Probability and Statistics

Welcome back! Get a calculator!

My site revamp isn’t finished but you need information. Ready or not, here I go.

Welcome back!

Welcome back to Aiken High! I’m excited about the upcoming year. I anticipate it will be strong one. Since most of you are seniors, I want to stress that the quality of this school year depends in large part on you. Make it great!

Calculators for Probability and Statistics

You’ll need a certain type of calculator for Probability and Statistics class. I’m a huge fan of pencil and paper, but there are some calculations it would take 30 minutes or more to complete that way. That might set you back a little during a 30-minute quiz.

Below, I’ve listed many calculators that will work in this class. Note, these are not all suitable for AP Statistics. Some are graphing calculators, but that is not a requirement. Most of the calculators are relatively inexpensive.

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On independence

We’re having a quiz in CP Stats, tomorrow. On the quiz, I’ll give you one scenario. You will need to verify that the trials are Bernoulli trials (that is, like coin flips), prepare a probability table, and use your table to state probabilities. You’ll also calculate the expected value (or mean), the variance and the standard deviation of the binomial random variable.

The question most likely to trip students up is the question of independence. Like a coin flip, the outcome of a Bernoulli trial must not depend on what’s happened prior to it. Loosely speaking, we’ve said that a coin has no memory, and it certainly does not. The outcome of the next coin flip does not depend on the 50 or 100 coin flip outcomes that came before.

We must be careful not to overstretch this analogy, though. Literally speaking, a card in a deck has no memory, either. However, outcomes may depend on what’s come before. Consider the following probability question:

If I draw 20 cards out of a deck and I do not replace them, what’s the probability that the 21st card drawn is a red card?

Hopefully, you wouldn’t claim to know the answer to this one because so many cards have been drawn out of the deck. Your answer depends on the cards previously withdrawn. If all 20 cards drawn previously were red, the probability that the 21st is red is low (6/32 or 3/16). Draw out 20 black cards and the probability of a red on the 21st draw is much higher — 13/16.

So, be prepared to determine whether too many cards (or other things, like people) are drawn out of the population. For this purpose, we’ll say that “too many” is more than 10% of the population. In the context of our card drawing problem, we cannot draw out more than 5 cards (5% of 52 is 5.2) and still treat each outcome as being independent.

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CP Stats: Activity example

Here is the very short report I put together in class, today. Your work should be similar.

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CP Stats: Today's lesson and applet

Today, we looked at best fit lines and the residuals that they have. In particular, we made these points:

• A “best fit” line uses the overall pattern of a linear association to model the relationship between two variables in a scatterplot with a line.
• The model lets us make estimates. In today’s example (Chapter 7, Question 16), we looked at the relationship between marijuana and other drug use. For example, a country in which 30% of teens say that they have tried marijuana would, according to our line, have about 15% who say they have used other drugs.
• Estimates, being what they are, are sometimes wrong. The amount of the error is the estimate’s residual.
• A “best fit” line should minimize the size of the residuals.

We also used an applet to illustrate the concepts. You may find it helpful, too.

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