 Hi, this is Dr. Don. I have a few questions about how we construct histograms in this course. You will find if you do some research that there are a great number of ways to construct histograms. You need to pay attention to whatever statistics course and instructor you're working with. I'll show you one common way. We always start with getting the statistics for our sample. We get the count using the count function, the mean using the average, the standard deviation using the sample standard deviation, of course the min and the max. We calculate the range by subtracting the min from the max and in this problem I've given you the number of bins equal to 14 and I did that based on just my experience in looking at the data, something that would work. Selecting a number of bins and calculating the bin width are the reverse of that. If you know the bin width and you can calculate the number of bins can be somewhat of an art and you need to look at your data to come up with the best way. But there are some other techniques you can use. One to find the number of bins is called the square root choice and that's used sometimes in some Excel functions and it's just that the number of bins K is equal to the square root of the sample size N and I calculated it here and you would get 23.3 which would round up to 24, just the square root of the count. The other commonly used rule is called Scott's rule and it says the bin width is equal to a constant 3.5 multiplied times the standard deviation and divide that whole thing by the cube root of the sample size. And I did that here using just basic Excel and I get a bin width of .051. Remember because these are reciprocal. If you know the bin width you can calculate the number of bins and if you know the number of bins you can calculate the bin width. Going back to our particular sample I gave you 14 for the number of bins and then I calculated the raw width which is just equal to the range divided by the number of bins and that gave me a width of .099. And then I asked you to round it up to the nearest tenth and I used the roundup function here with the cell there L8 which is the value we're rounding and the comma one means round to one significant digit behind the decimal which be one tenth. The other concept you need to be aware of is whether or not you're being asked to do a closed lower open upper or a open lower closed upper type of intervals for your bins. Most commonly you will be asked to use the closed lower open upper and that's designated by a square bracket on the lower side and a common parentheses on the upper side. And what that means is that we use all the data points that are greater than equal to our lower bin limit but less than our upper bin limit. Our upper bin limit is not included in that particular interval. So how do we do that in this problem? I'm going to go here and click in this cell for the lower limit of my first cell equal and we just start with the min value there hit enter and that gives me the lower limit for the first bin. To get the lower limit of the second bin hit equal again I'm going to start with that value plus my bin width and that's going to be the rounded bin width there. Now I want to lock that down so I can copy this from there quickly using the function four key to get the double dollar size whoops hit that again there we go double dollar signs and that gives me my next lower limit. I'm going to drag this down all the way one past my number of bins to get what I call the over bin and that gives me my lower limits for this particular data set. Now with the upper limits because we're using this closed lower open upper that means this next upper limit cannot include the value that we would get by just copying the lower limit over to here. So what I like to do is just hit equal that next lower limit and then I'm going to subtract a value which would be appropriate for my data here. Now my data if you see has two decimal places and so what I want to do is subtract a very small value and I'm going to subtract one more decimal place which would be 0.001 in this case and hit enter and that gives me a lower limit so that when I use the standard excel histogram it knows that I don't want to include that 4.620 in this limit and all I've got to do there is just drag this down whoops to get my upper limits for the 14 bins and that's all I need to use the data analysis histogram tool so I hope this helps.