 Hi, this is Dr. Don and I want to go over problem 2.1.17 which was on the second quiz. Unfortunately, some of the academic problems you will encounter in homework and quizzes and exams are really at an awkward stage and this is one of those problems. It is too simple for Stat Crunch or Excel to provide a tool to do everything for you and yet it is almost a bit too complicated to do using an handheld calculator although you can do that. I like to do these using Excel using the native functions and I'm going to show you how to do that. We start by clicking on the little rectangle and then opening this data in Excel. This blue area is the way that the data opens in Excel. Everything else that is in white I have added using basic Excel functions. The first thing you need to do is to create a column labeled the lower limit and one upper limit. There is no easy way to do this. It is much faster just to go through and type in 18, 29, 40, etc. and then 28, 39, 50, etc. Much faster than trying to create an Excel formula to parse that although you can do that. The midpoint you can almost do in your head just by expecting. Looking at that, that is a class width of 10, half of 10 is 5, 5 added on to 18 is 23. But you may run into a class width that is not quite that easy to do in your head and so that is the reason I break things out. The midpoint I use just as simple formula is equal to the lower limit plus the upper limit minus the lower limit divided by 2 and that gives me 23 and then of course I just copy that formula down to give me the midpoints which is one of the answers they require. The next column I label relative frequencies and you need to be careful with this. It can be confusing because of the way that my stat lab and the text uses the terms relative frequency, cumulative frequency, and cumulative relative frequency. You need to differentiate those latter two. The relative frequency is just the number of counts in that particular class divided by the total and in this case it is B2 which is the count in that first class divided by the total. The total down here I got using the Excel sum function, sum B2 to B28. And then in this cell the dollar signs mean I lock that down using the F4 key or just manually inserting the dollar signs which means that as I copy down this formula you'll see that the relative cell changes appropriately but we've locked down the total so that as I copy this down I get the right relative frequencies and the relative just means what percent of the total are the counts in that particular class. The thing I saw a lot of students miss is this next column, the cumulative frequency. A lot of people gave me the cumulative relative frequency. You need to differentiate the two. Cumulative frequency refers just to frequency which is the counts. So this is the cumulative count starting with the number in the first cell and then adding on the numbers in the subsequent cells G2 plus B3 and then all the way down G3 plus B4 until you get to the total 365 which hopefully matches that. If they had asked for a cumulative relative frequency and I'll just show you that C, C, I'm going to call it CRF would be equal to the relative frequency in the first cell and the second cell would be that plus the relative frequency there and you copy those down and they should equal one. That's the cumulative relative frequency and a lot of folks gave me that answer instead of the cumulative frequency. So be careful of that. Look for that term cumulative frequency just means the sum of the counts. Cumulative relative frequency means the sum of the percentages. So I hope that helps.