Statistics Notes

Math 121 - Spring 2025

• Class Notes
• Schedule & Syllabus
• Software & Tables

Week 1 Notes

Mon, Jan 13

Today we covered data tables, individuals, and variables. We also talked about the difference between categorical and quantitative variables.

• Example: Class Data

1. We looked at a case of a nurse who was accused of killing patients at the hospital where she worked for 18 months. One piece of evidence against her was that 40 patients died during the shifts when she worked, but only 34 died during shifts when she wasn’t working. If this evidence came from a date table, what would be the most natural individuals (rows) & variables (columns) for that table?

• Example: Accident Fatalities by State (source: CDC)

2. In the data table in the example above, who or what are the individuals? What are the variables and which are quantitative and which are categorical?

3. If we want to compare states to see which are safer, why is it better to compare the rates instead of the total fatalities?

4. What is wrong with this student’s answer to the previous question?

Rates are better because they are more precise and easier to understand.

I like this incorrect answer because it is a perfect example of bullshit. This student doesn’t know the answer so they are trying to write something that sounds good and earns partial credit. Try to avoid writing bullshit. If you catch yourself writing B.S. on one of my quizzes or tests, then you can be sure that you a missing a really simple idea and you should see if you can figure out what it is.

Wed, Jan 15

Today we did our first in-class workshop:

• Workshop: Histograms & stemplots

Before that, we talked about how to summarize quantitative data. We started by reviewing the mean and median. We saw how to find the average in Excel, and we talked about how to find the position of the median in a long list of numbers (assuming they are sorted).

Then we used the class data we collected last time to introduce histograms and stem-and-leaf plots (also known as stemplots). We also talked about how to tell if data is skewed left or skewed right. One important concept is that the median is not affected by skew, but the average is pulled in the direction of the skew, so the average will be bigger than the median when the data is skewed right.

Until recently, Excel did not have an easy way to make histograms, but Google Sheets does. If you need to make a histogram, I recommend using Google Sheets or this histogram plotter tool.

• Example: US Household Income (2010)

1. Which is greater, the mean or the median household income?

2. Can you think of a distribution that is skewed left?

3. Why isn’t this bar graph from the book a histogram?

Fri, Jan 17

We introduced the five number summary and box-and-whisker plots (boxplots). We also talked about the interquartile range (IQR) and how to use the $1.5 \times \text{IQR}$ rule to determine if data is an outlier.

• Workshop: Boxplots

We started with this simple example:

1. An 8 man crew team actually includes 9 men, the 8 rowers and one coxswain. Suppose the weights (in pounds) of the 9 men on a team are as follows:

    120  180  185  200  210  210  215  215  215

   Find the 5-number summary and draw a box-and-whisker plot for this data. Is the coxswain who weighs 120 lbs. an outlier?

Week 2 Notes

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Week 14 Notes