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XN US /o 4random sample "Dlestrag "ou6 days L recent year, conlidence L gasoline prices had a Aheean 8 H...

Question

XN US /o 4random sample "Dlestrag "ou6 days L recent year, conlidence L gasoline prices had a Aheean 8 H

XN US /o 4random sample "Dlestrag "ou6 days L recent year, conlidence L gasoline prices had a Aheean 8 H



Answers

Here are box plots of weekly gas prices for regular gas in the United States as reported by the U.S. Energy Information Administration for 2009, 2010, and 2011.
(FIGURE CAN'T COPY)
a) Compare the distribution of prices over the three years.
b) In which year were the prices least stable? Explain.

Okay. What we want to go ahead and do is, um what we know is that in 2013 the price of gas, um, in the United States, spite very early. Then gradually, um, dropped the average monthly price, um, incense per gallon of unleaded. And we're talking about just of unleaded regular. Glad gas is show in the following in the foot following graph. And so, um, we're gonna go ahead. I have it shown in, um, this graphing utility. And so this would be January, February, March, April, May, June, July, August, September, October, November, December. Okay, so this is what the graph looks like. And so what we want to do is one we want to impart a we want to find. Actually, we want to find the average rate of change in the price of gas. Um, permit for the following months. We want to do it from January to march. Okay, So if we go back to the graph we noticed in January were noted the month to be zero instead of one, it was 3 39 then in March, um, which is so February march? Right, right here. Martin, second month, which he actually is. The third month it was at 3 78 So what we want to dio is January is the 0.0 comma, um 3 39 and marches to comma 3 78 And so we know the average greater change is given by the difference of why. Why values divided by the difference in my ex values. So this is gonna give me 19.5. And so it's 19.5 cents per gallon permit. So that is the average. And so that means that the price of gas increased 19.5 cents per gallon from January to March. Okay? And so now what we want to do is we want to find the average rate of change from March two December. And so if we go back off course March waas the second month, Um and that waas, um 3 78 And so December is going to be the 11th month I'm in that 3 36 So we're gonna go, um, 11 to 3 36 So we're into 3 36 minus 3 78 divided by 11 minus two. And so we get this, we get a native 4.7 sense per gallon permit. And so we had a decrease in, um, the price of force 4.7 cents per gallon per month from March to December. And then we want to do from January to December. And so coarse December is 11 3 36 January Um waas 03 39 so zero and 3 39 and so is average is 3 36 on his 3 39 divided by 11 minus zero. So that is going to give us a negative 00.27 cents per gallon permit. So that means the price from January to December, even though it originally increase it, did have an overall average decrease of 0.27 cents per gallon per month in that year.

So they give us the price of gas in since on average per each month in the U. S. And they want us to find the average rate of change of the price of gas per month per gallon over each of the three time periods that they have listed there. So let's just go ahead and start with a well before we do that. It may be a good idea to actually list out what the's bunts are as a number, because we can't really subtract July from January. So January is the first month of in July should be the seventh, and then December would be the 12th. And you could always just count the tally marks to get those now for January to July. So we want the points would be one and then 3 29 and then for July at 74 35. And then let's just go ahead into December. So December is 12 1 95 suffer January. We're going to use the point for July in January, so it's gonna be 4 35 minus 3 29 if we just follow the average rate of change formula they give us in the book and then it be seven minus one. And so for 35 minus 3 29 10 7 minus 16 So divide those, and that should give us something around 17.67 cents to remember this is in dollars. But since and then for July to December, we want to use these two points. So it's going to be 1 95 minus 4 35 all over 12 minus seven. So we would have someone 95 minus for 35 is negative 240 then in the denominator 12 minus seven. Once we divide those, that should give us negative 48 since and then, lastly, will have January to December, and that's going to have 1 95 minus 3 29 all over 12 minus one, and so in the numerator would have won 95 minus 3 28 which is negative 1 33 Then we would divide by 11 in the denominator, not 1 28 1 or 3 29 I should say, uh, but you re divide those. That should give us negative 12.18 cents, so these would be the three average changes. Pour gas. Her month per gallon

Yeah. In this problem of scientific measurement we have given that sometimes ago a U. S. Citizen traveling in Canada observed that the price of regular gasoline was, this is 1.299 Canadian dollars per liter. So this is the price of gasoline is 1.299 Canadian dollars. So this will be Canadian dollars per liter. So this is per liter price per liter. And the exchange rate at the time was 1.1 Canadian dollar Per $1. This is equals two $1. Or we can say one U. S. Dollar. We have to calculate the price of Canadian gasoline in units of U. S. Dollar per gallon. So this would be just before the traveler had paid $3.759 per gallon in the United States. So this is 1.299 Canadian dollars. So this would be Canadian dollar. Or we can say this is Canadian dollars per liter. And now we have to convert into U. S. Dollars. So this would be one A US. Dollar makes. This is 1.1 Canadian dollars. And also we have to calculate this value in in gallon. So this would be Now we have to convert later in together. So this will be 3.7 85 liter, 3.785 L. makes a gallon. Mhm. And now when it's already the city close to 4.912912 US dollars. So this will be U. S. Dollars. Portugal. Um So this is the price of the gasoline in U. S. Dollar per gallon.

All right. So let's say we're given some data Which represents the average price of us gasoline from January 2008 Up until May 2011. We've graphed this data here and are asked to update the graft with more recent data, Comment on any trends in the average price of gasoline since May 2011. And finally asked to interpret the graph to see if there is an increase in the average price during summer months. So to update the data set with more recent data, you can head over to google and search for it. We can just search the average U. S. Gas price monthly. And this first result should give us data that we can quickly download and bring into our existing accession. So you can click download serious history here to download an Excel document. This will give us data on the U. S. Gasoline and diesel retail prices from the Energy Information Administration. We'll click on this data tab here and focus him on a column B. Here which represents the US all grades, all formulations, retail gasoline prices. You need to scroll down and get the data that we are missing. So Remember our data set contained the average price of gasoline from January 2008 Up until May 2000 so I'll get June 2011 and up until more recently. So to do this I'm pressing shift and the right arrow key and then control shift down to quickly select all this data. I can copy it with rosie but back into my original work fit and then paste this data below my existing data. Do so just taste it. You can see that more recent data is now in here to update the graph. I just need to go into the chart with design select data again just like my data here so this I can see my previous state has already selected. So I You control shit down again. It's looking the bottom of my day to sit. What country? Okay. All right. I just roll back up now. We can see. But the more recent data is now represented in my chart. So question # two. Let's comment on the trends in the average price of gasoline since 2011. So Since 2011, May 2011 or Dataset ended, we can see some increasing and decreasing trends up until about uh June 2014. In June 2014, we see a pretty significant decreasing trend up until about February 2016 where the trend reverses. We see generally increasing trend Until May 2015. The trend that switches again to a decreasing trend until about mm april 2020 where it starts to increase. So to answer the answer, this final question, does the graph show an increase in the average price during summer months? Um This one is open to interpretation a little bit. But using our data we can check this trend. So you see some increasing trends right about here. So this is from February 2016 to June 2016. So have some summer months in there in that increasing trend We see here is a little bit of an increasing trends of March two me, A little bit of summer months in there. We see it also here January two May, so we've got some summer months in there as well And then May 2022, 2020. So we do see another increasing trend there with you know, some of our summer months included there. So I would say it is valid that during summer months the average price does increase.


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