While teaching measures of central tendency in Intro stats, I have shrugged and said: "Yeah, mean and average are the same thing, I don't know why there are two words. Statisticians say mean so we'll say mean in this class." I now have a better explanation than that non-explanation, as verbalized by this podcast: The average is thrown around colloquially and can refer to mode, while mean can always be defined with a formula. This is a fun podcast that describes mode vs. mean, but it also describes the research the rabbit hole we sometimes go down when a seemingly straightforward question becomes downright intractable. Here, the question is: What is the modal American? The Planet Money Team, with the help of FiveThirtyEight's Ben Castlemen, eventually had to go non-parametric and divide people into broad categories and figure out which category had the biggest N. Here is the description of how they divided up : And, like, they had SO MANY CELLS in their des...

Crash course website produces brief, informative videos. They are a mix of animation and live action, and cover an array of topics, including statistics. This one is all about measures of central tendency: Here is the listing under their #statistics tag , which includes videos about correlation/causation, data visualization, and variability. And, you know what? This is just a super cool web site, full stop. Here are all of their psychology videos .

This website is associated with Agresti, Franklin, and Klinenberg's text Statistics, The Art and Science of Learning from Data ( @artofstat ), and there are dozens of great interactives to share with your statistics students. Similar and useful interactives exist elsewhere, but it is nice to have such a thorough, one-stop-shop of great visuals. Below, I have included screengrabs of two of their interactive tools. They also explain chi-square distributions, central limit theorem, exploratory data analysis, multivariate relationships, etc. This interactive about linear regression let's you put in your own dots in the scatter plot, and returns descriptive data and the regression line, https://istats.shinyapps.io/ExploreLinReg/.  Show the difference between two populations (of your own creation), https://istats.shinyapps.io/2sample_mean/

Warning: This isn't an easy story to listen to, as it is about life expectancy and terminal cancer (and how doctors can best convey such information to their patients). Most of this news story is dedicated to training doctors on the best way to deliver this awful news.   But Aronczyk, reporting for NPR, does tell a story that provides a good example of high-stakes applied statistics . Specifically, when explaining life expectancy to patients with terminal cancer, which measure of central tendency should be used? See the quote from the story below to understand where confusion and misunderstanding can come from measures of central tendency. " The data are typically given as a median, which is different from an average. A median is the middle of a range. So if a patient is told she has a year median survival, it means that half of similar patients will be alive at the end of a year and half will have died. It's possible that the person's cancer will advance quic...

On November 3, 2014, Hyundai and Kia were fined a record-setting $100 million for violating the Clean Air Act. In addition, they were fined for cooking their data and misreporting their fuel economy, using the unethical (cherry-picking) techniques described below by representatives of the federal government: " "One was the use of, not the average data from the tests, but the best data. Two, was testing the cars at the temperature where their fuel economy is best. Three -- using the wrong tire sizes; and four, testing them with a tail wind but then not turning around in the other direction and testing them with a head wind. So I think that speaks to the kinds problems that we saw with Hyundai and Kia that resulted in the mismeasurement." Video and quote from Sam Hirsch, acting assistant attorney general.    Here is EPA's press release about the fine .  How to use it in class: -Hyundai and Kia cherry-picked data, picking out the most flattering data but not the...