# Elementary Statistics: Organizing Quantitative Data, The Popular Displays

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### Elementary Statistics: Organizing Quantitative Data, The Popular Displays

this is organizing quantitative data the popular displays and first the first item is a histogram this is constructed by drawing rectangles for each class data the height of each rectangle is the frequency or relative frequency of the class the width of each rectangle the same and the and the same and the rectangles touch each other there we go now we’ve got a frequency distribution this is stated values either individually or by groups of intervals lot of their corresponding frequencies or counts companies laid in a bar chart show this maybe I have ages and that goes from 0 5 10 15 n s goes to 4 and this one goes to nine this one goes to 14 and this one goes to 19 then we have frequency it is 5 in this range to anas range 12 minutes range in three in this range that’s an example of frequency distribution now we can also display that with a histogram construct about draw rectangles for each class date and we’ll see more of this in a little bit now I’m just like before we had a frequency distribution you can have a relative frequency now the relative frequency you’re going to some these together five plus seven x plus two is seven plus 12 is 19 then 22 then for our relative frequency will take each one of these frequencies / that total and then multiply it times 100 so this one will be 2 / 22 x 100 so will be 12 / 22 x 100 and this will be 33 / 22 x 100 now let me do this I’ve / 22 x 100 and I’ll round it though I don’t know one decimal place 22.7 percent 2/22 x 109 into one decimal place to be 9.1 percent and then 12 / 22 x 100 would give us 50 54.5 % 3 / 22 x 100 would give us a thirteen point six percent now typically you like these add up to one hundred percent you know like this point seven plus one is point eight it gives us 14 19 so I do the nine carry the one so I really want one of these to be great or like thirteen point seven percent now technically we’ll leave it this way but if you’re in the workplace well somebody when you take this to a meeting they’ll sit down a DS together and they’ll Wars a missing point one percent it’s like it’s rounding leave me alone but he’ll they’ll do that so now we’re also have something called a cumulative frequency so let’s go ahead and talk about that now cumulative frequency it adds up that current frequency plus all the ones above it so this one’s five this one’s too plus all the ones above it which is five so I gives us seven then this one is 12 plus all the ones above it so two plus five that gives us 1 19 and then the last frequency which is 3 plus 12 plus 2 plus 5 and that gives some 22 so that’s your cumulative frequency now you can also have your cumulative relative frequency where you add up all the the relative frequencies plus all the ones above it so this one’s twenty two point seven percent this next one will be nine point one plus twenty two point seven percent

and I’m not very good decimal splits in CS point 8 130 130 one-point-eight percent let me add up in my calculor 9.1 plus been a long day and create videos all day haha then our next one will add up the current percent plus all the ones above it now all the ones above would be this one plus this one which we are guides 31.8 so to save space I add up the 31.8 because that’s already the ones above it okay so 54.5 plus 31.8 gives us a tee 6.3 and again in theory if i take this the current percent and all the ones above it that should be the eighty six point three percent which should give us a hundred percent Machar’s gives us ninety-nine point nine percent because of rounding but that’s a cumulative relative frequency if any of the problems we refer to that so that’s how you get all of your different different frequencies let’s see just to briefly show that in Excel okay so if i have my ages here now to get i’m going to put a single quote otherwise it’ll think it’s a numerical measure and just soon as I find my 024 so do 0 dash four and then five dash nine we’re going to see that there is a reason why you’d want to even separate these and separate columns but I won’t do it yet 10 to 14 and 15 to 19 okay so we got our frequency here and we got five to 12 3 okay so let’s find our relative frequency well for the relative frequency I need to add these together so I’m click down in this cell here I want my home tab and then I will click the autosum and it’ll guess what you want do the sum on and that’s fine b2 through b5 is what I’m wanting so I click this check mark here or press enter now for relative frequency here i’m going to equals and i’ll do be too because that’s where that number is the number 5 / and i want to / b 6 but specifically i’m gonna put a dollar sign be dollar sign 6 around that then x 100 we’ll talk more about that later but for now that’s our formula okay so now if I click this cell i just created put my mouse in the lower right-hand corner till it becomes a plus click my left mouse button and hold down and drag it down then it’ll on build those and i see i got 22.7 9.1 54.5 13.6 so the same same values now if i look at each individual formula here you notice this says be three which is this cell / b6 let me press escape to get out of that let me click this one click in here be 4 / be six now so is it as a filled it down it’ll just itself based upon what row its up but by putting the dollar signs before the B and dollar sign before the six that’ll hard-code it so it’ll always point to this no matter how much how much I fill it fill it down okay our cumulative frequency I’m going to do an equals and it’s on the current frequency plus all the ones above it so I do five here this one I can do and if I don’t want a hard coded by the way I do equals B to not point to the five this one I’ll do an equals B 3 + b2 so I have the current frequency plus all the ones above it this one I’ll do equals B 4 plus B 3 plus B to the current one puts all the ones above it now there’s a very quick way to do this but and then equals and then b4 b5 sorry plus B 4 plus B 3 + b2 now I specifically show this so you can see the exact formula for cumulative frequency now press Enter

ok so now from wanting cumulative relative frequency all I add the current percent puts all the ones above it so this one’s bc to this one will be be at C 3 plus c2 so I’m adding the current for a relative frequency plus all the ones above it this will be equals C 4 plus C 3 plus c2 current crimpers relative frequency plus all the ones above it and last one will be C 5 plus C 4 plus C 3 plus c2 then I’ll give me my my how to press ENTER now notice I didn’t have any kind of rounding issues here because I’m in excel in it it keeps all the decimal places for me but that’s how you build all of your different frequencies the excel now it also says a frequency distribution besides listening data values on the corresponding frequencies can be displayed in a bar chart and we’ll see more of that here in a little bit now we got something called our lower class limit this is smallest numbers can be long to the different classes so let’s take a look at this my lower class limits LCLs and my upper class limits UCL’s so for my example above my lcls would be 0 5 10 and 15 my upper class limits would be 49 14 and 19 like that and actually I meant to draw it over here my pin to work there goes ok so my lcls and my UCL’s so what was it 0 5 10 and 15 and there are benefits to listen II separately that’s 49 now you notice this went from zero to five to 10 the went by it’s increasing by 5’s isn’t it so over here i’ll increase by five so i don’t need to go and look 0 4 plus 5 is 9 9 plus 5 14 14 plus 5 is 19 that’s called class width so on this one our class width is equal to 5 okay well if I get back there there’s my powerpoint so lower class limits upper class limits casada actually I’m put that on there there we go now we got open into dissipations this is the first class has no or lower class limit or the last class has no upper class limit so maybe you want just greater than 15 maybe there’s so many oddball characters out here past 15 that the list them all would be ridiculous so we just do greater than 15 now this is the way your your class classes go from smallest to largest now that isn’t written in stone I you could go from largest to smallest but this way I think actually makes more sense now we have gap this is difference between lower class limit of one class and the upper class limit of the class right above it or below it depend upon data being ascending or descending here oops our gap is dif tring where this one ends and this one begins so this goes from four to five so that’s gap of one then you got half the gap this is multiply the gap by point five so half the gap o point five times one gives us 0 point five okay we got an upper class boundary UCB and we also got a lower class boundary lcb and I auto-reverse these actually right there okay so let’s take a look at a lower class boundary in our upper class boundary with their upper class boundary we add half the gap so half a gap is 2.5 so this would be 4.5 now this would be 9.5 we adding half the gap but the fact that i know the class width is 5 i can easily come up with us four point five plus five is 9.5 plus another 5 gives us 14.5 plus another 5 gives us 19.5 now over here lower class boundary we subtract half the gap so 5 minus 0 point 5 gives us 4.5 and add 5 that give