Analyzing Scatter Plots

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I like to introduce scatter plots visually at first.  Students can really start talking about what the data means when they realize that some things are associated, and others are more random.

So one time I figured I would try something new; something to do BEFORE looking at the different types of trends; something the opposite of visual, something blind.  So I gave my students a full sized piece of graph paper, told them to work in pairs and had them draw the x and y axes to show quadrant 1.  Most relevant data for people occur in this quadrant, and it provides a nice large area to create the plot.  Then I told one of the students to uncap a marker and put on a blindfold.  This student had to place dots on the graph.  The other student could direct them in case they went off the paper, but the idea was to place a bunch of dots on the graph.

I then gave prompts to different groups.  Some guiding students told the blinded student to put dots all over the place, completely random.  Other students could prompt their partner to try to make a group of dots in a line going up, or a line that started high and the dots traveled down.  The key was that these trends needed to be made up of a series of dots – a scatter plot.

It was great!  When the students took off their blindfolds we had a bunch of scatter plots to observe and analyze.  I know that the plots were not created with data, but the trends were there and we could see patterns of how to analyze scatter plots.  I was able to show scatter plots of data and we then thought of various ways to label each axis.  For example, if we had a scatter plot showing a positive association, I asked about what type of data this could represent.  An example of positive association could be the larger your feet, the taller you are.  So we talked about how the x could be foot size and the y could be height.  Students start to discuss how some of the plots have stronger correlation and others kind of look like a line, but the dots seem looser.  Discussion and analysis grow from our conversation and observations of the different patterns of dots.

So, since the visual plot lends itself to description and analysis, I decided to make a BINGO game to help students find patterns, learn keywords and match up descriptions and analysis for various trends and data.

Set up for Analyzing Scatter Plots Activity 

  1. Have examples of scatterplots available to show the various relationships and help with analysis and discussion.
  2. Pair up the students and provide blindfolds or something to shield their eyes.
  3. Give each group blank graph paper to draw x and y-axes to show quadrant 1.
  4. Give each group a marker, to easily make dots on the graph.
  5. Provide each student a BINGO board with terms.
  6. Provide tokens or cheerios, or some sort of tool to mark their boards.  (If you have paper protectors, then students can slip the BINGO cards in the clear sleeve and mark their boards with a dry erase marker and wipe it off to play again).
  7. Print out calling cards or project each scatterplot for the students at random.
  8. Have small prizes, pencils or stickers for the winners.
  9. Provide each student with the Analyzing Scatter Plots Worksheet.

Launch the Analyzing Scatter Plots Activity

Tell your students that they will be creating their own scatterplots, but first they need to draw the x and y axes on the graph paper to create quadrant 1 of the coordinate plane.  See example below: (create an image similar to the one below, but maybe make it look like a piece of graph paper?)

Now, have the students put on a blindfold and uncap a marker.  Hand out various instructions to the guiding, unblindfolded student, so that you will end up with different scatterplots.

Instructions include:

  • Place 15 dots as randomly as you can, all over the grid
  • Start by placing dots close to the lower left corner. Try to form a line of 12 -15 dots going up and to the right
  • Place between 12-15 dots in a zig zag
  • Place 12-15 dots in a straight line
  • Place 12-15 dots in a line that goes down from the top
  • Place 12-15 dots in a group

Once the scatter plots have been made, have the students take off their blindfolds and look at their work.  Then start asking questions and have them discuss what they see.

Here are some questions that should help spark discussion:

  • How would you describe the trend of your graph?
  • What do you think a group of dots clustered together along a line would be called?
  • Outliers: Do there appear to be any data points that are unusually far away from the general pattern?
  • If you drew a straight line through the dots, and kept it as close to as many points as possible, what direction would it go? Which graph seems to have a line or trend that would have a negative slope? (decreasing) A positive slope? (increasing)
  • Which of these scatter plots could be data collected where the x axis is the age of a puppy from birth to age 3, and the y axis is the weight of the puppy? Why?
  • Which of these show no association of data, and it is difficult to predict the outcome?
  • Does it appear to have a linear or nonlinear association?
  • Let’s look at some of the positive trends or associations – Do they appear to have a strong or weak association? What’s the difference?

Tell the students to record keywords on their worksheet as they talk and think about the graphs.

Keywords:

  • Positive association
  • Negative association
  • Outlier
  • Cluster
  • Trend
  • Weak association (positive or negative)
  • Strong association (positive or negative)
  • Perfect positive association
  • No association
  • gap

Once you have shared and recorded some keywords, you can show them some scatter plots and trends.  You can also ask for examples of data that may present itself in the various ways.

Here are some examples of scatter plots:

Note: The above links will take teachers to online samples.

Tell the students that they will practice their analysis of scatter plots by playing BINGO, so have their cards out and ready to play!

BINGO PLOTS: Analyzing Scatter Plots Activity

After the blindfolding activity, make sure the students have some of the keywords written on the worksheet.  Tell them to keep the worksheet out while they play BINGO in case they want to add it to their list.

Tell your students to have their BINGO cards out and ready to mark.  They can all mark the free space before they begin.

(Note: Bingo cards can be found here )

Explain that you will show a scatter plot and the students must find the matching term.

You can decide whether to play any line, a diagonal, a  + or full board.  (I recommend playing any line, at least for the first game.)

Remind students to shout BINGO!  And winners can check their analysis and win a prize!

Pick a card. Hold it up, or project the scatter plot on the board and give the students time to find a match on their board.

Reflecting on the Analyzing Scatter Plots Activity

Discussion naturally results from the blindfolded introduction.  You can also review the different trends of data that can occur.

Ask questions about trends in data or predictions of what a scatter plot might look like for certain data.

For example:

  • What would you expect a scatter plot for shoe size and height?
  • Shoe size and birthday?
  • Baby weight and age in months?
  • Age and income?
  • The weight of a baseball player and the number of homeruns he has?
  • The speed of a swimmer and the length of his/her toes?
  • The size of a dog and the amount of food he/she eats?

Students should complete the questions on the worksheet as well.

Extensions

  1. Have students research and find a scatter plot for each of the following: Positive correlation, negative correlation, no correlation, linear relationship, non linear relationship. The scatter plots that they find must have labeled axes in order to show what is being compared or analyzed.  These can be found in the news or in an area of interest such as sports.
  2. Have students choose data to collect.  They can collect data directly, such as ask questions and take measurements in a survey, or they can look up information online. Students should plot their data in a scatter plot and then analyze the data that they collect.  (Some example could be:  hair length and age, car price and age of car, size of car and gas mileage)
  3. Read the website http://thedailyviz.com/tag/scatterplot/ , analyze and discuss a scatter plot that you found interesting.

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