Consider the data set given in the accompanying table. Construct a relative frequency marginal distribution. Click the icon to view the data tableConstruct a relati...

Marginal distributions aren’t the whole story Here are the row and column totals for a two-way table with two rows and two columns:
$\begin{array}{cc|c}{a} & {b} & {50} \\ {c} & {d} & {50} \\ \hline 60 & {40} & {100}\end{array}$
Find two different sets of counts $a, b, c,$ and $d$ for the body of the table that give these same totals. This shows that the relationship between two variables cannot be obtained from the two individual distributions of the variables.

Okay but you probably want to use the regression feature to find a quadratic model that relates the total revenue to cue the quantity produced and sold. So to do this we're going to use Excel okay. Mhm. Or a calculator. And then we want to plot data. Black data, put the data then add trying to blank and then um one we did a trend line. It's going to be a allergy. The regression features can be quadratic model or polynomial with order to. And then after that we want to use derivatives because what will end up getting is the revenue. This is the revenue function and then find marginal revenue. Take the derivative of our function. So then we'll have our marginal revenue.

All right. So we're looking at independence, democrats and republicans and we're classing them into three different classes. Um This is the variables are, sorry, the data that is grouped into this table here. Um we got zero and two and three for the independence. Not very many independence, but I guess we added them in there anyway. The kind of outliers, but not actually outliers in this sense of the word of the graph, but they're definitely a minority in this case. So what we're looking at here are totals for the types and then our totals on this side for the political beliefs, Political standings, whatever you wanna call it. So what we'll do to find out our marginal and distribution probabilities, sorry, the conditional distribution and the marginal distribution of party within each class, That's going to be our two divided by two. So party we got our party over here and our party sums over there. So we do is divide this guy by that guy, and that's how we get these rows right here. Mm Now for our marginal distributions it looks like I forgot to do them here, but I will get them. Oh they're on the bottom, whoops. All we have to do is divide our these guys down here by our sample size to get these guys right there and then we're going to repeat the same process, but in reverse. So to get these numbers over here, um actually I'm gonna size this down is this thing is too long. There we go. Uh we're going to divide this two by the column total. And that is how we're gonna get six, and then we'll repeat that for the other datas here. And then finally for the marginal distributions, we get those by dividing the totals on this side the totals for the political beliefs by our sample size right there. And that's how we get that. Notice that none of these numbers in these two tables are identical. Therefore, we can conclude that there is an association between being your political belief and 12 and three are class, so to speak.

Heard the ship off. The distribution is uniforms because the bars are approximately have the same height.

Yeah. This is an observational question that we have. We want to say whether the shape of the distribution in the history Graham that is given to us in the textbook is Sima Trait or uniforms or skewed. What does the diagram look like? We're not going to draw the exact diagram, but it's going to look something like this, right? This is what it looks like, something like this. Now, by looking at this diagram, I can straightaway safe that this is skewed to the right. Now, what exactly is when rescued to the right, what would be separately if it would be symmetric on both the sides of the mean right? Like this is the bell shaped her mean median and mode online in the center. This is a metric what would be left skewed left skewed will be something like this. Like, this is skewed to the left. Okay, this is more spread towards the left before the meeting. What is right? Skewed right. Skewed would mean something like this. Or maybe yeah, something like this. This would be right skewed. So we can see that are diagram that we have does resemble this kind. So we can say that the distribution is right. Skewed, skewed to the right to Yeah, this is our answer.