[am4show have='p156;p158' guest_error='guest_error_msg' user_error='user_error_msg' ]There are over 40 videos on this page, so please take your time when working through the content. Most students will cover all of the content in 4-8 weeks.
Probability deals with figuring out how likely an event will happen in the future, based on mathematical models that we create that make use of knowing which factors will influence the likelihood of the event happening.
Statistics analyzes things that have already happened, like how much lemonade you sold, how long it took to get to work in rush hour, or how many students skip school close to a holiday.
By combining both, we can make better predictions about the future, which is especially important if it's related to decisions involving resources like time and money.
Download your In-Class Statistics Workbook
Due to the nature of Statistics, it’s easier to take notes during class from a workbook instead of writing down all the data sets from the chalkboard. In class, Doug may reference this workbook and use example problems from it. Use the buttons below to download your workbook and bring it with you to sessions #3 & #4 Statistics Math Lessons (video recordings below).
Math Class Sessions
These Math Classes will start you out on the right path as we explore the analytical world of statistics. After watching the math lessons, continue to practice the concepts using the Data & Statistics Lesson Packet, activities, games, projects word problems and have fun learning! There are FOUR sessions for statistics, eight videos total (2 videos per session).
Statistics Packet: Sections 1 & 2
This session uses a packet of lessons that we will be working through in place of a workbook. In addition to the content in the packet, you'll find activities, a quiz, a study guide and a test to complete at the end when you've completed all the content in the packet.
Math Activity: Our Class & Group Samples
If you have a group of classmates or friends, let's do an activity that really demonstrates the difference between sample and population. You can also do this using your entire family as the sample and your town as the population. Let's get started!
Math Activity: Population and Samples
If you weren't able to do the first activity, then give this card sort a try! We're going to match up cards and then decide which is the population and which is the sample. You can cut these out before you start the video, but keep each sheet of cards separate so you can find their match more easily.
Math Activity: Drawing Inferences from Samples
This is a "solve & color" activity where you are looking at a set of data and answering questions based on the data. It's good practice of the concepts we're learning about inferences!
Statistics Packet: Sections 3 & 4
These next two sections study the "center" of statistical data. We are going to learn about the median (middle of the data set) and the mean (average) of statistical data. When data is skewed left or right, we use the median, and when it's symmetrical we use the mean. We'll learn more about when to use each in sections 5 & 6. First, we need to learn how to calculate both the median and the mean. Here we go!
Math Activity: Measures of Center
The median is the middle of a set of data, meaning that 50% of the data points have a number smaller (or equal) to the median, and 50% have a value higher (or equal). The median give you more insight than the average, depending on the data itself. Let's get good at calculating both!
Math Activity: Measures of Variability
It's not enough to know what the average (mean) or even the median. We also have to have a way to know how spread out the data is from these numbers. This is known as the "measure of variability" and we're going to practice calculating it with our activity!
Statistics Packet Mid-Unit Quiz
After you've completed parts 1-8 (Student Handout & Homework Sections 1-4), it's time to review everything we've covered with a quiz. Use this quiz more as an assessment to make sure you've comfortable with everything we've covered so far. If you find you need more time with a particular area, go back to that section and review the material a little more.
Statistics Packet: Sections 5 & 6
This is the last section of the Data & Statistics Packet that explores dot plots and box plots, and we will discover how to compare each to make sense of statistical data that is represented graphically. Make sure you've completed sections 1-4 above before starting on the second half of the packet. (Note: the PDF download included all six sections.)
Math Activity: Interpreting Data from Dot Plots
Let's practice working with real data represented in dot plot form, and really understand how much there is to read from two graphs!
Math Activity: Comparing Box Plots
This is a fun activity that has series of box plots from data taken from different professional sports teams. Let's see how you do with each one!
Statistics Packet: Study Guide & Unit Test
After you've completed all of the Data & Statistics Packet and all the activities (Student Handout & Homework Sections 1-6 and all seven activities), it's time to review everything we've covered with a study guide before taking the final test. Use this test more as an assessment to make sure you've comfortable with everything we've covered. If you find you need more time with a particular area, go back to that section and review the material a little more.
Bonus Content: Histograms
Histograms show us frequency in the form of a picture. These graphs classify data into "bins" or "range groups", which count up how many data points belong to each of the bins. The vertical height represents how often the variable appears. It's an easy way to get a feel for what the numbers are saying without getting lost in the numbers.
Statistics Applications
Probability deals with figuring out how likely an event will happen in the future, based on mathematical models that we create that make use of knowing which factors will influence the likelihood of the event happening. Statistics analyzes things that have already happened, like how much lemonade you sold, how long it took to get to work in rush hour, or how many students skip school close to a holiday.
Statistics and probability often work together, because the more you understand patterns about the situation and things that influence it, the better your prediction for the future will be. It's a lot easier to figure out how much inventory to buy for this year if you already have records of how many sales you made over the last few years. Let's practice using both the statistics and probability math skills we've been learning with this set of data labs.
Math Challenge
I have a special Math Challenge for you to work on. Although this particular challenge is based in probability, I will want you to give it a try (do make sure you've worked through most of probability before attempting this challenge).
Remember, the goal for these math challenges is for you to be able to communicate your great ideas with your family and friends, without them being in a math class or having any knowledge of a specific area of math. You should be able to convey math ideas to most people that are interested in hearing what you have to share.
We want you to learn how to not only communicate your great ideas but also be able to listen to others and understand their solutions as well, and perhaps you can all come to a newer, improved solution that no one had initially!
Tips for the Math Challenge:
You can model this problem by having someone toss two different coins, a penny and a nickel, and then make a statement about the result. For example:
- If both coins are heads, say: "At least one coin is a head". If both are tails, say: "At least one coin is a tail." If coins are different, say: "At least one coin is ... (and pick heads or tails at random.) What is the probability that both coins show whatever side is called?
- The tosser has agrees in advance to call out "At least one coin is heads" only when this is the case. If no coins are heads, he says nothing and tosses again. What is the probability that both coins are heads?
- The tosser agrees in advance to call out how the penny fell, regardless of whether it's heads or tails. What is the probability that the coin is a match?
- The tosser agrees in advance to call out "At least one coin is heads" only when the penny is heads. What is the probability both are heads?
