 Hi, this is Don, and I want to show you how to solve this problem in the 5.1 homework. This is a problem in which we need to create a histogram and then to calculate the mean and standard deviation. Now you can do this going through each of the formulas and taking the very deliberate approach to developing the histogram, calculating the upper and lower limits of each bin and the midpoint of each bin. But for our purposes here, you really can use the technology and answer the requirements of this problem without spending all that time. So let's go ahead, I'm going to click on the little icon here, and the first way I'm going to solve this in Excel, so I'm going to open that data. This is the Excel worksheet once the data opens. And the first thing we want to do is to sort this data so we can tell what is the maximum and minimum fairly easily. And we can do that clicking on the column to select that column and then going to data, A to Z sort. And we sorted it from smallest to largest, so our minimum value is 23378, our max value is 48052. So the first thing we want to do is to find the range, and the range is nothing more than the largest value minus the smallest value, 2476. We want to create, I'm going to double check, I think it says five classes. So we have five bins. And then we want to know the width of the bins. And that is the range, sorry, equal the range divided by the number of classes or bins, is 4934.8. Now when we're doing histograms, we want to use integer values, so we'll round that to, I'm just going to go ahead and use a formula, O, U, N, D, and the formula would be comma and the closing parentheses. And it rounds it to 4935, that's the width of our histogram. So what we need to do is to come up with the bins. Okay, we want to give Excel the upper endpoint for each of the five bins. So let's click in that cell and we'll calculate the first upper endpoint by going to the minimum value plus the bin width. And so our first upper endpoint is 28313. The next endpoint will be equal to the preceding endpoint plus the width again, but we want to make that an absolute reference, so I'm just going to click F4, and that gives us the second bin ending at 32248. Now because I've made the bin width an absolute reference, I can drag it down for the remaining three. And we get our bins' upper endpoints at 28,000 to 48,053, and we can check and see that that does cover everything since we're going from the min all the way to a bin that will include that final value. Once we have those upper endpoints, we can use the data analysis histogram, click OK, and we want to give it the data ranges, A1 to A16, I'm going to click on that little icon to insert that, and then our bin ranges, those five values there, click on that. We don't have labels, I want an output range, I'm going to click and put it over here, that point, insert that, and then we click OK. So we've got now our frequency distribution, 23632. So we can create our histogram. Now that we have our frequency distribution, we can create the histogram, and I'm going to just select those cells, the upper endpoints, and the frequencies, I'm going to go to insert recommended charts, and it comes up with a column chart, and that will give us the basics of a histogram, and we really could just stop here because in this problem, we're trying to see if the data is normally distributed, and you can tell that from this pattern right here. You don't have to go ahead and actually create a formal histogram. But just to show you how to do that, I'm going to double click on one of the columns and that opens the format data option, and here at the gap width, that's the major thing wrong with this histogram, I'm going to put in zero, and that should get rid of the gaps. I'm going to leave the data selected, I'm going to go here and click on the line and fill, and in this case, we want a border to be a solid line, and double check to make sure that's black, which it is, and so now we've got our basic histogram. If you were doing this to submit for homework, you would double click on the title and put in the right title. These are the upper bin widths. You could take a few minutes, and by using the lower limit and the upper limit dividing by two, you can come up with the midpoint and label these that way. Again, what we're trying to do is to see if our data is normally distributed, and it appears that way, and so if we go back into the homework, the histogram that matches that is this B, and again, they've gone through in detail and calculated the lower and upper and the midpoints, and you can do that. But for this purpose is we can just click B. I'm going to, next, part of the question that says we've got the right answer, continue, and is it reasonable to assume that the lifespans are normally distributed and why, and the correct answer is yes, because the histogram is symmetric and bell shaped. Click yes, check answer, fantastic, and we want the mean and standard deviation. So we're going to go back here to our data, and we can use the data analysis, I'm going to close out that chart data analysis tool again, and this time we click on descriptive statistics, okay, our data range, I'm going to select that data, insert it, and go down here, we need to check and make sure that we've selected summary statistics. The output range, I'm going to click on that, and I'm going to select that cell, insert that data, now we can click okay, and we've got our descriptive data. I'm going to widen that cell so you can see here, our mean is 35,296.9, and our standard deviation is 6,300.1. So that gives you the data that you need to answer this problem.