# Activities

• • • ##### Subject Area

• Math: Algebra I: Linear Functions

• ##### Author 9-12

60 Minutes

• ##### Software

TI InterActive!™

• ##### Other Materials
This is Activity 2 from the EXPLORATIONS Book:
TI InterActive! Math for High School

## 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.

• 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