# MATH 1127 Section 2.2

all right let’s talk about organizing quantitative data and again quantitative it’s dealing with numbers so we’re first gonna discuss organizing discrete data in tables and remember discrete we’re over here discrete data was thinking about something that’s countable alright so if the number of observations are a relatively small quantitative data can be treated the same way as qualitative data so this is where we would actually go through and look at our data and we would start the tally so this example here is gonna be the number of people arriving during 15-minute intervals during lunch time at Wendy’s so they randomly selected 40 15-minute intervals during lunches and recorded how many people came through the drive-through or came to the restaurant so literally they’re just gonna go through and they’re gonna tally up how many customers came during each of these 15-minute intervals they recorded it another tallying so for the number so there was only one 15-minute slot with one person and they recorded that here the number of 15 minute slot but had two customers arrive it’s gonna be six so there was the one two three four five and six and again and as we showed and tallied here so the process would be to go through all of that all over the raw data organize it into this table by tallying up how many how many times each of these occurred and then we would go ahead and write it out as the frequency and then the relative frequency this is gonna be the number of occurrences that happened for that one particular thing so the number of times one customer came through the window out of all 40 of those observations so the relative frequency is the probability or is is very closely related to the probability whenever we’re coming up with relative frequency these will all when we add them all up they will add up to you’re never gonna have a negative relative frequency so it has to be between zero and one for a relative frequency all right so if we wanted to go through and do an example with the number of siblings that everybody have we would go through and figure out how many have zero siblings so we will assume that five people have zero siblings maybe seven have one maybe another seven have two maybe nobody has three siblings and maybe one person has four and that we don’t have any with five six or seven so this is assuming that we have 20 students and that our 20s have our 20 students five of them have no siblings seven of them have one sibling seven have two siblings and one has four siblings so the relative frequency we’re going to take this frequency and divide by the total number of students so if it divided by the total number of students or observations so we said 20 so this is going to give us 0.25 for our relative frequency our seven over 20 0.35 and again seven out of 20 is then give us 0.35 the relative frequency here will be 0 and the 1 out of 20 then give us zero point zero five and again zero for the rest of these all right so let’s about a histogram so a histogram is constructed by drawing rectangles for each class of data the height of each rectangle is the frequency or the relative frequency of the class the width of each rectangle is the same and the rectangles touch each other so keep this in mind the width of each rectangle is the same and the rectangles touch each other so it’s gonna look like a bar graph only it’s a little bit more specific because again the width is the same and the rectangles touch each other so if we were to take that same data of the number of people arriving and the 15-minute intervals at Wendy’s and turn that into a histogram then we would have 1 through 11 and because of the

so this is 25 up to just before 35 this will be 35 up to just before 45 so on and so forth so this first table here is showing us us residents age 25 to 74 who’ve earned a bachelor’s degree and then over here this table is showing us us residents on death row as of December 2006 and again where we’ve got the ages split out by class and then how the the frequency of our on the right or how many people fall into each of those classes alright for our next example we’ve got the three-year rate return of mutual fund so this is going through different mutual fund and showing their rate of return recording that and again because of all of these decimals it makes more sense to have a class then it does for us to go through and try to count each individual number so instead of us having for instance ten through eleven point nine nine then here we have a ten point nine nine so we’d actually have to have a category of ten point nine nine we’d have to have a category of eleven point three two so on and so forth if we were treating us like discrete data and again discrete being countable and this because we’re gonna have a range instead of a class so our classes are running from ten to eleven point nine nine twelve or thirteen point nine nine so on and so forth and if we want to figure out the width of our class we’re gonna do the twelve minus ten we get two so we know that each class has a width of two so the books already been nice enough to go through and do the hard work of tallying for us we’re literally that we just go through each piece of data and put a tally mark and the proper class and then we’re going to count those all up and there were forty different pieces of data so we’re taking whatever our number was dividing by 40 and that’s gonna give us our relative frequency so let’s actually work through a very similar example so dividend yield a dividend is a payment from a publicly traded company to its shareholders the dividend yield of a stock is determined by dividing the annual dividend of a stock by its price the following data represent the dividend yield in percent of a random sample of twenty eight publicly traded stocks of companies with a value of at least five billion dollars with the first class having a lower limit of zero and a class width of point four we need to go through and construct a frequency distribution and then we want to Hadden construct a relative frequency distribution okay so let’s set our classes up first so it’s telling us that the first class has a lower limit of zero so there’s going to be zero through and then it’s time to have a class width of 0.4 and again remember to find our class widths we are gonna actually take the beginning of one class and subtract the beginning of idea and another class so the lower limit of one class subtracting the lower limit of the class before it so we know that the big I’m just going to put the lower limits at the beginning of each of the classes down so we’re gonna have 0 we’re going to have 0.4 we’re gonna have a point 8 and again we’re just counting by 0.4 zeros we’re going to have one point to one point six two point oh two point four two point eight and three point two all right now from that now I’m gonna do the lower limit and we could have done the first at the lower end upper limit of each class individually but I find it having the lower limit of the next class makes it a little bit easier so here I’m going to have a 0 through just before this point four zero sure enough through 0.39 and then the 0.40 through just before this point eight zero so zero point seven nine the zero point eight zero through one point one nine that’s just the four one point to the one point two through one point five nine the one point six zero through

one point nine nine with the 2.0 through two point three nine the two point four through two point seven nine two point eight zero through 3.19 and this 3.2 is gonna be through three point five nine all right so now we have all of our classes set up so we can just go through and start tallying our data and see if I can actually pull it down just a little bit for us so we get all on the same screen okay and as we tally I’m going to actually mark through so the 1.7 it’s going to fall here zero one point one five point six two one point zero six two point four five three point three eight three is alright two point eight three two point one six one point zero five one point two to one point six eight zero point eight nine zero make sure mark it out so I don’t count twice there’s the zero and now we’re to the two point five nine zero again one point seven point six four point six seven two point zero seven point nine four two point zero four zero zero one point three five zero zero and zero point four one okay and so now let’s actually write out the frequency here so we’ve got seven for the 0.39 class we have four for the next five for the next two three four two and one and it turns out we don’t actually need this bottom class it’s just gonna work that one out we’re not going to use it and the reason we’re not using it because if at the end of the data are the end of the classes so now we’ve got all of this worked out now we can do our relative frequency so to figure out how many observations we had we can see a quick multiplication so there’s gonna be seven columns and four rows which means that we have 28 observations so let’s do that work right quick so we’re gonna have seven over 28 which is gonna be 0.25 four out of 28 which is gonna be zero point one four two nine five out of 28 there’s going to be zero point one seven eight six two out of 28 just going to be zero point zero seven one four three out of 28 which is gonna be zero point one zero seven one get that decimal in there four out of 28 which is even at zero point one four to nine again two out of 28 which will still be the zero point zero seven one four and one out of 28 which is gonna be zero point zero three five seven all right so our frequency distribution is gonna be this column so we would have the class and this the relative frequency distribution is going to be the classes and the relative frequency column all right let’s continue talking about our histograms so again