4.18: Scatter Plots
Have you ever wondered the temperature ranges in Alaska?
Well, believe it or not, the temperature in Alaska can have a broad range depending on where you live in Alaska. Take a look at this data for Juneau, Alaska. Here are the average high temperatures.
January 29 F
February 34 F
March 38 F
April 47 F
May 55 F
June 61 F
July 64 F
August 62 F
September 56 F
October 47 F
November 37 F
December 32
Now you can take these temperatures and look for a correlation. Each month of the year has a number and each temperature has a number.
Can you figure out if there is a positive correlation, negative correlation or no correlation?
This Concept will teach you all that you need to know.
Guidance
A scatter plot is a way of representing real-world data in a visual way. A scatter plot is a graph showing many data points. It allows us to determine if there us a relationship between pairs of data. A scatter plot can show a positive relationship, a negative relationship, or no relationship, as shown below.
Here is how we can determine the relationships between the data on a scatter plot.
- If the points on the scatter plot seem to form a line that slants up from left to right, it shows a positive relationship.
- If the points on the scatter plot seem to form a line that slants down from left to right, it shows a negative relationship.
- If the points on the scatter plot are scattered randomly, it shows no relationship.
For the first two plots shown above, you could draw a straight line through the points called a line of best fit. That line would not go through every point, but it would show the general trend in the data.
A teacher wants to know if there is a relationship between the amount of time her students spent working on a social studies report and the grade each student received. She surveyed 10 students and recorded the data below.
Student | Number of Hours Worked | Grade |
---|---|---|
Ahmad | 5 | 90 |
Becky | 3 | 80 |
Darrell | 3.5 | 80 |
Emma | 1 | 60 |
Guillermo | 4.5 | 90 |
Helene | 1 | 70 |
Kiet | 3 | 75 |
Nykeisha | 4 | 85 |
Ollie | 2 | 70 |
Zivia | 2.5 | 75 |
Make a scatter plot to show the data in the table.
First, make a scatter plot for the data. The teacher wants to know if the number of hours worked is related to the grade a student earned, so use the horizontal axis of the scatter plot to show the number of hours worked. In the table, the numbers of hours worked range from 1 to 5, so give that axis a scale of 0 to 6, increasing by intervals of 1.
Use the vertical axis to show the grades students received. The grades in the table range from 60 to 90. Showing every grade from 0 to 100 would make the plot very large, so include a break in the axis between 0 and 60. Use intervals of 10 for the rest of scale.
Plot a point for each pair of data in the table. For example, Ahmad worked for 5 hours and earned a grade of 90. So, plot a point at (5, 90) on the scatter plot. Do this until you have plotted all 10 data points and the scatter plot looks like this.
The scatter plot above represents the data that is in the table.
Now, let's interpret the scatter plot and use it to make a prediction.
Interpret and make a prediction based on the scatter plot you created.
a. Determine if there is a relationship between the number of hours worked and the grade received. If so, describe the relationship.
b. Suppose an eleventh student spent 6 hours working on her report. Based on the scatter plot, predict the grade you would expect her to receive.
Let's look back at the scatter plot.
Draw a line of best fit for this scatter plot. Remember, a line of best fit will not go through every single point on the plot, however, it will fit the general trend of the data. Here is how a line of best fit might look for this scatter plot.
The line of best fit slants up from left to right. So, this scatter plot shows a positive relationship between the data. That means that, in general, the longer a student spent working on the project, the higher the student's grade.
Now, let's predict what a student who spent 6 hours working on the project would probably receive as a grade.
Find 6 hours on the horizontal axis. Move your finger up. You can see that the line of best fit predicts that if a student works for 6 hours, she will receive a grade of about 100.
So, that would be a good prediction of the grade the eleventh student would receive.
Now make a few predictions on your own.
Example A
True or false. If there is a pattern to the ordered pairs, then there isn't a correlation in the data.
Solution: False.
Example B
True or false. If the data is plotted in a random way, then there is no correlation in the data.
Solution: True
Example C
Does a line of best fit on a plot with a positive correlation go up to the right or down to the left?
Solution: Up to the right
Here is the original problem once again.
Well, believe it or not, the temperature in Alaska can have a broad range depending on where you live in Alaska. Take a look at this data for Juneau, Alaska. Here are the average high temperatures.
January 29 F
February 34 F
March 38 F
April 47 F
May 55 F
June 61 F
July 64 F
August 62 F
September 56 F
October 47 F
November 37 F
December 32
Now you can take these temperatures and look for a correlation. Each month of the year has a number and each temperature has a number.
Can you figure out if there is a positive correlation, negative correlation or no correlation?
Looking at this data, it looks like there is going to be a positive correlation because until August, the temperatures continue to increase each month. But then in August, then begin to decline again.
We can say that there is no correlation to this data.
Vocabulary
Here are the vocabulary words in this Concept.
- Coordinate Plane
- a plane with four quadrants where locations are marked according to coordinates.
- \begin{align*}x -\end{align*}axis
- the horizontal line on the coordinate plane
- \begin{align*}y -\end{align*}axis
- the vertical line on the coordinate plane
- Origin
- the point where the \begin{align*}x-\end{align*} axis and the \begin{align*}y-\end{align*} axis meet
- \begin{align*}x-\end{align*}coordinate
- the first coordinate in an ordered pair.
- \begin{align*}y-\end{align*}coordinate
- the second coordinate in an ordered pair.
- Scatter Plot
- a data chart that uses points to show the relationship between data and events.
Guided Practice
Here is one for you to try on your own.
Look at the following set of ordered pairs. Would this scatter plot have a positive correlation, negative correlation or no correlation?
(1, 2)(3, 5)(7, 10)(9, 15)(4, 8)
Answer
This scatter plot will have no correlation because there is not a pattern to the values.
Video Review
Here is a video for review.
- This is a James Sousa video on scatter plots and includes a technology integration.
Practice
Directions: This scatter plot shows the relationship between the last digit of ten students' phone numbers and their vocabulary quiz scores.
1. Does this scatter plot show a positive relationship, a negative relationship, or no relationship?
2. How many students have a six as the last digit in their phone number?
3. How many students have an eight as the last digit?
4. How many students received a grade of 70%?
5. How many students received a grade of 60%
6. How many students earned 100%?
7. How many students earned a 75%?
8. True or false. No one earned below a 60%.
9. True or false. No one earned an 80%.
10. True or false. No one earned an 85%.
Serena wants to know if there is a relationship between a person's age and the number of DVDs they purchased in one year. She surveyed a group of people and recorded the data in the table below.
Person | Age | Number of DVDs Purchased |
---|---|---|
Person 1 | 18 | 14 |
Person 2 | 19 | 13 |
Person 3 | 20 | 13 |
Person 4 | 20 | 12 |
Person 5 | 21 | 11 |
Person 6 | 22 | 12 |
Person 7 | 22 | 11 |
Person 8 | 23 | 10 |
Person 9 | 24 | 9 |
Person 10 | 25 | 9 |
11. Use the grid below to make a scatter plot for the data in the table. Draw a line of best fit for the scatter plot.
12.True or false. The scatter plot shows a negative correlation.
13. True or false. The scatter plot shows no correlation.
14. True or false. The scatter plot shows a positive correlation.
15. If the trend in the scatter plot continues, predict the number of DVDs you would expect a 27-year-old person to buy in one year.
axis
The axis is the horizontal axis in the coordinate plane, commonly representing the value of the input or independent variable.coordinate
The coordinate is the first term in a coordinate pair, commonly representing the value of the input or independent variable.axis
The axis is the vertical number line of the Cartesian plane.coordinate
The coordinate is the second term in a coordinate pair, commonly representing the value of the output or dependent variable.Coordinate Plane
The coordinate plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin. The coordinate plane is also called a Cartesian Plane.correlation
Correlation is a statistical method used to determine if there is a connection or a relationship between two sets of data.line of best fit
A line of best fit is a straight line drawn on a scatter plot such that the sums of the distances to the points on either side of the line are approximately equal and such that there are an equal number of points above and below the line.Origin
The origin is the point of intersection of the and axes on the Cartesian plane. The coordinates of the origin are (0, 0).scatter plot
A scatter plot is a plot of the dependent variable versus the independent variable and is used to investigate whether or not there is a relationship or connection between 2 sets of data.Image Attributions
Description
Learning Objectives
Here you'll learn to make scatter plots of paired real-world data to recognize patterns and make predictions.