Constructing a Frequency Distribution

hi we are going to construct frequency distribution with this raw data in this data just so that we can use it as we move along is collection of 40 pennies so in 99 class of students collected 40 pennies and then they wrote down the year of each of these pennies and so we're going to organize these 40 data values into frequency distribution first thing that you want to kind of decide when you when you can start to frequency distribution is the number of classes that you want the number of classes on your frequency distribution and to to kind of get there we first look at the range and then we kind of think about the amount of data that we have and how big we want these classes to be and what their class width is so we'll kind of go through that process now so let's find the range the range is the difference between the highest data value and the smallest data value our highest data value should be 99 and it is because this was in 99 when we collected the pennies and our lowest value that's right here it's 66 so we have range of 33 so as we think about how many classes that we want we want to keep in mind that we don't want to spread them out too much and have you know 20 classes for range of 33 that would become silly there wouldn't be much data in each class maybe just one one or two pieces of data but we also don't want to get too small we don't want three classes and then then they get all collected into those three classes and we don't see the significant shape of the data either so but most of the time we want number of classes between 5 and 15 is kind of rule we can bend it but that's kind of the the role that we deal with when we construct frequency distribution and then for the data that you guys are going to be analyzing in this class you're probably going to stick around 5 6 7 maybe up to ten but probably not tried few things tried six and seven and landed on seven pretty quickly because when took 33 and divide it by 7 this is how you find the class width which is the next thing you want to do so this is to find the class width you take the range and you divide it by the number of classes that you want when did seven got four point seven one and class width we've had ceiling function on this and the ceiling means to round up the value to the nearest whole number always round it up so even if this was four point zero one we would still round it up to five okay and like class width of five it's odd we like an odd class width because then our midpoint is whole number it's it's reasonable value like having five data values and we just like the number five so saw that quickly and was like seven classes it is so six think gave us four and so that was little bit small for class width and it was an even number so went to seven and that was that was what decided on so keep in mind our class width is five and we want to start our class limits for our frequency distribution so this is our class limits our frequency distribution also keeps up with tally I'll show you why we do that in just second and then our frequency okay our class limits always start with our smallest data values so here it would be 66 our class width is 5 and so the difference between 66 and our next lower class limit is should be 5 so 66 plus 5 is 71 so that's going to be our next lower class limit and the reason why it's this way vertical and not horizontal is because we our class width is the number of data values that are in that class the number of data no data values but the number of numbers that would land right there so 66 67 68 69 and 70 so that makes five and so that's why this goes up to 70 all those values 66 67 68 69 and 70 is going to land right here and that's what our class width is representative of so that's why we're adding five vertically as we come up with our class limit so we'll keep on doing that until we get seven classes so 76 which would make this 75 81 which would make this 8086 ninety-one and of course that is seven so now we have seven classes and we of course just add four to get to this last because this would be hundred and one if we added five and so making this last class limit upper class limit hundred so you can kind of go out down and check you should be able to add five and get to all these and difference between all these should be five which they end in five so that's nice alright so frequency distribution just simple frequency distribution has the class limits and then the frequencies and so we using the tally column here though just to make our life simpler and it's how we arrange our data into this so taking this raw data and arranging it into this frequency distribution and think the best way to do this is just to start right here with your first data value and hitting Itali where it lands so 96 of course it's going to be right here and I'm just gonna put tally because that's where it is then we'll move on to 98 and it goes here 97 96 83 is gonna be our first one in different class it's gonna be right here and we'll just keep doing this for every data value and hitting Itali where it lands so stopped 83 all right so just tallied up the data got it into the frequency distribution tallies here and now can count up my tallies and record my frequencies so the tallies are just to get us to be able to record our frequency count them up and we get our frequencies okay so there's frequency distribution of this raw data and now we can look at it and start analyzing it so much easier now that we can organize it and just this very simple and easy way