"Old Vehicles In Exercises 31–34, use the figure shown at the ...

Question

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Table showing the average age of vehicles on U.S. roads from 2014 to 2021, with years and corresponding ages listed.

Scatter Plot Construct a scatter plot of the data. Show y and x on the graph."

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So, first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. The following table displays the average age in units of years of vehicles on roads over 8 different years. Year 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021. Average vehicle age in years, 11.4, 11.5, 11.6, 11.7, 11.7, 11.8, 11.9, 12.1. Construct a scatter plot of the data above, then plot the parentheses X bar, where X bar is the mean of the years and Y bar is the mean of the average vehicle ages. Awesome. So it appears for this particular problem we're ultimately asked to create a scatter plot of this data that is provided to us in this table by the prom itself. So essentially we're going to be taking this table that is given to us by the prom itself, and we're asked to create a scatter plot of this data that is provided to us, and we're also asked specifically to plot the parentheses X. Y. And in in order to do that, since we're gonna be plotting this point, we're gonna use a different color to indicate that point because that's a specific. Part of the problem that we're asked to solve for. So with that in mind, now that we know that we're ultimately trying to solve for two separate things, so essentially we're trying to create this scatter plot that's the main part we're trying to solve for. And in our scatter plot we're asked to indicate the parenthesis X Y bar. So with that in mind, our first step that we need to take in order to solve this particular problem is we need to compute the mean of years which we're trying to solve for X bar first. So once again, X bar is the mean of years, and X bar, the mean for the years, is equal to 2014, and we're gonna take 2014 plus 2015. Plus 2016 plus 2017 plus 2018 plus 2019 plus 2020 plus 2021. Fantastic. And then we're going to divide everything by 8 because there are 8 different data points. And when we do, we will determine that X bar. is equal to 2017, so 2017.5, when we perform that calculation in our calculator. So now, our second step now is we need to compute the mean of the ages. So we need to solve for a Y bar now, and Yb bar once again is the mean of ages, so we need to take 11.4 plus 11.5 plus 11.6 plus 11.7 plus 11.7 plus 11.8 plus 11.9 plus 12.1. Fantastic. And once again we have to divide everything by 8. And when we do, we will find that Y bar is approximately equal to 11.71 when we round to two decimal places. Fantastic. So now our third Step is we need to determine the mean point, which is one of our final answers that we're ultimately trying to solve for. So we're trying to solve for parentheses X, Y, and this is our mean point and our mean point will be equal to parentheses 2017 or 2017.50, 11.71. And that's a combination of the two values that we solve for together earlier. So now we're at the point in our problem where we can safely graph our scatter plot. So we need to plot the eight different points on our scatter plot, and we need to mark our parentheses X Y bar. As a different color on our scatter plot. Once again, we're going to take parentheses 2017.50. 11.71. We're going to indicate that plot that point on our scatter plot in a different color to indicate the means. We're asked to plot this specific point in our scatter plot as part of our final answer, and when we do, we should be able to produce the following graph. It should look as follows. So it's very important whenever you graph your scatter plot that you indicate your X and Y axis. So our x axis indicates the year from 2013 to 2022. It's sometimes it's really good to do a year before your data points start and a year after, so you have a little bit of a gap, so it looks more organized on your graph. And our Y axis indicates the average vehicle age in years, so it's important too when you label your axises that you label the units, and you also put a title for each of your axis, so you know what each thing is measured, so which which each axis is measuring. And as you can see for average vehicle age, we have it start at 11.3, going up to 12.2. And we have our 8 data points labeled in blue dots. And then we have our mean point, our mean point, which is parentheses X Y is equal to 2017.50.11.71 indicated in orange. And that's it. That is our final answer. So this problem is very easy to solve for as long as you have a strong understanding how to create a scatter plot, and you can easily use Microsoft uh you can use Microsoft sheets, or you can use sheets in Google or spreadsheet to plug in all your data points and have the computer software produce a graph for you or you can create one by hand. But as long as you understand the basics of creating a scatter plot, solving a problem like this is very easy to do. And that's it, that's our final answer. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

"Old Vehicles In Exercises 31–34, use the figure shown at the left.

Scatter Plot Construct a scatter plot of the data. Show y and x on the graph."

Key Concepts

Scatter Plot

Independent and Dependent Variables

Trend Analysis

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