Sketching a Scatter Plot, sketch a scatter plot of the data shown in the table. The table shows

Sketching a Scatter Plot, sketch a scatter plot of the data...

Key Concepts

Scatter Plot

A scatter plot is a graphical representation used to display the relationship between two quantitative variables. It involves plotting individual points on a coordinate plane, where one axis represents the independent variable and the other the dependent variable. This allows viewers to easily observe patterns, trends, or correlations in the data and can help identify anomalies and clusters.

Cartesian Coordinate System

The Cartesian coordinate system is a framework that uses two perpendicular axes, typically labeled as x and y, to define the position of points in a plane. Each point is specified by an ordered pair of numbers, which represent its location along the horizontal (x-axis) and vertical (y-axis) dimensions. This system is fundamental for graphing data in scatter plots.

Independent and Dependent Variables

In data analysis, the independent variable is the one that is manipulated or represents the input, while the dependent variable is the outcome or response that is measured. Plotting these variables on a scatter plot helps to visually analyze how changes in the independent variable may affect the dependent variable, revealing potential relationships or trends.

Data Visualization

Data visualization is the practice of representing data through graphical elements like charts, graphs, or maps to communicate information in a clear and efficient manner. It is a crucial tool in data analysis and interpretation, allowing viewers to quickly grasp complex data sets by revealing patterns, trends, and outliers that might not be apparent from raw data alone.

Transcript

00:03 We are given a table of data and we are asked to sketch a scatterplot of this data.

00:11 So the data tells us the lowest temperature on record and a certain location for each month, where the months are labeled using numbers 1 through 12.

00:24 So for example, 1 means january.

00:30 Now, in order to sketch a scatterplot of this data, we'll have to draw our cartesian plane.

00:35 And to do this, we'll draw the x and y axes.

00:39 Now, notice that on our x -axis, where we have the months, the months only range from 1 to 12, so it makes sense to only draw the right side of the x -axis.

01:01 And we see that this ranges from 0 at the origin up to 12 on the right, and let's divide this up into 12 parts.

01:11 So we've got halfway between 0 and 12, is 6, halfway between 0 and 6 is 3, and so on.

01:20 Then we divide 0 3 into thirds, so we have 0, 1, 2, 3, and so on.

01:37 Now on the other hand, we see from the table that our temperature data has a much larger range than our month data.

01:44 So our temperature can range anywhere from negative 39 degrees fahrenheit up to 35 degrees fahrenheit.

01:50 Height.

01:51 So i want to draw both the top and bottom parts of the y -axis.

02:00 And we'll want the y -axis to range from approximately negative 40 to positive 40.

02:25 I'm sorry, i'm having some issues at the graph here.

02:41 I'm actually going to move the y -axis over slightly.

02:46 The same principles still apply.

03:07 And i'm not going to divide this up into 40 segments above and below the x -axis, partially because of time, but also because i don't think it's going to really clarify the data much more than we need to.

03:23 So instead, i'm just going to divide this up into four parts.

03:28 So we have intervals of 10 on the y -axis.

03:33 So we have halfway between 0 and 40 is 20, halfway between 0 and 20 is 10, and so on.

03:51 And now that we have our x and y -axis set up, we can sketch our scatter plot.

03:57 So for each row in this table, this corresponds to a point in our scatter plot, where the x coordinate of the point is the month, and the y coordinate of the point is the temperature of that row.

04:23 So, for example, our first row is 1 -39.

04:29 Which corresponds to the point 1 negative 39 in our cartesian plane.

04:37 So, in order to find the location of this point, first i'll draw the vertical line at x equals 1, and then i'll also draw the horizontal line at y equals negative 39, which lies slightly above y equals negative 40.

04:55 And i'll find where these two lines intersect.

04:57 And we see from a graph here that our two lines intersect here at this green point.

05:04 And so i'm doing some of the drawings that i made.

05:10 This is the location of our first point, which, because we have a lot of points to draw, i'm not going to label it...

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