Detailed Frequency Distribution

hi this time we are going to look at frequency distribution but we're going to get much more in depth so you probably should look at the previous video on frequency distributions where constructed this frequency distribution but now I'm going to take it and just get whole lot more in-depth with it look at the class boundaries the midpoints the cumulative frequency and the relative frequency okay so let's start by I'm just going to get my Class limits on here since we're going to need them just rewrite them real fast because we'll need them to find our Bal boundaries which is what we're going to do next it's nice to just see very large frequency distribution with all the little details on it and that's what we'll be doing okay so we're going to do the class boundaries next and the class boundaries are if we were to have this data unrounded which means it was rounded to the nearest whole number here of course we are dealing with years on pennies so they are whole numbers they are discreet so we don't really have this issue for this data set however our class boundaries do allow us to construct histogram whole lot better and it also kind of shows how there are no gaps in between our classes and it's really important if we had continuous data continuous data is data that can take on values that are not whole numbers so decimals or fractions we would round all those numbers to whole numbers and then record them in class in in classes and in our frequency distribution so the class boundaries would show us the unrounded data where they would land if it was unrounded okay so in order to get our class boundaries we kind of have to think of it in that way and we know that if we have class limit starting at 66 if we had unrounded data then this would actually go down to 66.5 65.5 anything at 65.5 65.6 would be rounded and be put into this class all the way up to 70.5 but not including 70.5 cuz that would be in our next class so that's that's what our boundaries are they are up to but not including this value and it shows that there's no Gap in between our classes if we were to round our data 70.4 13 would land here okay it would be in this class even though that's greater than 70 it's not greater than 70.5 so that's why we want our class boundaries especially for continuous data but even for discret data which is data that is whole numbers it helps and simply put this is just adding 05 to our upper limit and subtracting 0.5 from our lower limit all right so there's our class boundaries we'll also look at our midpoint I'm going to use MP for midpoint our midpoint is used when we construct our frequency polygon so it's really nice to have intentionally chose classes so that and class width so that my midpoint would be whole number chose an odd class width this is why and to get that midpoint and put the formula just right here so you can refer to it to get midpoint you take the lower class limit you add the upper limit and you divide by two just like regular midpoint you do it just like that so take the lower limit of 66 and divide that value by two and you get your midpoint here of 68 okay right in the middle of that class used for frequency polygon but other things as well to look at you know the midpoint for there you can use this for mean of frequency distribution if you ever did that as well so we go on and find the midpoint of the next class is going to be 73 this one's going to be 78 and get these lined up and your class midpoint point should also have the same difference between them as your class limits which is five okay 66 + 5 is 71 it's our class width the difference here should also be five let's now look at relative frequency relative frequency is what it sounds like it gets everything in relative terms so this is representative of 40 pennies but what if we wanted to kind of infer inferential statistics as to what the layout would kind of be like if we were to have th pennies the relative frequency we can look at it and see what that would be like this percentage of pennies should be between 96 and 100 for example and so it allows us to do some inferential statistics the way you get relative frequency is it's finding the percentage or the ratio of the amount of data in each class so you simply take the frequency of that class and you divide it by your sample size our sample size is 40 if you add these up you should get 40 that's the number of data values that we had when we did this frequency distribution so that is our and so will take for my first class I'll take my frequency of one divide it by 40 to get my relative frequency and this came out as nice decimal so went ahead and and took it to three decimal places you could round this to 03 and then we take our next frequency of 3 divide it by 40 we're going to get 075 we'll do that for each class so 4 / 40 is 0.1 6 / 40 .15 this is 253 have that zero there or not keep it consistent all right so that's our relative frequency so we can look at this even as percentages just left them as decimals but this could be like 30% of the data is between 9 and 100 so kind of get it on relative terms for if we were to apply this to larger data set okay let's finally look at our cumulative frequency I'll say that okay cumulative frequency accumulates As you move on much like cumulative exam it includes everything that you've studied thus far that's how cumulative frequency of frequency distribution works it's everything thus far and so for our first class our cumulative frequency is just what we have so far which is just the one but as we move to the next class now we've cumulated these three data points but also the one from the previous class so it's going to be four okay move on to the next class have four that I've cumulated so far on the one and the three and now I'm accumulating four more so have eight accumulating four more in the next class so now have 12 accumulating six so now have 18 then 10 so 28 and then 12 and this should add up and it does to 40 all right so there's much more detailed frequency distribution including the class boundaries the midpoint the relative frequency and the cumulative frequency we can use this to construct graphs or even to just analyze our data little bit more okay