by: Diane R Koenig

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now that we have our class width of our frequency distribution table work that we're going to do in making our five classes we want to make sure that we get the lower number and the upper number for each of our five classes in order to set up and find our frequencies now with setting up the lower class limit and the upper class limit we want the data to be the same accuracy as the data set that you have and that there's a couple different ways you can start your process we are going to start by having our lower class limit of our first class being the smallest number within the data set so remember we have this data set and in the first segment we looked at how to find the class with the smallest number within all of these data values is 15 so we're going to start our lower class limit of our first class with 15 and then because we want to class with of our 7 our best way to kind of do this is to think of we want the spans and values for each of the classes so we're going to have 5 different lines here since we want 5 classes and what we're going to do is take for each lower class limit get the next lower class limit by adding our class width in this example 7 to each of the previous class widths so our first or class limit is 15 our smallest data value and when we take our 15 and add a class width of 7 we will get 15 plus 7 is our 22 when we take our 22 and add our class width of 7 we get 29 when we take 29 and add our class width of 7 we will get 36 and we take the 36 and add our class with those seven we will have 43 and notice there are now one two three four five of our classes that we've just found the lower class limit for each quest so far now each of these classes are spans of numbers that we want to see where our data values fit in and then we'll do a tally for our frequency we still need to also do the upper limit for each class now the upper limit for the first class is going to be a value that's right before the next class to the same accuracy that you have with the data set our data set is to the nearest one so the nearest whole number right before 22 is 21 so this first class will have a lower class limit of 15 and an upper class limit of 21 the number right before the whole number at 4:22 now the third class is going to start at 29 so the second class had to end at 28 the third class begins at 36 so excuse me the fourth class begins at 36 so the third class had to end at 35 the fifth class begins at 43 so the fourth class had an end at 42 and when we're looking at finding the upper class limit of the last the fifth pass for this example our upper quest values our upper class limits are also the same class with the way so if you'll notice 21 plus 7 is our 28 28 plus 7 is our 35 35 plus 7 is going to give you 42 and 42 plus 7 is 49 so these are stands of numbers for each of our class we have our first class spans from 15 and 21 the second class from 22 to 28 third plus 129 to 35 the fourth class from 36 to 42 and then the last us from 43 to 49 the next thing we're going to do is take and just do a tally for now and then we'll change it to the numerical representation so we're going to tally for each of these data values which class they fall in and we'll systematically go through this so for example with data value 32 that falls in the third classes span of numbers 32 is a number somewhere between 29 and 35 so I'll put a frequency callee have one there the next number 15 bags in the span of numbers from 15 to 21 so I'll put a frequency tally there and so we do this for each of the data values 27 is in the second class our 18 is in the first class 16 is also in the first class 24 is in the second class 36 is in the fourth 5 21 is in the first 5 42 is in the fourth class 32 is in the third 546 is in our last class 15 we have in our first class 17 is also in the first class 38 is in the fourth class 42 is here 15 again here 24 is in the second class and then finally 37 is in the fourth class so we're going to take these tallies and we're going to turn them into their numerical representation my first class I have five six seven so I'll just go ahead and replace back with some ii files I have three tally marks all right three in a third pot five two in the fourth bus there are five and then I have 1 data value that fell in that last class just kind of a quick double check if we add up the data values we have here so we have 7 plus 3 is 10 plus 2 is 12 plus 5 is 17 plus 1 is 18 and I had 1 2 3 4 5 6 3 rows of 6 which is 18 data values so that helps us do a double check now sometimes the limits are actually instead of doing the lower Testament and the upper crust limit as the lower data values and the upper data values that they present they actually will give you not only where the data values could be in the stands but actually if we are the classes we kind of meet halfway between and those values are called the class boundaries and I'll have a lower class boundary and an upper class boundary for each class so we'll write on this far end lower class boundary

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and on the other side of the upper-class limits will write upper-class father it's just another way to denote your classes pay the boundaries our way they meet so look at where this first class ends at 21 and the second class starts at 22 those bars if you graph them on graph would not touch and we want to have this information where we might be able to use it for a histogram so we want to have where the bars would touch so we're going to share the distance between 21 and 22 which would mean that we would end this first class at 21.5 and as a upper class boundary and start the second classes lower class boundary at all so that 21.5 so we're meeting halfway for that point of our lower class boundary in our upper class boundary so for the second class it will go up to twenty-eight point five and twenty eight point five is the lower class boundary of the third class thirty five point five is the upper class boundary of the third class and so that would give us thirty five point five as the lower class boundary of the fourth class and then for the fourth classes upper class boundary about forty two point five and that's the lower class boundary of the fifth class and then the last thing we need to do is make sure that the spans are all equally wimped so we would need to go down a half on our first entry of our first class so this will have a lower class boundary 14.5 and the last class will have an upper quest found tree of forty nine point five so another way to denote your classes the last thing I want to do for this segment is to also get some information that we would need if we are looking at trying to use the information off the frequency distribution table to graph a frequency polygon and with the frequency polygon we want to find what the midpoints are of each class and the midpoints we just take and add the two class limits the lower class women and the upper class limit divided by 215 plus 21 is 36 and 36 divided by 2 is 18 you could have also have added the class boundaries of the class and divided by 2 and you would get that same number 18 now we can do that for each class however your class midpoints are also going to be the class width apart so once you have your first class midpoint you can find the rest of them by just adding the cuts width to it to get the rest of them so 18 plus 7 is twenty five twenty five point seven is thirty-two thirty-two plus seven is 39 and 39 plus seven is 46 notice that with each of these if I were to do the other way of the average 22 plus 28 is 50 and 50 divided by 2 is 25 I would still get the same answer 29 plus 35 is going to of me 64 and 64 divided by 2 is from a 32 etc through all of it so here we have ways of getting the information for our frequency distribution table this is a frequency distribution table and working with a frequency distribution table so that we have all the information we need to pull it off and draw histograms and

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