Activity Overview
In this activity, students will collect the Women's 5000 meter progression of world record data and find the median - median line and the linear regression for the data. They will investigate the appropriateness of each of the models.
Before the Activity
See the attached PDF file for detailed instructions for this activity
Print pages 13 -16 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Enter the year of each of the world records and each of the world record times in minutes as lists
Graph the time (y-axis) versus year (x-axis) data
Separate the first third of the data as group 1, second third as group 2, and last third as group 3
Find the median of each of the three groups and record the coordinates as (x1, y1), (x2, y2) and (x3, y3)
Find the slope and y-intercept of the line passing through points (x1, y1) and (x3, y3)
Find the equation of line y1 = mx1 + b1 and plot to see how well it fits the data
Solve y2 = mx2 + b2 and find the y-intercept of line passing through (x2, y2)
Observe line y2 is parallel to line y1
Check how new line y2 fits the graphed data
Define b3 = (b1 + b2 + b1)/3
Plot the line y3 = mx3 + b3 and see how well this median - median line fits the graphed data
Use linear regression function to curve fit the data
Compare the median - median line and the regression line, and note which one fits the data better
Observe that the linear regression line does not pass through any points in the data set
Note that the median - median line interpolates data better and that the linear regression is a better model to extrapolate the data
After the Activity
Students complete the Student Activity sheet.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary