Stat minna Tnne ets Edit Rename Data Set Row Factor A Factor BDataStatGraphHelpValue 64.9 59.3 32.9 594 533 442 46.2var4vars51.9 61.8 685 65.8 50.7 3 384 50.7 40.2 ...

Make (a) a boxplot and (b) a modified boxplot for the data.
The annual home run production data for Mark McGwire in Table 9.6 (page 696)

In this video. We have a data set containing these 16 observations that we see here. But we want to obtain as a box plot as well as a modified box plot. So the first step in this process is that we sort the data either by hand or using technology. The data is pre sorted here, and we found that the minimum value is 16. The maximum value is 73. And we could include those in the five number summary we see here. Next, if we average the middle two observations that be observations eight and nine, we'd be averaging 34 which produces our median value. Likewise, we averaged the two middle values in the upper half of the data set 25 to get the first quartile and the two observations on the lower half of the data set 40 and 42 to get the third quartile of 41. Now we're ready to begin constructing the box plot. We start with the first quartile, which is at 25 and draw vertical edge that looks about like this. The next edge we draw is the median, which is at 34. So it's called us 35 that looks about like 34 when we try to make that a little bit more straight. There we go. Next, go to the third quartile, which is at 41 draw another vertical line segment. So these are the three quantities which are going to make up the inner part of the box. We can finish out the box portion in this way, and now we throw on the minimum value, which is at 16 but use a slightly shorter edge, so we have a whisker going left in that direction. The maximum value is 73 which was about here. So this is the construction of the box plot features to notice about the box plot is the width of this whisker is less than the width of the inter quartile range, which goes from quartile 1 25 to quartile, 3 41 in length. That tells us that there is no outliers on the lower end. However, the length of this whisker is quite large conspire to this length, which is the or inter quartile range, so we could have potential outliers on the upper end. That's where the modified box plot will come in. It takes the box plot we just constructed, and it shows us where that outlier or outliers could be to determine where the cut off is for outliers. We're going to first calculate the inter quartile range ventricle. Tell range is just the length of this box we see here and buy formula. It's 1/3 quartile, minus the first quartile for us, that is 41 minus 25 which results in a value of sex. 16. Next to determine if there's outliers on the upper end, we take the third quartile and add to it 1.5 times the inter quartile range. For us, that will be 41 plus 1.5 time. 16. This comes out to value of 65 so any value or observation that's larger than 65 is going to be considered an outlier on the upper end. Let's go to this value 65 and noticed there is exactly one observation that's going to be considered as an outlier. We're going to plot this outlier at 73 just using an ordinary dot like this. Next we go to plot the same box plot that we had before. So that's going to be a edge at 25 an edge at 34 an edge at 41. So there's our inner box. We had the minimal value, which is at 16 sold draw a smaller edge about here for 16 and now we have to complete the segment between quartile three edge and the green. Doctorates represents the outlier. To do that. We go back to this data set, and we look at the values that are not considered outlier. The largest such value is at 49 and that's where the next edge goes roughly here. Actually, that looks more like 50. Let's move it. Just a touch to the left. So that's our edge. Going off to 49 then This is the modified box plot that tells us there was really no values in this segment. It only goes up to here with an outlier clear over there

Here we are given a set of X Y coordinate points that could be used as their data set, and we are asked to determine the function of best fit, whether it's linear, quadratic cubic or cortex to begin. I entered these data points into my stat options on my graphing calculator, and then I grafted. I graphed the scatter plot that you see at the bottom right of the screen just to get an idea as I'm moving forward, of which one I I would like to think it's gonna be the best, and given the look of it, I'm guessing that it's going to be cubic. That's just what the function looks like to me. But we still want to double check our work mathematically rather than just visualizing it, because visually we could be wrong. So going back to our stat options scrolling over two K elk, we can then scroll down to our linear regression option. Here we find that we have a linear function where y is equal to 0.9 x plus one point oh one, and we also want to take a look at our R squared value so that as we're going forward. We compare each one of these functions using that R squared given r squared of a linear function equal to 0.488 interpreting that it's telling us that about 48% of the variation and why is explained by X in this function doing the same thing. But now, to form a quadratic function, we get Y is equal to 0.11 x squared plus 0.4 x plus 2.35 And here we have an R squared value equal to 0.511 This is looking a little bit better than our linear equations telling us that now we have 51% explain variation of why buy X as compared to the 48% or linear function moving on to the cubic function. Let's also keep in mind that this is the one that we are predicting it's going to be based upon. The look at the graph gives us why is equal to 0.288 Exe cute minus 3.354 x squared Yeah plus 11.849 x minus 8.42 and here we have an R squared equal to 0.899 so that's getting even better. We are very close now to entire variation explained. Getting to cortex now. We also have y is equal to negative 0.13 x to the fourth, minus 0.57 x cubed minus 4.533 X squared plus 14.295 x minus 9.585 And here we have an R squared value equal to 0.901 so it looks like the cortex function explains the most variation at 90.1%. That suggests to us that the cortex function is actually our line of best fit for this particular data set.

Their data. Given in this question, Can Middleton in the form of a table with X and Y values? The X values are zeal. Five then 15 Frankie 25 30 35 Party party Faith Be and and their corresponding values are 795 one by 90 6 50 minus 30 minus four pp, minus six. Lifting minus five. Brandy minus 55 625 1630 2845 and for three by zero. So to create No, first, a scatter plot off this given data, we'll use the pH for graphing calculator in you goto the start option and select the first auction. That is no wonder it did weaken. Enter the values are X and y in these two columns l one and l two. So here we have angered the X and y values in less corn and list. Now, to get this got a plot breast zoom and then press nine, which is zoom Scott. And this will give us selenia more. No, as we can see here this nature off this guy, the plot resembles that of a parabola. Therefore, we must use quadratic model here instead of Lini Ahmadi. No, To find the quadratic model or to create a quadratic model, go back to stack. Rest decide Arrow Togo to calculate list. And here the fifth option is quadratic regulations of a select by now, under your list one and list was selected as X and y values. Now, before we calculate the model notice, store the created model in a given in question. So the story as a function press of ours go to the side when you find rivers. No, the first auction is function in here will select what you want. Therefore, whatever model or whatever quadratic model is created for this given data will be stored as a function of Are you on? No, we go toe calculate and presenter. So the calculator will now give us a quadratic model. No, we know any quadratic equation in its general from is a X squared plus B x plus e on the values off A, B and C are given us. So this is quadratic Morning. No, if we want to write this by taking maybe two decimal points approximations, we'll get it. Does a will be five point b can be taken as minus 2 74.56 and see, really to a toe 0.3 toe. Therefore, we can write this quadratic model, as are you feeling ex clear plus minus. It was 74 Boeing 56 plus to a so 2.32 This is a quadratic model of this given later. Now, to plot the quadratic model as a craft, we go back to the drafting calculator here now, repressed resume and zoom start, which is an induction. And God will give us the graph off the modernity of just created. So, as you can see, this is ah, barely are quite an accurate model as it covers all the data points. No, to find the exact date of values are the function values. This morning we go toe second and table. Yeah, The white one column will give us function values off the model at these values. Off picks? No, in our question, we don't need intermediate values because I was data given Does not have values like 123 or four. So to change that, we can go toe second and David seconds. India. We can start the table from zero and we can make our table increments. So now we go back to table, really Get for table where the X values are similar or same as that, as in our data. So now we can compare these Y values to the values, give any normal question. So here we have copied the able react in function values off our model, and we can compare it with the values off way. No, As we can see, these values are fairly close to each other. Therefore, we can say that this is a fairly accurate model off the given data.

We need to find our change in our exes, which is our input. Change our final change in our wives, which is our output. And determine if this is a linear. So if we look at our access, they are increasing by 10 every single time. So changing outputs. No no outputs inputs. Yeah, is the same. That's 10. When we look at our outputs um 24.8 minus 12.4, that means we added 12.4, but 49.6 minus 24 point eight here, we added 24.8. So the change in outputs is not the same. So. And since we don't have the same change that we don't have the same, a constant rate of change in the wise. And in the exes, this is not linear. Yeah.