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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video, you will be able to understand scatter plots and line graphs. You will also be able to use them to tell people a story about what you see and observe. You will also be able to read them.

Look up at the night sky, and what do you see? You see a bunch of stars everywhere. Now draw a line straight up and down and draw another one going left and right, and you have yourself a scatter plot of the locations of your stars. In math, we define a **scatter plot** by calling it a graph of points that show the relationship between two different pieces of data.

Going back to our night sky illustration, we see that the left and right line that we drew in the sky can stand for the left and right locations of the star, and the up and down line can stand for the up and down locations of that same star. So, a star that we see at point (1, 2) on the graph is located 1 point to the right of the center of the graph and 2 points up.

Instead of having the horizontal and vertical lines intersecting at the center, our scatter plots will have the up and down line and the left and right line meeting at the bottom left corner, and all our points plotted in the space to the upper right of that intersection.

The axes are generally labeled with the information that they represent, and the scatter plot will have a title explaining the point of the information presented. Looking at our scatter plot, we see that the scatter plot shows the number of donuts sold depending on the number of customers served. We see that each of our axes is labeled with what that particular axis is about. Our horizontal axis, the one that goes sideways, also called the **x-axis**, tells us the number of customers that are being served. Our vertical axis, the one that goes up and down, called the **y-axis**, tells us the number of donuts sold.

To read a point on this scatter plot, we look at a particular point and we draw an imaginary line straight down and another one straight to the left to find out what information that particular point contains. The one point I see that is on the line that goes from 60 on the vertical axis tells me that for this particular point, 60 donuts are sold when 20 customers are served. That is how you read one particular point on the scatter plot.

But the beauty of the scatter plot comes when we take a bird's eye view of matter. So, looking at the scatter plot as a whole and looking at all the points together, I see that there really isn't any pattern to the donuts sold. I see that sometimes more donuts are sold even though there are fewer customers.

How am I getting this information? First, I look to see if the points form a pattern or if they were scattered all over the place. In this case, they are scattered all over the place, so there is no pattern to the donuts sold. Second, I compare the points to one another. What I see is that the points where there are fewer customers are sometimes higher than the points for more customers.

Specifically, I am looking at the points for 10 and 30 customers and comparing it to the points for 35 and 40 customers. The points for 10 and 30 customers are higher than the points for 35 and 40 customers. Thinking about selling things to people, I would think that more customers mean more sales, but I see this is not necessarily the case. You can get a lot of information by reading the scatter plot as a whole.

Now, if you wanted to create one for yourself, you would look at your data. In my case, I have a number of customers and a number of donuts sold for each number. I then plot each data point on my scatter plot the same way I would plot on the Cartesian coordinate graph. I look for the number of customers, and I follow an imaginary line straight up until I reach the number of donuts sold that I want and then I place a point there. I do this for all my points and then I am done.

You can see how useful scatter plots are at showing information. Business people use them to see how their business is doing, teachers use them for their students and scientists use them to look for patterns. All kinds of information can be placed on a scatter plot to see if there is a pattern and to look at the information as a whole.

Let's talk about line graphs now. They're a bit different from scatter plots. A **line graph** is a graph that shows information via a connected line. Usually, line graphs show data that occur over time. The data points keep moving to the right, and the data points are connected with a line. Just like scatter plots though, the x and y-axes are located at the far left and far bottom of our graph. The points are plotted the same way, as well.

The only limitation that a line graph has is that there can only be one point for each value on the x-axis. Scatter plots can have more than one point for each x-value. Looking at our line graph, for example, we have a point for the value of 2 on the x-axis. Because we have a point there, we can't have any more points that also have an x-axis value of 2.

What we've used our line graph to show is the speed of a car as it speeds up from 0 seconds to 6 seconds. We see that the car started from 0 miles per hour and ended at 60 miles per hour at 6 seconds. That's a fast car! By looking at the line graph, we can see how fast or how much something changes just by looking at our line.

Line graphs are often used to show anything that happens over time, such as population growth over time or your bank account balance over time. And yes, how fast your car can go in 6 seconds.

Now that we've covered both scatter plots and line graphs, let's review what we've learned. A **scatter plot** is a graph of points that show the relationship between two different pieces of data, while a **line graph** is a graph that shows information via a connected line. Both have a horizontal axis called the **x-axis** and a vertical axis called the **y-axis**.

Both use the **Cartesian coordinate graph**, which looks like graph paper with a darkly colored horizontal line, and a vertical line that acts as our x and y-axes and lets us pinpoint specific points on our graph. Both are good for getting information at a glance. Scatter plots are useful for sharing information and looking for patterns from observations, while line graphs are good for seeing changes over time.

The information in this lesson could provide you with the knowledge necessary to:

- Explain and graph a scatter plot
- Discuss and graph a line graph
- Compare a scatter plot with a line graph

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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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