Education Technology

The Women's 5000 Meter World Record Progression: The Median-Median Line

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