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Problem 20 Medium Difficulty

The table shows the number of people per day who died from SARS in Singapore at two-week intervals beginning on March 1, 2003.
(a) By using an argument similar to that in Example 4, estimate the number of people who died of SARS in Singapore between March 1 and May 24, 2003, using both left endpoints and right endpoints.
(b) How would you interpret the number of SARS deaths as an area under a curve?

Answer

a.left $14[0.0079+0.0638+\cdots+0.4630]$ right $14[0.0638+0.1944+\cdots+0.2897]$
b. see explanation

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Video Transcript

So problem. 5 20. We have a data chart here that shows people who died per day From SARS in Singapore. So we've got two columns of data the date and that is measured in every two weeks. Every 14 days. And then we have deaths per day. So we want to look and say can we estimate this? And they ask us to get an estimate using two methods here, using the left some and then also using the right some. And what I mean by that is if you take the data and you look at it in rectangles, okay? So if I use the left point of that to estimate the height versus the right point to estimate the height. Okay, So if I'm using the left point, that means that you start with your first height. That's the left side of this rectangle. So that's going to be what is the distance? So if I look at the distance between each of these dates is 14 days. So I can just write 14 1 time out here because that's going to be the width of each rectangle and then the height will be determined by the data element on the left. So that's going to be zero 79 Plus .638 plus .1944 Plus .44 35 Plus .562 plus 4 +630 plus point 4630. So that's going to give me my left some When I put all of that data in and then on the right some it's just going to be the same with 14. But I'm going to start with the right side of that first triangle. So it's .06 38 Plus .19 44 Plus .44 35 Plus 5620 Plus the last one with its 463 out To me. 463 Oh. And then the last one there .2897. Yes. So this will be the difference between the left some and the right. Some and you can control this out. The next question they asked. How would you interpret the number of SARS death as area under a curve? So I've got discrete data you know that is here and it's not necessarily drawn to scale but data under a curve. Well if somehow if I could somehow come up with a curve you know I could fit a curve there that might do if I could fit a curve. This continuous then I have the ability to look at these rectangles and make them increase the number of rectangles. Okay so in this case if I look at this these are all positive. You know death is a negative concept but the numbers are all positive. So all of those numbers are sitting above the X axis. So if I had a curve or some kind of extrapolation or some kind of model, then I could divide that up in rectangles, add the sum total of all of the rectangles and that would approximate the area under the curve. But right now I only have the 1234567 discrete data points. So that means I can use six rectangles or six rectangles in the absence of having a curve. So having a curve then I can divide into more rectangles. Get a more precise estimate for the area under the curve, which would be the total number of deaths. So in this case when you add up all of these, you're getting the total number of deaths Over that time frame from March one To May 24