9 5 Distribution of Data

hello everyone mr schultz here welcome to integrated math 1 we're talking about notes 9.5 distributions of data so don't forget to put your first and last name up here as well as your period number it's jumped little bit so we're going to talk about distribution distribution is where we have graph or table that shows how data has been doled out so for example we could have some like bar graph and we can see that hey look it looks like this it's like if we look at probability it's most of the stuff's going to be in the middle and it's going to be kind of have center thing like that now what this would look like is we look hey look we could have box and whisker plot like this and so we could see that this is once again it's like it's evenly distributed or we could have like dot plot where this is evenly distributed out so those are all examples of how you know the data has been doled out or distributed out all right let's go on so graph could be negatively skewed so this means you know it's going to lean one way or another so this means that there's fewer data on the left so that looks like this so we could have something where this bar graph or histogram is going to it looks like it's linked like it's huge on the right it has lot on the right and then when you get to the left there's little tail like here's the head here's the tail or when it looks like this we could have something like where the the box plot looks like this and then it comes out this way so it's most of the data is going to be on the you know right because there's fewer data on the left now we could also have something that is positively skewed distribution and so this is where fewer data is going to be on the right and so this would look like the opposite so give me second in there so on this most of the day is going to be on the left side and then you have like for this you have like the big head right there and then tail going this way for this one it's like hey look 50 of the data is to the left of these lines just drew right here 50 is this way so most of the data is right here it's like it's leaning one way fewer data is over here all right let's go on so here are some links here's the desmos histogram that's blank you can go ahead and fill it in and here's box plot example on decimals go ahead and look at that when we get to that so you're going to need graphing calculator eventually in high school if you're going to get into after integrate math 2 you will need graphing calculator but for now you can use for some free emulators or browser based computers on like desmond so let's write that in desmos.com next up that's page one let's continue what we're to do is we're going to analyze the distribution by using technology so we're going to plug in this information to figure out what does this histogram look like so go ahead and click that and i'm going to show you click the link on the histogram in three two one all right so looking at this what you're going to do it doesn't matter about the left side but on the right side you're going to fill in all the all the bits of information you received now if you look you should get 16 of them now going down you will need to change the number of pins or bars in histogram because if it looks little different go back there like if you change it little it's going to look little different now actually like if you make it too big it's going to let your many it's going to not look like anything so we have to we want to change in order to get good shape so for example it says big seven to ten looking at this this is approximately what this one is approximately what it should look like now it's like rough rough sketch on here now if you actually had graphing calculator you'd be wonderful but we don't live in that luxury so let's continue all this information here is our histogram now what else do we need to do now well if you look right above here there's little arrow that says share graph go ahead and click that you're going to see export an image go ahead and you can download it and then what do is look at it and right click and put copy after that go straight back over here have random in there and then can paste it so let's see if got paste so let me see so don't have page but what could do is could save it on google drive and then take it from google drive and place it in here i'm going to do that right now my my drive and then images and fields named it know it's desmos so find it right here and then can click it select it and boom can click and drop it right here easy as just copy and paste them bam there we go so going on we can do the same thing as making box plot so what we're going to have to do is we're going to have to copy the data and then bring it on over hold up if we bring the data over here all we have to do is now paste it all right what we're going to do is we're going to create the brackets we're going to say hey we're making list we're going to have brackets and we're going to put it in god and bam all we need to do is say hey here's list list hey want to make box out of it and then once again copy paste bring it back in well actually for you guys you guys are gonna have to save it to your google drive and then pull it in can do the copy paste thing but that that's on me alright guys let's go on with our information in three two one all right so looking at this i'd probably want to resize it make it little bit bigger since have some more space look at this there's my histogram here's my box plot you can make your box plots pretty easily using that list but the histogram you'll probably want to use that histogram desmos link and redo that every single time all right let's go on guys example two use appropriate statistics by using histogram or you know box plot it doesn't really matter because we can get the data from desmos all right so what we're going to do is i'm going to use this data and we're going to figure out what is the mean standard deviation maximum minimum have two maximums let's delete one of those and make it or let's cross out one of those and make it minimum all right the median lower card and the upper quartile so i'm not going to write it in but you will so let's go on in three two one all right so if we are in desmos and we have our list and we say hey we want to make it box plot we can continue with that we don't even need the box plot but it's nice to have it we can create some guess you could say programming we're saying hey we want to know this so the mean of list or the mean of because we're saying is this list it will tell us 16.375 st dev stands for in parentheses stands for the standard deviation of list right here or which is list max is the maximum the minimum of for the min for minimum and don't forget to make sure you write down these numbers in the far right hand column going on in three two one all right now we're going to talk about the quartiles we have the median or quartile number two so basically we're saying hey on this element right this list what is the quartile number two or the median at seventeen about quartile one and three 11.5 21.5 the program will do the work for you so let it do it for you plug in the data let the calculator do it all right going on in three two one all right so hopefully guys wrote in that data right here so now we're going about learning extreme data points so drawing tool now the least and the greatest values in set of data are called extreme values if value is more than 1.5 times the interquartile range above or below the closest quartile it is considered an outlier all right all right so let's go on in three two one now here's here's like the basic of it an outlier is something that is far away that skews the data either making it seem bigger or smaller remember those zeros on test because they didn't take it it brought the average score down but the average score was like minus but because of those people who didn't take it it brought the average down to ac so that's kind of these outliers change the data drastically all right let's do our last example and go on so example 4 choose appropriate statistics with extreme data points okay so i'm gonna have you guys follow along with me sharks the links and feet of adult sharks and various species are shown describe the center and spread of the data using appropriate statistics and identify the effect of extreme data points okay so here's all this data what are we going to do well the first thing want to do is i'm going to highlight all this and i'm going to put it into my calculator my desmos calculator so go over here can delete this and can put the new data so looking at this can now figure out what is my information so looking at this know my mean it tells me all this information right here so i'm going to let you guys look at this for second and then we're going to go with the data so it looks like the mean go ahead and write this in it looks like the mean is 13.815 it looks like the standard deviation is about 10.9 the maximum is 46 the minimum is 0.6 now the median the middle number quartile 1 is going to be 5.85 and quartile 3 is 19. now you need to write that information down i'm going to take those last two bits of data right there so let's go on in three two one so it looks like the lowest one was 5.8 5.85 5.85 and it looks like the upper quartile was 19. so if subtract those out get 413.15 all right so now so now on your calculator or using your knowledge we're going to have to see is is the distance 46 is it greater or than or equal to 13.15 times 1.5 the distance from here to here let's see let's subtract by 19 and we get so the distance between the extreme and the third quartile is 27 units is this bigger or smaller well it's bigger so that means this 46 is an outlier so if we look at it we can click hey we want to hide outliers and so now look it'll show that outlier as little circle little point and it'll exclude it from the data and it changes it all right guys that's it for no notes for 9.5 make sure you use this effectively and wisely because tools do exactly what you want them to do as long as you understand what it is you are asking it to do alright guys have great day and i'll catch you guys in class bye