Statistics: Quiz Monday

There will be a quiz on chapters 5.1-5.3 on Monday. Oddly, I didn't capture that board but it has been up in class the past 3-4 days. Questions I have been assigning from the text will be the focus of this quiz. Binomial distributions (5.4) will not be on this quiz.

Statistics: Confidence intervals and Binomial

We continued discussion of confidence intervals today, for 90%, 95%, and 99% confidence levels. In addition, we talked about using the sample standard deviation instead of the population standard deviation in the formula for determining a confidence interval.

We also discussed properties of binomial experiments, what makes up a binomial experiment, and the difference between dependent and independent events.

The notes in the book for these two chapters are quite excellent and superior to any notes I could post here since they also come with explanations.

Homework is p. 205 #20,22,27 p. 211 #28,29,30 (assume sample size of 30) p.216 #1,2,3

There will be a quiz on Monday on ch.5.1, 5.2, and 5.3. A summary has been posted in class.

Statistics: Confidence intervals

We first discussed the interesting property of the Central Limit Theorem, in which you take any type of distribution, calculate the sample means, and those means are distributed normally.

Following, we looked at confidence intervals, p.202-205. Homework was p.207 #21 and 23.

Statistics: Central Limit Theorem

Central Theorem, you can refer to the notes on the boards or the books.

If you are getting confused by terminology ("Mean of sample means ...") and the symbols in class I would highly recommend you take some time studying them (definitions in 5.3 and at the beginning of 5.1). It will definitely pay off in aiding your understanding. At this point, having put about a week into it, I am using them with the assumption that you are familiar and comfortable with them.

Statistics: Sample Distribution/ Sample Means

No pictures today, sorry. However, most of the work we did in class was covered in the text book, and the text book is actually quite good for this chapter.

p.187-190 'Sampling methods' - We talked about these for the first half of the double as well as working on questions 1-3, 5 on those pages. Descriptions for the different sampling methods are in the book.

p.191-192. We looked at taking samples of size 40 from a known population mean and population standard deviation. We took 6 samples using the graphing calculator, checked which was the closest to the sample mean, and which was the furthest. Someone in the class had a sample mean that was essentially equal to the pop. mean. Another person had a sample mean that had a difference of 8 for the population mean.

Taking the mean of these sample means have us a mean that was in most cases (but not all) closer to the population mean than any of their recorded data. To make it more accurate, we looked at collecting more samples.

p.193 we ran the command in procedure A (this will take 5-10 mins to run to completion). This essentially collects 100 different samples of size 40, and finds teh mean of each of them (using the known population mean and population standard deviation from the previous question). Homework is completing a Histogram of this data (you can use the bins on p.194).

Statistics: Bias

The board with data collected is from investigation 5.2 in the book. Population mean ended up being 3.05 ... the random data sampling was much more successful than the class at picking the mean.

No homework for tonight.

Statistics: Grade 10 Review

Sorry for the image quality, I'll workon rectifying that with the new white boards.

Homework: p.176 #1-5 p.182 #12,15,16,17

Not necessary to show your work when calculating standard deviation, etc.

Matrix Multiplication +

There were four sheets handed out in class today which offer a wealth of practice on matrix multiplication, determinants, and inverses.

For Tuesday, homework is p.120-1 from the sheets handed out in class, #1a,2,3

If you want to check that your answers are correct, your TI calculator is a great friend for this!

Enter the dimensions and data of the first matrix (matrix -> edit -> A)
Enter the dimensions and data of the second matrix (matrix -> edit -> B)
Multiply the two of them together (matrix -> names -> A -> matrix -> names -> B -> enter)

Voila!

There are also examples worked out in detail on the sheets (in addition to the numerous questions done in class)

So, why are we doing this even though the calculator can do the work for us?
i) necessary skills to do other applications of matrices
ii) helpful when applying this to word problems
iii) if you have to multiply matrices which have variables instead of constant numbers, your calculator will not be up to the task (but you will!)

Presenting tomorrow:

The History of Pi
Triangle Centres
Creating a Sundial
The Mathematics of Gambling

On "stand-by" (should still be ready to present):

Number Systems
The Golden Ratio