence or in a textbook, but as we can see, they are widely different. An analogy that is very helpful to recognize the difference is the following:

Probability is like starting with an animal and determining the footprints it will likely make.

Statistics is like seeing a footprint and determining which animal made it.

Activity

Apply what you have learned in this lesson by taking a short 8-question quiz, which can be found by clicking here.

Lesson 2: Applications in the Real-World

As much as we hate the question, “When will we ever use this in the real-world?”, our students do have a point. When they graduate and enter the workforce, most of the information we told them was important to know in high school will not be applicable to them. Unless they decide to further pursue mathematics, most of what I’ve taught my students becomes useless information. They might not need to determine the missing side of a right triangle or use the quadratic formula, but they might use probability and statistics. By the end of this lesson, you will be able to identify different real-world applications of probability and statistics and why they are useful for your everyday life.

Examples of Applications of Probability:

Weather planning
Sport strategies
Gambling and other card games
Lottery
Clinical trials
Political polling

Examples of Applications of Statistics:

Financial markets
Weather forecasting
Insurance
Medical studies
Political campaigns

As we can see from the lists compiled above, there is often an intertwining between probability and statistics. This is why one must know the difference between the two and why therefore Lesson 1 in this Unit was so important. These two lists are just a small representation of the different applications of probability and statistics there are. There are still plenty of places that were not mentioned.

Still feeling a little unsure about the applications? Watch the video here on applications of probability or watch the video here on applications of statistics.

Reflection

Throughout the duration of this mini-course, you will be asked to reflect on the material that you are learning and to compile your reflection in an Outgoing Learning Journal. Be sure to make a copy before editing. You will be using this copy for the entire mini-course. For this lesson's reflection, you will be asked to answer the following: What are some other applications of probability and statistics that are not listed above that you personally use in your everyday life? How do these applications help you?

Lesson 3: Career Paths Involving Probability and Statistics

It is not uncommon for high school students to be uncertain about their futures and potential career paths. Students are not often familiar with how many different choices they have depending on the degree they pursue if they choose to go on to higher education. By the end of this lesson, you will be able to identify different career paths involving probability and statistics and identify opportunity to introduce such career paths to your students.

In August 2023, the Outlier compiled a list of the top ten popular jobs and their average wage for someone pursuing a degree in Statistics. This list shows such a wide variety of career paths and opportunities ranging from the healthcare industry to politics.

Data Analyst - $74,822
Data Scientist - $100,910
Statistician - $96,280
Actuary - $105,900
Biostatistician - $114,610
Business Analyst - $63,920
Operations Research Analyst - $82,360
Financial Analyst - $95,570
Quality Assurance Analyst - $109,020
Political Scientist - $122,510

Research

Select one of the the careers from the list complied by Outlier to research. In this research, consider skills needed, education level needed, job security, job location, and job satisfaction. Summarize your findings in a Career Research document. Be sure to make a copy before you start editing.

Reflection

Please answer the following in your Ongoing Learning Journal: What kind of opportunity exists when pursuing a career involving probability and statistics? How can you encourage students to consider pursuing this type of career?

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