All right, So in this question, we are given data regarding the costs of deliveries and we want to find a range in the sample standard deviation for this dataset. Um and what I've done here, I was actually just organize the data from least to greatest, which is helpful because when we want to find the range, that's actually just going to be the biggest minus the smallest, so it's going to be 34, 70 -16 84. So if you organize it from lowest to highest, the highest to lowest, um it's very clear which ones those are, especially when we're dealing with a lot of numbers or what big numbers, it's good to sort that out. Um so this difference is going to be 1,786, that's going to be in dollars. So the range is $1786 to find the example standard deviation. Um Well, that actually relies on the square differences from the mean, so we actually have to figure out what the mean is and well the mean is just going to be the sum of all the terms. You add them all up and then divide by the total number of terms, which in our case is If you add them all up and divide by eight, that's going to give you a mean of $2,589.4 um and that gives you the average cost of a delivery. Well, the important reason we need to know the mean aside from giving us useful information about the data set, is that, like I mentioned, the standard deviation relies on the square differences from the mean, namely right for each data point, we are going to calculate the square difference from the mean. So we're going to subtract, so we're going to start with the first data point, subtract the means to 5 8 9.4. And we are going to find that square different. So we're going to square it. And in this standard deviation expression in the numerator is the sum of the square differences from the mean. So we're going to some Across all of our terms. So this is our second term -2 means this is our third term minus the mean squared minus mean tree. 94 Weird. Right? And you do this for all of your terms, right? Our denominator is simply going to be N -1. So and in this case is eight. So our denominator is seven. All right. Well, our setup is done. All we have to do now is political calculator. And be careful. That's also what computers are for their very helpful with this. But when you add all of that up and do your squares, you'll get three million and 84,000, 890 approximately. That's going to be divided by seven and that all simplifies to be $663.9 as extended deviation. And they accessed around 21 more data point or one more decimal than is provided. And that is precisely done. Yeah.