in this video we're going to discuss how to construct frequency distribution tables now frequency distribution tables are really important uh for taking a large amount of data and we're going to do a simple example at first where we only have 25 observations but um you could take hundreds of observations and break it down into a table that you can easily view um you know maybe with only 10 different uh rows right 10 10 different things to think about as a ver is looking at a 100 different observations right it's a way to summarize um you know large data sets Okay so we have 25 observations of the number of hours of exercise per week so we asked 25 different people how many hours they exercise and they reported uh these numbers okay um we're going to construct a frequency distribution so we're with only five classes so we're going to use um five classes now the number of classes will always be provided for you so five classes or sometimes classes are called bins they're interchangeable terms okay so we're going to take 25 um observations of data and break it into uh this table here that will um you know capture that data in five different rows um so five different um you know rows to examine versus looking at all 25 uh data points all right uh so this is what a frequency distribution table looks like it's not filled out yet we're going to fill it out but basically what we do is we notice okay our data ranges from what's the lowest observation um actually I'm going to go ahead and copy this and bring it down so what do we see uh let's see um what's the range of our data uh the smallest data um is zero looks like it's no no hours of exercise and the largest is 13 okay so we're going to take um all that uh from 0 to 13 and break it down into five different groups so five different classes five different bins and we're going to count how many um data observations fit into each of those um five bins okay so we got to break down that um range from 0 to 13 into five different bins and then count the frequency and that's what a frequency distribution um does all right so let's go ahead and do this uh there's basically three steps to doing it um the first is going to be determining the class width right so like I said we're taking uh data that ranges from zero to 13 and breaking it down into five different um classes so determining class width do this uh what we'll do is we'll take the range and we'll divide it by the number of classes right that that will take the 0 to 13 and divide that amongst these five different classes okay so um in our data the range remember range is um max minus the Min so the biggest number minus the smallest number in this case our number of classes is five so that' be 13 minus 0 over five which is just 13 over 5 which is 2.6 all right so our class width is 2.6 well you know actually 2.6 we should always um round up what we find in the um Range divided by the number of classes oh we should just round it up a little bit um and in this case let's see uh we want to round up to the next convenient number um so we'll round it up to three right so convenient number to count by okay so it's easy to count by three it's a little harder to count by 2.6 right so um you can you know always round up never down up is definitely key um always round up uh to you know the next uh convenient number in this case that would be be three all right so next uh we need to determine the upper and lower class limits okay so now we know that our class width for each of these classes is going to be three so now we need to determine the upper and lower limits for for the um for those classes all right so let's start with determining the lower limits and then we'll go to talking about the upper limits okay it's always easier to start with the lower so you should always start with the lower now for lower limits we'll start at zero which is our Min so always start with the smallest number and then go to the next lower limit is going to be the this lower limit plus um the class width that you determined okay so 0 + 3 is three 3 + 3 is 6 uh 6 + 3 is 9 99 + 3 is 12 and that's all I need 1 2 3 4 5 right I have five classes so I sto there with five lower limits right my upper limit will go to the the number that's right before um the number that's right before the next lower limit so the upper limit will go to the number that's right before the next lower limit um if you had data that consisted of decimals so like say people reported to you that they exercise 2.5 hours then you would want to um you know take the number that's right right before three so that' be 2.9 right but because our data doesn't involve decimals um people only reported whole numbers for the number of hours that they exercise per week I can just take the number that's right before three which would be two right and I can take the number that's right before six so that'll be five right before 9 9 so that' be 8 right before 12 be 11 and then for the last um for the last class I can think of well what would be the next class the next class 12 + 3 is 15 so right before 15 is 14 right so these are my class limits 0 to 2 3 to 5 6 to 8 9 to 11 12 to 14 so once I have this I'm ready to the for the last step which is to just go ahead and construct your frequency distribution table so let's go ahead and write in those class limits that we just calculated uh 0 to 2 3 to 5 6 to 8 9 to 11 12 to 14 right so now I just need to tabulate how many observations are between 0 and two all right let's go ahead and find those so there's 1 2 3 4 5 6 7 8 eight observations between 0 and two how many observations are between three and five all right so let's see one 2 3 4 how many observations between 6 and 8 1 2 3 4 five let's see I didn't cross that one out so that should have been here so that four should really be a five all right that four should have been a five because I missed this four here so okay um okay between 11 and 9 sorry between 9 and 11 9 and 11 oh you know what I missed that seven as well so this should have been a six got to be real careful when you're tabulating these that you don't miss any numbers so that should have been a six missing anything else no okay so between 10 um between nine and 11 okay so one 2 3 four five okay so that's five and then between 12 and 14 just one okay so you can double check that you didn't make any mistakes like the way I did you know Miss any numbers what you should do is you should add up these numbers so 8 plus 5 + 6 + 5 + 1 and you get 25 which is the total number of observations in your data set and so you should always kind of double check that the total number of observations in the data set matches um the frequencies and that you reported in your table okay so now that once you have this frequency table you then you can answer questions like how many people exercise less than five hours you could say okay well um less than five hours that' would between zero and five so I can add up these two and I can say oh well 13 people ex 13 out of the 25 exercise less than 5 hours so you can answer some pretty um interesting questions using this uh this simple table um in the next uh video we're going to talk about you know expanding this table um talking about not just class limits but class boundaries and class midpoints