# Lectures: Stat 203 Fall 2016

From Sean_Carver

## Contents

## August 29, 2016

- Today, we had an introductory discussion and greetings, then discussed our syllabus, and finally covered the first two chapter of The Data Professor's Guide to Basic Statistics.
- Reading: Please read about the optional extra credit opportunities in our syllabus.
- Reading: Please read the first few chapters of The Data Professor's Guide to Basic Statistics, which is linked here and also passed out during class.
- Next class: I plan to discuss the projects and cover chapters 3-7 of The Data Professor's Guide to Basic Statistics. (Chapters 6 and 7 will be passed out on Wednesday.)

## August 31, 2016

- Today, we reviewed the first two chapters of The Data Professor's Guide to Basic Statistics, then continued with that document until
*Distributions*. - Homework: I passed out and we worked on Homework 1, due September 7, 2016.
- Reading: Moore, McCabe, Craig, pp. 1-8.
- Next class: We did not discuss projects today, and I meant to, so we will do that tomorrow. Then we will review
*Concepts of structured data*.*Kinds of variables*, and*Distributions*of The Data Professor's Guide to Basic Statistics, do two more homeworks, then continue with*Exploratory data analysis*from the same document.

## September 1, 2016

- Today we covered displaying distributions with pie charts, bar graphs, stemplots, and histograms. We also covered
*Exploratory data analysis*from The Data Professor's Guide to Basic Statistics. - Homework: We worked on Homework 2, due September 8, 2016.
- Homework: I also passed out, but did not yet assign Homework 3, due September 7, 2016.
- Reading: Moore, McCabe, Craig, pp. 9-23
- Next class: We are going to continue our study of exploratory data analysis and graphing distributions with a laboratory exercise involving a diamonds data set. Then we will proceed to talk about summary statistics (mean, median, quartiles, percentiles, 5 number summary, standard deviation) and the box plot and modified box plot.

## September 7, 2016

- Today we reviewed the concept of a histogram with the new material being the meaning of the axes. The x-axis is the range of the values of the quantitative variable whose distribution is being visualized. This range can be restricted by adjusting the "where" input in StatCrunch. There are 3 choices for the y-axis in StatCrunch: frequency (the count of observations in each bin), the relative frequency (the proportion of observations in each bin) and the density. The point of the density was to have a vertical scale which is independent of the number of observations and bin width. If F(x) = "proportion of observations less than x (in the limit of many observations)" then the density is the derivative of F. Finally, we discussed skewed and symmetric distributions, tails, center and spread, unimodal, multimodal, and bimodal distributions. We also discussed mean and median, quantiles, and percentiles, resistant to outliers versus sensitive to outliers.
- Homework: Homework 2 is due next class, September 8, 2016.
- Homework: Homework 3 is now assigned with a due date of September 14, 2016.
- Practice Problems: Practice Problems for Week 1.
- Reading: Moore, McCabe & Craig, pp. 30-36.
- Next class: We will continue our tour of summary statistics with the 5-number summary and the related box plot and modified box plots, we will pass out homework 4 and 5, talk about the sample standard deviation, and transformations. Then, if there is time we will proceed to talk about sampling -- to understand Bessel's correction in the definition of sampling standard deviation, but also because it is a main course objective.

## September 8, 2016

- Today, I presented the 5 number summary and related box plot and modified box plot. We also talked about standard deviation and transformations. I handed out the last of the chapters written last summer in The Data Professor's Guide to Basic Statistics to cover sampling and Bessel's correction. Finally there was a discussion in class about density curves, however if you did not follow it, don't worry: it will make more sense after we cover probability.
- Solutions: I passed out Solutions to Practice Problems for Week 1
- Homework: Homework 4, due September 15, 2016.
- Homework: Homework 5, due September 15, 2016.
- Reading: Please read
*Mean*,*Sampling*,*Counting Samples*, and*Standard deviation*, the four chapters I handed out today in the The Data Professor's Guide to Basic Statistics. - Reading: Moore, McCabe & Craig, pp. 37-47.
- Next class: We will go through the reading from the The Data Professor's Guide to Basic Statistics.

## September 12, 2016

- Today we started with the data discussion for the extra credit project. Then we moved on to discuss
*Sampling*and*Counting Samples*from the The Data Professor's Guide to Basic Statistics. We also discussed Bessel's correction and the sample standard deviation. - Next Class: We will start to discuss probability.

## September 14, 2016

- Today we discussed some of the rest of chapter 1. Chapter 1 has a lot of simple material that usually takes a lot of time to cover in Stat 202. For Stat 203, I want to cover it more rapidly so that we can cover more advanced topics.
- These are the topics from Chapter 1 that I either briefly covered on the 14th or will cover and review on the 15th: (I didn't do this on the 15th)
- (1) transformations,
- (2) density curves and relationship to cumulative distribution function.
- (3) the relationship between density curves and histograms
- (4) the fact that all density curves describe a distribution, but to be a density curve: necessarily the area under the curve must be 1 and whole density curve must be on or above the vertical axis bell curves
- (5) the relationship between bell curves and the normal distribution (bell curves are the density curves for normal distributions)
- (6) Bell curves have a very specific shape that depends on only two parameters: mean and standard deviation
- (7) knowing mean and standard deviation you can write down an exact mathematical formula for the bell curve
- (8) If mean is mu and standard deviation is sigma, the unique normal distribution is denoted N(mu,sigma)
- (9) mean, median, and mode of a density curve: for a bell curve these three things coincide at the peak
- (10) at one standard deviation from the mean of a bell curve you will find the inflection points where the curve goes from smiling to frowning or vice-versa (remember: bell curve means normal distribution, this doesn't work for other distributions).
- (11) Another property of a normal distribution: if you do a linear transformation and the old variable is normal, the new one is normal, too. If the new variable is normal then the old variable must have also been normal.
- (12) The 68-95-99.7 Rule, the percentage of area falling one, two, or three standard deviations from the mean.
- (13) Pseudo-random numbers, simulating pseudo-random number in StatCrunch,
- (14) The concept of seed, including fixed seed and dynamic seed.
- (15) Standardizing observations and the z-score.
- We talked about definitions of random and probability.
- We talked about set theory and the concepts of set and element of a set, union, intersection, null set, subset.
- We talked about the sample space of a random phenomenon and its events.
- Need to talk about complement of a set.
- Need to talk about disjoint sets.
- Need to talk about independent sets.
- Need to talk about axioms of probability.

## September 15, 2016

- Today, we plowed ahead with probability theory, leaving chapter 1 for later. We reviewed set theory and talked about complement of a set, disjoint sets, independent sets and the axioms of probability. I introduced random variables, with the example of tossing three distinct coins and counting the heads. We discussed the distribution of discrete random variables.
- Homework: I passed out Homework 9, the due date will be discussed during the next class.
- Next class: I will review and expand upon the foundations of probability. I will discuss section 4.5 (
*General Probability Rules*) in the book, except that we will leave Bayes Rule for later. Then we will go on to review and fill in more details concerning random variables and discuss the binomial random variable. I will pass out Homework 10.