 Hi folks, this is Dr. Don. I want to go over a problem that popped up on the midterm exam and it's about developing a frequency distribution for a data set. I have another video which covers most of this but unfortunately that video began with a problem which did not ask you to determine the upper and lower limits of the class. So I think it's worthwhile to go over this again and show you how to do this step by step. I did mention that some of the academic problems you get in a statistics course are not really set up to make best use of the technology tools. Stat Crunch, for example, doesn't really have a way to calculate all of these intermediate data points. It'll do the frequency distribution, the histogram, lickety-split and it will give you the frequencies but it won't give you these upper and lower limits very easily. So I want to show you how to do it using basic excel. Remember if you're in stat crunch you can click on the little rectangle there and then open your data directly into excel and that's what I did. This is the spreadsheet that I use when I'm doing these types of frequency distribution problems and I set them up so that I can reuse them fairly easily. I have a column over here the A column where I always put my data and that's in blue if you followed my series on excel workbooks. Blue cells indicate inputs and white cells indicate intermediate outputs and I use the basic excel functions to get the count which is just the count function and the range of that data and I use the min function to get the minimum number of zero the max function to get the maximum value the range is just the max minus the min which would be 39 in this case we were given again it's in blue the cell five bends is what they wanted the width is just equal to the range divided by the number of bends at 7.8 and then we always round that up to the next highest integer and I use the roundup function with zero decimal places to get eight the next part of my table I want to get the upper excuse me the lower upper and midpoints for each of these bends now the lower begins for bend one at the minimum and then we just go up by the width so I'm going to equal that cell plus the width over here the rounded width and if you remember in excel you want to lock down cells that you don't want to move and I'm going to highlight that d7 you can see with a cursor up there click f4 adds the dollar signs and that makes that lock down now once it's locked down I can just drag that formula down to get my lower limits for the five bends since we're dealing with integers the upper limit for the first bend is going to be equal to the lower limit of the second bend minus one and that gives me my upper limit for my first bend and then to get the subsequent ones we want to take that value and add again our bend with and we're going to lock it down again with the f4 key and that gives me my upper bend with and then I can just drag that down to get the bend with upper bend limits for each of the remaining bend the way I like to get the midpoint is to create a formula in excel and it's equal I start with open parentheses and that's the upper minus the lower close the parentheses divide by two and add back to my lower to get that first midpoint and then I can just drag that formula down to get the midpoints for the other bends to do the frequencies we use the excel frequency function and what we need to do there it's a little bit different because it's an array function we want to drag down and select all the the cells that I want the values for each of the bends plus one in case there's something that falls out so always go for each of the bends plus one and then we want to click our frequency formula f or eq and it offers that up and it says the data array which is over here those 20 cells comma and the bends array they want the upper limits for the bends and I'm going to close that now the way we enter this is a little bit different it's control shift enter and that gives us the frequencies for each of the bends and of course there's no spill over here it it correctly found our our frequencies for each of the five bends our relative frequency is equal to our frequency in that bend divided by the total number which is my count over here and click on that in that 15 and what I forgot to do is to lock down my count with an f4 and now I can drag this down to get my relative frequencies and my cumulative frequency this is something students tend to mess up they because it's the next they think the cumulative is just the addition of these that would be the cumulative relative frequency this is cumulative frequency so I need to accumulate the frequency column and that's just equal to the first value for that cell whoops and now the next cell is equal to that cell count plus that and then I can just drag that formula down to get my cumulative frequencies and that's how you do it it's a little bit cumbersome but once you get the procedure down and save your basic table format you can reuse it on other problems so I hope this helps