Transcript for:
Numerical Data and Means Overview

We're starting Chapter Nine today. Super, super exciting that we're starting Chapter Nine because what we're going to do is some of the same and some a little different. What we're going to do is rehash sampling distributions, Central Limit Theorem, confidence intervals, and hypothesis testing. We're going to talk about those same ideas again, except now in the context of looking at numerical data, now in the context of looking at means. What do I mean by that? Well, ultimately, what we did throughout all of Chapter Seven and Eight was look at categorical data, categorical data like "What is the color of your M&M?" And we know that categorical data was ultimately data that was collected using words, using descriptors, using labels. And that, ultimately, what we studied when looking at categorical data was then the proportion, was then the proportion that had a specific successful characteristic. Like, as we know, M&M's have multiple colors, but the successful characteristic was red. And so, ultimately, what we did throughout all of Chapters Seven and Eight was study categorical data, was study the proportion, the proportion of successes. So, for instance, throughout Chapters Seven and Eight, we were looking at "What is the success of red M&M's?" Six M&M's out of 20 M&M's or 30% of those M&M's were red. And so, what we're going to do now here in Chapter Nine is shift gears and stuff, study the other type of variable, numerical data. So, instead of looking at Bob's M&M's and looking at their colors, we're now going to look at Bob's running time, where as we can see here, this running time of eight minutes, nine minutes, eight and a half minutes, 11 minutes, and seven minutes is all time, it's all numbers. And remember, when we're studying numbers, we are ultimately studying a numerical variable. And that, just like how with categorical data we studied proportions, we studied that single number that would represent my sample's results, in the same way, we can study a numerical variable by looking at a single number, mean, to represent all of that. And so, in the same way, we are going to look at this single number here in Chapter Nine to represent my numerical data, except now instead of looking at proportions, we're now going to study means. We're now going to study means. Remember, mean is ultimately the idea that if you take all of those data values, the run times of eight minutes plus nine minutes plus 8.5 minutes plus 11 minutes plus seven minutes and divide by the fact there are five run times, we then get an 8.7 minutes. Ultimately, the idea that I wanted you guys to see here is we are looking at vastly different variables now. We are looking at number-based variables, not word-based variables. We are going to look now at means instead of looking at proportions. And so, I've emphasized the fact that some things will be similar, but some things are going to be different. And so, a large part of Chapter Nine is going to be me trying to help you see where are things similar, similar to what we studied in Chapter Seven, even with categorical data, and then what are things that will be unique and different here in Chapter Nine as we study numerical data.