Today we spent the bulk of class time flipping coins and rolling dice. We discussed the basic idea behind the probabilities behind what is going on.
If we roll a coin 10 times we expect to get 5 heads. There were 30 students in the class so this gave us 300 flips.
Given an experiment and the probability of a fixed simple outcome being p, then running the experiment through n trials, leads to the random variable
X equaling the number of times the experiment was a success (i.e. the outcome occurred).
Then the expected value is
E(X) = n p
The harder question is to determine the probability that out of the n trials, exactly k many successes occurred.
For example, if we flip a coin 4 times what is the probability that we get exactly
0 heads = 1/16, 1 head: = 4/16, 2 heads = 6/16, 3 heads = 4/16, 4 heads = 1/16
We discussed the sample space of rolling two 6-sided dice: has 36 outcomes. We drew a chart representing the outcomes and calculated that the
expected value of summing up the two dice is 7.
We discussed a game where you roll two dice and sum up the faces. If you roll a 7 or 11 you win, if you roll a 2, 3, or 12 then you lose.
If you roll either a 4,5,6,8,9,10 then then you roll again until you roll the same number again (in which case you win) or you roll a 7 (in which case you lose).
What is the probability you win?
Our discussion was about the remaining topics in Chapter 1 and Chapter 2 of the text.
We covered the 5 number summary: min=Q0, Q1, Q2=Median, Q3, Q4=max.
The Q refers to quartiles. Q1 is the 25th percentile and Q3 is the 75th percentile.
Look at page 101 for an algorithm on how to comute percentiles by hand. However, I do not focus on this as different books have different methods.
Measures of center: mean and median.
The median is resistant to outliers, whereas the mean is not.
Measures of spread: range=Q4-Q0, Interquartile range (the middle 50%) = Q3 -Q1,
standard deviation, and variance. We discussed how to find the 5 number summary using the Ti-84. i) STAT/Edit to create a list, ii) STAT/Calc/1-Vars Stats.
This produces the 5 number summary as well as the mean x̄ and standard deviation Sx.
Visualizations: line graph, histogram, stem-leaf, box-whisker plot, modified box-whisker plot.
The stem-leaf has similar properties to the histogram but captures all of the data.
We discusses the difference betwen population and sample, as well as the difference between a parameter and statistic.
We discussed levels of scale: nominal, ordinal, interval, ratio.
The main difference between a bar graph and histogram is that the former is used for categorical data while the latter is for quantitative data. The minor difference is that a bar graph has space in between the rectangles.
We talked about line graphs as well as frequency, relative frequency, cumulative frequencies, and cumulative relative frequencies.
We went into the lab and found that the mean height of the class is 65.6" while the median is 66".
An example of a cell is B:7.
We disucced how to sort data, undue sorting, changing data from general to number, add and decrease significant digits.
The mean of a population is denoted by μ while the mean of a sample is denoted by x̄.
The standard deviation of a population is denoted by σ and the s.d. of a sample is denoted by Sx.
We went over the syllabus and towards the end of the period we started a discussion from Chapter 1 (and a little bit of Chapter 2).
Looked over the book and pointed out that at the end of each chapter there is a list of Key Terms as well as a Practice problems. The practice problems are what I am calling HW problems. (HW is not to be turned in. It is there to help the student with understanding the material.)
-- two types of data: categorical (qualitative) and quantitative. Most of the class will be spent on quantitative. There are two types of quantitative data: discrete (counted) and continuous (measured).
-- gave an example of "visualizing" statistics: pie charts are useful for illustrating categorical data.
On Thursday we will discuss the terms: population, sample, parameter, statistic, variable (P.15). We will also discuss the difference kinds of levels of measurement: nominal, ordinal, interval, and ratio (P.36).
Then we will discuss measures of center and measures of spread.