Scatterplots Scatterplots
Objective: When done with this lesson, you will be able to you will be able to create a scatterplot to display a set of data and determine what, if any, type of correlation the data exhibits.
Approximate completion time: 3 hours
So far in this unit we have considered how coordinate systems locate items. Did you know that you coordinate systems can be used to display information and make conclusions?
Using the same principles we used to locate objects, we can graph information. Take a peek at this graph.
Do you notice that:
- The graph does not describe the location of any object, but rather it displays information.
- The graph has each axis labeled clearly. (Both have the type of measurement with units included.)
- The graph has a title that helps bring meaning to the graph.
- There appears to be a strong relationship between the time and the height in the graph. The plotted points are not random.
- The graph can be used to make predictions. (Do you think the sunflower from the graph will grow to be 300 cm tall?)
- The points are not connected. (Do you suppose the height was continually measured?)
BACKGROUND TERMS:
When working with scatterplots, or graphs for that matter, the following terms are important.
- Horizontal axis
- Vertical axis
- Labels
- Units
- Scale
- Title
Look closely at the example above and you will find each of those items.
What is the vertical scale?
What are the vertical axis units?If you answered 90 for the vertical scale and "cm" for the units, then you're right!
INVESTIGATION #1:
You will be turning in your results from this investigation, so open up a new word document to record your results.
The number of power outlets in a room seems to be related to the size of the room. You will be investigating this relationship.
Consider at least 7 different rooms in your house or other buildings.
1. Collect data and complete the following table.
# of power outlets
Perimeter of room (in feet)
2. Plot your data on a graph.
To plot your data, choose one of the following:
- use a program like Microsoft Excel (quick tutorial here).
- use graph paper of your own and take a digital image (scanner or camera)
- use digital graph paper and a program like Microsoft Paint to do your plotting. (This grid would work well if you don't have your own.)
Please define your horizontal axis to be the "perimeter of the room" in feet. Don't forget the labels for the vertical axis or your graph's title.
Be careful on how you choose the scale of the graph. You may want to have the horizontal scale be different than the vertical scale.3. Describe any pattern you see in the data.
4. Explain how the graph does or does not support this statement: "The number of outlets in a room depends on the size of the room."
MORE BACKGROUND TERMS:
Scatterplots, like the one you made in investigation #1, show the relationship between two variables or data sets.
Did your scatterplot in investigation #1 show a positive correlation?
Scatterplots that show either a positive or negative correlation often have a line of best fit drawn. Did you see that in the negative correlation example? Could you draw in a line of best fit for your investigation #1 results?
So in effect there are five different ways to describe correlation:
- Strong Positive Correlation
- Strong Negative Correlation
- Weak Positive Correlation
- Weak Negative Correlation
- No Correlation
THINKING:
Be careful on what you read from a graph. Two data sets might have a strong correlation, yet that does not speak to the causes of that relationship. All a scatterplot will show is that data sets are related or not related. A scatterplot will not tell you why they are related. There are often many factors to consider to determine causation.
