TASK #4 Math II - Standing Long Jump Background Information: The standing long jump is an athletic event that was featured in the Olympics from 1900 to 1912. In performing the standing long jump, the springer stands at a line marked on the ground with his feet slightly apart. The athlete takes off and lands using both feet, swinging his arms and bending his knees to provide forward drive. In Olympic rules, the measurement taken was the longest of three tries. The jump must be repeated if the athletes falls back or uses a step at take-off.

The men’s record for the standing long jump is 3.71 meters (12 ft 2 in). The women's record is 2.92 m (9 ft 7 in). What is your class’s record?

Men and women are often separated in the Olympics and also in high school sports for various reasons. In terms of the standing long jump, do you think that they are separated due to the reason that men in general jump farther than women. Or, do you think that men can jump farther because they are generally taller and have longer legs than women?

Collect Data: Jump three times according to the method described above. Record the class information in the table below.

Create a ‘back to back’ stem and leaf plot at the right that compares: A. Students with shorter legs to longer legs B. Male students to Female Students.

Male Leg Length 37” or shorter Female Leg Length 37” or shorter Leg Length (in.) (Waist to Floor)

Jump Distance (in.) (Best of 3 Jumps)

Leg Length (in.) (Waist to Floor)

Jump Distance (in.) (Best of 3 Jumps)

Male Leg Length taller than 37” Female Leg Length taller than 37” Leg Length (in.) (Waist to Floor)

Jump Distance (in.) (Best of 3 Jumps)

Leg Length (in.) (Waist to Floor)

Jump Distance (in.) (Best of 3 Jumps)

Mean Jump Distance of all

students 37” Leg Length or shorter:

Standard Deviation Jump Distance of all

students 37” Leg Length or shorter:

Mean Jump Distance of all students taller

than 5’5”

Standard Deviation Jump Distance of all

students taller than 5’5”

Leaf of students with Leg Length

37” or shorter Stem

Leaf of students with Leg Length taller than 37”

1 2 3 4 5 6 7 8 9 10 11 12 13

Leaf of Males

Stem

Leaf of Females

1 2 3 4 5 6 7 8 9 10 11 12 13

Mean Jump Distance of all males

Standard Deviation Jump Distance of all males

Mean Jump Distance of all females

Standard Deviation Jump Distance of all females

Original Task developed by Georgia Department of Education 2008 © Math 2 – Unit 4 Modified by M. Winking e-mail: wiseone@mindspring.com

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Explain how the distributions of jump lengths compare between students with longer and shorter legs.

Explain how the distributions of jump lengths compare between males and females.

Make a scatter plot of all of the data points of (Leg Length, Jump Distance).

Describe the correlation.

Using your calculator find the least squares regression line and correlation coefficient.

o Starting at the home screen of the TI-83/84, we will have to set up the calculator. To do this push STAT , 5 , ENTER. Then, to enter the data push STAT, ENTER which will bring up a table.

o However, the list may contain data from a previous use. So to clear the list press the , this will highlight the “L1” at the top then press CLEAR , ENTER. This should clear the “L1” list. We will need to the same for any other lists we intend to use. Finally, we can start entering the data we collected earlier.

o Next, we can create a scatter plot of the data. To do this push 2nd , Y= , which will

bring up the following menu shown at the right.

o Press 1 . Select the “On” position by moving the cursor over “On” and push ENTER (as shown at on the last screen at the right).

o To view the scatter plot, press ZOOM , 9 . This will select the appropriate

window range that will show the entire scatter plot.

Leg Length

Jum

p D

ista

nce

Highlight L1 and press CLEAR, ENTER

Original Task developed by Georgia Department of Education 2008 © Math 2 – Unit 4 Modified by M. Winking e-mail: wiseone@mindspring.com

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o Now, we will have to determine if the line regression trend line is a good fit. To help make this determination we need to turn the diagnostic tools on. To first turn on the diagnostics push 2nd , 0 . Then, push the , key until the arrow points at “DiagnosticOn” and push ENTER twice. (You can also press ALPHA , x-1 to have the

catalog skip to the “D’s”)

o Next, press STAT , , 4 , ENTER. “r” represents the correlation coefficient. The closer the value is to 1 or -1 the more linear the data.

o We could super impose a graph of the equation over the top of the scatter plot by putting this equation into Y= . Rather than re-typing the equation in by hand you can paste the equation by first placing the cursor by Y1=, and then pressing VARS , 5

, , , ENTER,GRAPH.

o We could use the trend line to make predictions by pressing TRACE or we could use the trend line as a sliding scale ‘benchmark’ to see which jumps are above average based on leg length.

Original Task developed by Georgia Department of Education 2008 © Math 2 – Unit 4 Modified by M. Winking e-mail: wiseone@mindspring.com

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