AP Statistics Assignment for 5/6

We did some review of probability today, in particular parts of chapters 14 and 15 of your textbook. Your homework tonight is:

In addition, I’d also recommend you look at Question 3 from the 2008 Free Response, as well as Section 8 of your review book.

Review my answers here before class tomorrow so we can address any lingering questions you may have more efficiently.

Intermediate Algebra Assignment for 4/9

Today, we reaffirmed that the Expected Value is a long-term average. Meaning the results of a small handful of trials are unlikely to produce the same average as the expected value, however increasing the number of trials will produce averages more in line with what you expect.

Don’t forget that our test on this unit will be on Thursday, April 11th!

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 4/5

We’ve introduced the last major topic from our unit on Probability: the Expected Value. This quantity is a long-term per-trial average, that gives you a way of determining what a typical outcome of a handful of trials should be. This is an important tool in the field of statistics, and will be something you’ll see again in later math classes.

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 4/4

We’re starting in on the second part of the unit today, about Probability Models. These are ways of listing/organizing all the outcomes of a random trial and their, often unequal, probabilities. This will be the basis for one of the most useful tools in statistics: the expected value.

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 4/1

Permutations and combinations tend to be tricky to figure out when you first encounter them, so we spent some more time looking at examples, including a modification to the concept to find arrangements of letters in a word.

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 3/29

The next part of the “counting” part of this unit is understanding the difference between two common patterns of counting: permutations and combinations. In brief, permutations are used to count the number of arrangements of objects, specifically when order matters like with ranked lists, unique assignments, or sequences. Combinations are used to count the number of groups of objects, specifically when order doesn’t matter like with committees or batches.

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 3/28

We did some more work with understanding the nature of mathematical independence today, including making some graphs to help illustrate whether or not independence exists in a group of data.

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 3/27

Today we discussed an important idea in probability and statistics: determining when events are independent and/or mutually exclusive.

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 3/26

We did some more work with the counting principle today, using it in a variety of applications. The trick is to carefully sort out the number of choices you have to make and the number of options you have for each choice.

Today’s links

Cumulative IXL Modules

Intermediate Algebra Assignment for 3/25

We started our second-to-last unit today, about tools of probability. Probability is all about chances and odds, determining how likely various events are to occur. We’ve started with some very basic ideas of probability, but we will quickly move to some more complicated and nuanced applications.

For more about the conversation about password security — and why ji32k7au4a83 is one of the Internet’s more common passwords — check out this article

Today’s links

Cumulative IXL Modules

AP Statistics Assignment for 1/17

First, some more about a big topic that came up at the end of class: The Difference Between an Assumption and a Condition

In order for a model (e.g., a normal model or binomial probability model) to be valid for a scenario, we must be able to make certain assumptions about that scenario.  These assumptions can include the results of individual trials being independent from each other, the distribution of results being sufficiently unimodal and symmetric, etc.

If it is appropriate to make these assumptions, then go ahead and do it. But if it is not appropriate to make these assumptions, you can still proceed provided certain conditions are satisfied.  These conditions mean that the scenario is “close enough” to allow the model to be valid.

For example, coin flips are independent.  There is no finite population of coin flips that you are “drawing” a sample from, and so each coin flip’s outcome is independent of the next.  Drawing cards from a deck are not independent, as the deck is finite and the probability of a certain outcome changes with each card that is removed. However, if the population is large enough, or more specifically if the sample is small enough in comparison to the population, then that probability change is very small, small enough to be ignored.

In general, as long as the sample size is less than 10% of the overall population, the probability change isn’t big enough to be worrisome. The reason why the magic number is 10% has to do with something called the Finite Population Correction Factor, and a thorough description of where it comes from and how it affects probabilities can be found here.

Your homework tonight

From pages 431-432, please do 19, 21, 26, and 28.