# Students Analyze Data With Scatter Plots

Scatter plot lessons can help students create different types of graphs by hand or with the aid of technology.

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Scatter plots are graphs that can be used to analyze a set of data each having an “x” and a “y” coordinate on the Cartesian plane. At the middle school level, students might first be introduced to scatter plots while studying different kinds of graphs. They can compare these types of graphs to histograms and stem-and-leaf plots. At the high school level, scatter plots can often be the starting point for regression analysis in specialized data projects of interest to students.

Older students might be interested in analyzing the rate of depreciation of a car by plotting the age of a car against its corresponding blue book value. Similarly, students could study the trend of how the population of a country, or of an endangered species changes over time. They could then predict future population projections after detecting a trend. Students often enjoy running certain experiments to analyze functions using scatter plot data. For example, they could measure how the height of stacked cups changes as one varies the number of cups stacked. Students might even run experiments on themsevles by measuring their heart rate after different time periods or types of exercise, and plotting those points.

If a teacher wants to use technology to examine scatter plot data, graphing calculators and certain kinds of spreadsheet programs allow students to see how certain families of functions (such as linear, exponential, or quadratic functions) best fit the data. For instance, the Macintosh spreadsheet program Numbers allows users to create a "trendline" and select from a linear, logarithmic, polynomial, power, or exponential function. Similarly, the TI-83 Plus graphing calculator allows students to create a regression model to approximate the relationship between two variables in two data lists, choosing from such models as linear, quadratic, cubic, logarithmic, exponential, logistic, and sinusoidal. Such technologies also allow for determining the correlation coefficient (r) and/or the coefficient of determination (r^2).

Scatter plots also allow students to identify clusters and outliers in data as well as determine correlation strength. A scatter plot unit may also be a good way for teachers to discuss the difference between correlation and causation with students. Here are some scatter plot lessons to get students started.

## Scatter Plot Lesson Plans:

Students use scatter plots to look at the correlation between heartbeat rate and aerobic exercise.

Students research unemployment data and construct a scatter plot. They then analyze what the plots can tell them about unemployment, and create a publication.

Mystery Liquids: Linear Function

Students collect data on the mass and volume of two “mystery” liquids. Then they construct a scatter plot of the data and determine linear equations for water and oil.

Da Vinci: Body Proportion Theories

Students measure each other’s height and wingspan and then create a scatter plot of the data. They then determine whether Leonardo da Vinci’s proportion theories are valid. Students then develop a clothing business whose sizes are determined by the plot results.

Students conduct experiments involving paper folding and M&M counting, and then use scatter plots to determine exponential models. Students then use their calculations to predict the future population changes of African Rhinos.