hi so we're on to co-requisite support activity 1e and it's back to fun with fractions decimals which we've already done a little bit of but now we're also going to do percents so um that's the review stuff whenever i get a chance i squeeze those in but we're also going to introduce or i'm going to introduce to you something called a contingency table or a two-way table which i want you to get familiar with it now so that towards the end of the semester when you're probably right up to here with all this stuff you will already be familiar with it so that's where we're headed and um i'm gonna turn on my share screen so we can jump right into it all righty so um we've already gone over a lot of this it's there for you to read but um what i want to say is oh come on oh did my pencil die no it's 90 percent okay there it goes cool all right um so percentage is what's what we haven't done before and i am giving you a reader's digest version of how i want you to approach fractions decimals and percents so some of the stuff we're going to skip so what you've done already is you know how to take a fraction and um turn it into a decimal and all of these can be referred to as proportions a fraction is a way of expressing a proportion a decimal is a way of doing that and so is percentage i will be using proportion to mean mostly the decimal part of it but it's it's uh two and now three different ways to describe the same thing my name is bronwyn braun wins my name call me bronwyn three different sentences kind of packaging the same information so what we're not going to do is reducing fractions i don't care about that so you could go you could just go straight from this fraction to the decimal but i'm going to start here so if you recall green's review we do top divide bottom and the divide that's what that signs all about and that's how you go from the fraction to the decimal that's going to take you to the decimal so in reviewing that we've got three divided by 4 and i know this is a very basic and when you when you throw that into your calculator i love our calculators so have your calculator handy for this one um you're going to end up getting that 0.75 okay and so now if you want to go to percent well this symbol that literally means for sientos it means out of a hundred so it means 75 out of 100 and if you put that in your calculator you would get that 0.75 so if you did that top divided by bottom so you could do it that way that's awfully long a nicer shorter way is to grab that decimal and move it two places and that's going to get you 75 but because you've moved the decimal you have to let people know that's what the percent the percent basically means you move the decimals because you're recognizing that it's being divided by a hundred that's what percent means um so if you do kind of move those decimals the way i did with the dotted down here make sure to erase it so that it's not confusing to me what so leave that the way it was so there it is that's a transition and we're using the beloved top divided by bottom gets you a decimal so then all you need to remember and most of you probably know it is to get percent move decimal to [Music] um to the left oh sorry to the right i never think of it that way i always think too bigger and write the symbol so you gotta have that symbol there to um to get that bam okay so um and i'll just write in the original journey is three divided by four okay so we are not going to be reducing fractions just get whatever fraction you have all right so when you do that using your calculator um you can get a if you wanted to convert this 0.6 to a percent well you might grab that calc you might grab that decimal point and you're going to move it two places to the right well you start doing that and whoops you don't have anything anywhere to go well true or false i can add as many zeros after a decimal point and i will not change its value is that true or false it's actually true as long as you're just adding you're writing those in so .6 equals six out of ten point six zero equals sixty out of a hundred point six zero zero equals six thousand six hundred sorry out of a thousand and they all are the same value so you can throw as many zeros as you want after so if you get some if you don't have enough places in which to move your decimal point just throw a bunch of zeros in and then move the decimal place so i'm going to grab that and i'm going to go one two bam and that then can be written as 60 because that's where it lands percent okay but um but it really is 0.6 that's probably the cleanest way to write it they're all the same though so that's a short decimal a long decimal it could just go on and on forever certain numbers do they're called transcendental like pi just goes on and on forever it's beautiful other times you may get a long decimal so when you get a long decimal like this you almost certainly want to round it so i want to before we get into rounding i just want to review place value so place value and you i'm never gonna i'm not gonna quiz you on round to the ten thousands place i'm not gonna say that i'm going to say round to the fourth place pass the decimal so the first page past the decimal place past decimal that is called and i'd better plan ahead here the first one passed is called the tense place okay the next one which in this case is going to be the three that is the hundreds and the one after that that's the thousands and the last one i'm going to mention even though we could it's so much fun we could do this all day long i don't think we will um that's seven right there that's the ten thousands so if it ever shows up on one of the practice problems um you know what the names of the first four places pass the decimal are but i'm just going to say the first place passed the second place passed the third place passed because so first place second let's pass the decimal etc because i never learned it till i had to be a teacher so you know um so you get the pattern and we're never really going to be interested in rounding uh beyond the fourth place past so when you're rounding if you want to do the fussy rule step-by-step thing we can do that but we're also going to do big picture so i'll write down the rule but i like the big picture better so the rule is look at the next number it's actually value to the right of the one you want to round if that neighbor number is 5 or greater than increase the number you're interested in and rounding so most of you know that rule um i mean i'm sure i'm sure you all know that rule i'd rather think about the big picture though and a big tip for decimals a huge tip for decimals is um tip for decimals and always and i think i said it in the last video think about money okay so if i say it around to the tenths place so we're going to round so the example here is i'm going to start with the hundreds place i'm not because what i'm going to say is round to the second place past decimal so you've got your number up here and you round you want to round to the second place past the decimal well then your value of interest is right ooh that was too big um your value of interest is right here it's the three and second place past the decimal is it's the hundredths place which is helpful because if this were money it would be your pennies we know all about money so if you ended up having this weird number come out maybe when you're doing calculations you and your friend are deciding to split a tip ooh i don't know what i just did there um and it came to this calculation well is that closer to 3 cents or is that closer to 4 cents so is this if we look to here well you look over to the next one oh it's it's more than halfway to being four cents so we're gonna round up so then point zero three five seven dot dot dot uh you're interested in this one so you look right next door and that is closer to .04 so you increase this one because it was closer to being .04 than .03 it was already more closer to that so similarly um for the um if i wanted to round to the tenths place it's closer to not having any money at all so you just say ah let's forget it um if you want to round to the hundredths place or two places past we did that one if you wanted to round to the thousands place three places pass you still go up so let's do some other examples and i'm going to change the terminology for how i'm actually going to want the questions i'm going to ask on the quiz probably so for number one you're asked to convert five 5 8 to a decimal and then do a bunch of rounding so if you would like to pause and try it on your own and then i'll go through it that'd be good so pause try it on your own and then go through it and let's throw percent in there just for fun too so around oh no let's not okay so um it is a good idea to show your work just so that you know when you're going to study for the exam um [Music] you got your work there to look at so it's going to be 5 divided by 8 because that line right here is the division so we have 5 divided by 8 and that turns into if you get out your beloved calculator i don't know about you but i love mine um i got the actual calculation is zero whoops color 0.625 so there it is and i'm just going to i i'm going to say here round to the nearest 10th well the 10th if i look at my notes is right there one place fast so i want to round to this i want to know it's either going to stay the value it is or it's going to go up so the question is if you're looking big picture is um 0.625 is it closer to 0.62 or is it oh no 10th my bad is it closer to 0.6 or is it closer to point seven if you and tip think about money if you are um if you have that much money do you do you have closer to 60 cents or 70 cents if you have 62 and a half cents basically well you're closer to 60 cents so if you want to do it mechanically you focus on your number of choice since it's tense but then you go and you look at the one next door circle it now so you look at the one right next door and you say is this equal to or bigger than five and of course 2 isn't so then you keep it stays the 6th value 0.6 so it's either stays 0.6 or it goes up to 0.7 in this case this is closer to the 0.6 so okay round to the nearest hundredth okay so it's the same number 0.625 but now you know one of the hundredth is going to be two places past so you're going to be looking here and the question is your choices are going to be are you closer to 62 cents or 63 cents if you have 62.5 well you're smack dab in the middle but you look at that five and decide is that equal to or greater than five yes so then this goes up to a three so there's your answer so the one that stayed in the other and thousandths hmm down to the nearest thousands that's very weird because well i guess you can imagine that actually you want to be really fussy this is that decimal and so um it is just going to be you drop all those zeros because they're way less than five so your final answer will be 0.63 oh 6 2 5. it's already there and you've dropped all those invisible zeros okay so that's rounding um so now this is the new stuff um this thing right here this table right here is called a contingency table it's called a two-way table it's breaking down information in subtotals and there is also a grand total or what i like to call a total total so your grand total goes here and then what you have um along this edge this is a subtotal and this is a subtotal those are both subtotals and what those subtotals have to do with um all the students who live on campus so whatever is over here you just kind of um that information has everything to do with all the students who live on campus and similarly this information so that row and this information this row has everything to do with all the students who live off campus so this is going to be all oops all students um [Music] okay and so it's probably pretty obvious but this is the grand total is all students we don't care whether they're on campus or off campus it's just all the students so that if you're looking i just was looking at the horizontal rows if i look at the vertical rows prefer the library and if i go down here then this subtotal looking in this direction is going to be all the students who prefer to study at the library last one go down here and let me look at that last bit right here so so we have the subtotals along both along the edges so all students [Music] study or would prefer to study elsewhere okay so um and that's why it's called a two-way table so and um so the subtotals are along the margins the grand total is um the grand total is right there and those subtotals are there and then the cell values like this cell value right here that cell value is both blue non-turquoise blue standard blue and yellow so these are all the students i'm not going to use the word all i'll say students who live on campus and prefer the library okay so that's that cell and i won't break down the other ones but um the next one down is going to be they live off campus but want the library so these two cells together if you add those two cells together you get the subtotal of all the students who like to live at the library or not live at the library but study in the library okay so that's a that's just a kind of a introduction to two-way tables so now what we're gonna do is we're going to um read the information and i like to call this um this game uh fill in the damn boxes and the one that's easiest to spot usually is the grand total probably because it's the biggest number but in context it's also easier to understand okay so let's go to here looking at number two at a certain college 150 students are enrolled in the statistics class of the 150 45 live on campus and 105 off campus so i noticed that these two seem to be making up that one and in context that's exact so they took a whole group of students and they broke them down into two different groups now what i like to do is i like to read through the problem once and then decide what i'm doing so i'll just keep reading the professor was curious about whether her students study in the campus library so she's not she's just wondering about us she has no idea how they live but she's wondering if they do that of the students who lived on on campus 20 said that they preferred to study in the library of the students who lived off campus 40 said they preferred the library okay so i know from experience they're going to ask all these questions but i know from experience that they're just going to want um me to fill in this entire table so i'm going to read it again and i'm going to look for where the grand and subtotals are and just go from there so if i read it again at a certain college 150 students are enrolled in a statistics class so we're looking at just statistic students of those 150 45 live on campus and 105 months off campus so i'm going to focus on this sentence um kind of run out of colors haven't i all right so of the 150 45 live on campus and five live off campus so that to me really sounds like grand total and subtotals so this right here is the grand total so i'll pop it in there so 150 students 45 live on campus so on campus is right here so the grand total total is 150 but the subtotal is going to be that uh 45 okay so and 105 live off campus so live off campus we don't know about their library habits yet but we know that that's going to be 105. and just a quick check it better add up and it does so i feel good about that okay so the next uh the next sentence the professor was curious about whether her students studied um in the campus library of those who lived on campus 20 preferred to study in the library so of those who lived on campus so that means i'm only focusing on this group of people so of that i'm gonna just so looking at that green sentence it's saying just consider the people who live on campus on campus just focusing on the on-campus people 20 said they preferred to study in the library so for this green row of those 20 preferred and sure enough this is the students who live on campus and prefer the library so i'm going to slap that 20 right there of those who live off campus off campus is all of those so of those who live off campus 40 said they preferred the library so considering only the gray row of data of that total group of people 40 preferred the library so i know i'm looking for an intersection between library and off campus and so that right yep okay 40. so that might be a little disappointing because the game is fill in the damn boxes right but if you have two boxes in a row you can figure out the third box so for example if 40 people are off campus and like the library and there's a total of 105 people then we know we can figure this out by just saying oh it's 105 take away 40. and god we won't do that by hand i wrote it down so i will you know i'm gonna um oh i'm gonna just put parentheses here because i'm working it out it wasn't actually given to me but 105 take away 40 is going to be um 65. so now i can that could that's really helpful but i still don't have enough information to figure out um this down here but i i do know if 20 for on campus if 20 like the library and there's a total of 45 that i can figure this out by just saying 45 minus 20 because this plus this is going to be everybody who lives on campus so that's going to be 25 oh crap 25 okay so now i have enough information to fi to fill in this and this because preferred the law to study in the library 20 on campus 40 off campus that's 60 all together so the inner cells add to be the uh the edges and similarly if um 25 people who don't like the library live on campus and 65 live off campus then we can calculate the total number of people who would rather not study at the library by taking 25 plus 65 you don't need to show your work i'm just writing it down in case i don't i don't want to lose anyone so i just won the game called fill in the damn boxes and only after i fill in everything and i really and i take my time with this and with practice it gets easier and easier but i i would take my time with these two-way tables so there's two pieces of information one is about their campus status and where they live and the other one is library preference whether they like or don't like the library so it's two different characteristics um so now that i have it filled out i can now answer the questions more easily so the first question what proportion of students enrolled in the statistic in this statistics class live on campus give your answer in simplified fraction form okay let's do this give you answer in fraction form decimal and percent okay so i'm going to get rid of all of everything but the um let me get rid of the colors be conservative about it okay so i'm going to produce that i like to mark it all up when i'm thinking about it why not okay so proportion is just part over whole i remember that just keeping that in my head what proportion of students enrolled in statistics class live on campus okay so we're interested in all of the students who are in stats um we're interested in everybody we're not interested in the people who live on campus we're not interested in the people who live off campus to take steps we're interested in all the students to take stats so our denominator the whole is going to be 150. so what proportion of students enroll in statistics live on campus so i also think proportion is kind of like peace um live on campus so of all the students how many live on campus it's going to be 45 so i got my decimal just from reading it so now i've got to do my calculations i'm going to show my work so it's 45 divided by 150 and i do want that i'm going to always have my calculator so um love that calculator and i end up getting 0.3 so this is the fraction and this is the decimal if i want to also put it into percentage then um i'm gonna i know that i have to move the decimal place at least a couple of times so i'm gonna throw in some zeros here so i'm gonna box my answer here this is my answer for decimal this is my answer for fraction and i don't want you to waste time reducing it um i crossed out to simplify but if i now want to do percent um if i want to do percent then i'm going to grab this decimal point and i'm going to move it two places each time you move it it's as if you are multiplying by 10 so every time you move that decimal point you multiply by 10. so i'm going to put a 0 that's where the decimal goes so it's going to end up being 30. um and but i moved the decimal multiplied by 10 multiplied by 10. that's weird what happened there um sorry so i move the decimal and i move the decimal uh multiply by 10 multiply by 10. oh that means to balance it out so that it's what it really was i give it this little symbol to say that's really 30 out of 100. so it's a little messy i want the original decimal to be seen for my teacher so there's the percent fraction just part of a whole decimal is top divided by bottom or numerator divided by denominator decimal is what gets spit out when you do that on your calculator and percent you move the decimal places two places and then remember don't forget the symbol because point three does not equal 30 it's never um 0.3 that's 30 cents is not equal to 30 so you've got to have that symbol there okay so um so i did that one probably way slower than you would like um so i would like you to pause and work out part c and then i will go over it um and then come back and do and then so do see see what i do check your answer because you don't want to practice it wrong and then do d see what i do and so and so on okay so for problem c what proportion of students enrolled in statistics so there's still just kind of lumping everybody together enrolled in statistics is still that 150 what proportion live off campus live off campus so off campus all the students who live off campus is the 105. so i'm gonna have my part is 105 and my whole i'm just dealing with the students and statistics and you don't have to show your work so 105 divided by 150 slam that into the calculator and you get 0.7 and if you carefully move the decimal points you're going to end up getting 70 but don't leave that there so here it is as a decimal here is percent and here it is as a fraction and i don't care about you reducing it all this is like english spanish and german three different ways three different ways of describing the same thing it's not fans okay for d so pause it and do it come back all right so for number d letter key what proportion of students enrolled in statistics class prefer to study the library so we're still interested and students all the students and want to study in the library i prefer to study in the library is going to be all of those students so we're not breaking it down by any living status so that's 60. and then we'll work it out top divided by bottom we end up getting um [Music] 0.4 which converts to 40 and it wouldn't be wrong to say 0.40 or 0.400 they all are acceptable um and a lot of teachers make a big deal about they want the zero this is probably the most favored answer so i'll jam a zero here and i'll jump zero there i don't care uh the less i have to write the better so just box all my answers so they stick out for my teacher um so that's d and i think what i'm going to do is i'm going to remove this table just so that i have it to look at oh it's kind of small a little faded but there we go okay so you guys can't do that but i can do that with my beautiful notability so what portion of the students who live on campus oh that's interesting what portion of the students who live on campus to study the library so are we looking at all of the students anymore are we looking at a subgroup of the students to begin with we're not interested in all the students we want only students who live on campus so if they live on campus so our eyeballs are only looking in that row right there the other students don't exist to us so maybe it's a coffee shop and they they're on campus and that's their audience so they're looking there so what portion of students so that's our whole world prefer to study at the library so of that green column the people who prefer to study at the library prefer to study at the library is going to be it's this whole row but if we're only looking at the green it's going to be these students right here those 25 students are the rare students who uh oh wait library whoops i was just making sure you guys were paying attention so prefer pick a different color just to make it a little bit more prefer to study at the library prefer to study at the library is going to be these students right here so in that green column that green row the only students who like the library within that green row are those 20. so it's going to be 20 out of a total of 45 students in the library sorry students who live on campus of those the students who like to study in the library so 20 divided by 45 run that through your calculator and you will get four 0.444 four four repeating forever so um round did they want did they ask for percentage simplify the fraction no we're just not going to give your answer as a fraction just press this one out got that and a decimal rounded to the nearest hundredths so a hundredth is here so i would say rounded to the nearest second place mass a decimal so does that four stay a four four go up to a five should i stay or should i go now that four well its neighbor is less than five so we're gonna and i'm gonna do wiggly lines to indicate it's almost equal to point zero um point zero four four so it's state of four okay cool oh no not totally cool because it also wanted um nearest whole percent okay so in order to do that and kind of run out of room here you first make it a percent so it's going to be i'll move it two places so it's 44 so it's automatically a whole percentage just the way it worked out okay so um pause it and do f and g and then we're done so um okay welcome back so for number f letter f what proportion of students who live off campus okay off campus live off campus off campus that's a subtotal what proportion of all those students out of those students who likes to study at the library so it's those of all these students the ones who like the library are right here [Music] so when you work that out it's going to be 40 divided by 105. you don't have to write that um 0.38 0 nine dot dot dot write as much as you want that's my decimal um round to the nearest hundredths well hundredth is pennies there are a hundred pennies in a dollar so does it stay in eight or does it go up to a nine well the number next to it's pretty not very helpful at all so it's gonna stay in in the eight place round to the nearest hundredths decimal around the hundredths okay so 0.38 and percent the nearest whole percent so 0.38 is the same as 38 because you you grab that decimal and you move to two places so we can answer all the questions that one last one in each in which group those who live on campus versus those who live off campus were students more likely to prefer to study in the library well so we've got the fractions here and it's hard to compare them because they don't have the same denominator 20 out of 20 out of 45 if you cut a pie in to 45 pieces and you eat 20 of them you've eaten a little bit less you've eaten a little less than half or yeah you haven't quite eaten half and same with this one didn't eat half i'm a half would be 20 22 and a half pieces of pie for this one and this is smaller and you can do similar logic on that so it's difficult to compare when they're in this form that it's hard to do a comparison but when you have the decimals and i would prefer decimals to percent because you're not doing any you you weren't really doing a lot of rounding so um well i guess you were that doesn't really make sense but we can either look at the the decimal here versus here it's pretty clear or these decimals which would you rather have 44 cents or 38 cents which one's bigger um so uh percent of a percent of students who prefer library from the on-campus group is going to be close to 44 or 0.44 and then percent those students who just serve the library for the experience on campus off campus group so the off-campus group is going to be this is the only campus group often this group is 38 4.38 both easy comparisons it's super clear that more people more [Music] proportionally speaking more people should i say that in this group relative to that group prefer the library is it that they prefer it or is it just that it's more convenient for them because they're on campus i wonder but um that's the wording so i'll stick with it definitely from the students who live on campus more of them are more likely to use oh so yeah more likely to use the library so we'll jump to the conclusion that they're also more likely to prefer it but it could be that the other students don't have cars or it's difficult to get there all right so we are done with this and um this is actually well we're done with this and um i'll i'll see you i'll see you in the next section all right bye