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?
Jump Distance (in.)
(Best of 3 Jumps)
Leaf of students
with Leg Length
37” or shorter
Female Leg Length 37” or shorter
Leg Length (in.)
(Waist to Floor)
Jump Distance (in.)
(Best of 3 Jumps)
Standard Deviation
Jump Distance of all
students 37” Leg
Length or shorter:
Male Leg Length taller than 37”
Leg Length (in.)
(Waist to Floor)
Jump Distance (in.)
(Best of 3 Jumps)
Female Leg Length taller than 37”
Leg Length (in.)
(Waist to Floor)
Jump Distance (in.)
(Best of 3 Jumps)
Mean Jump
Distance of all
students taller
than 5’5”
Leaf of Males
Standard Deviation
Jump Distance of all
students taller than 5’5”
Mean Jump Distance Standard Deviation Jump Mean Jump Distance Standard Deviation Jump
Distance of all females
of all females
Distance of all males
of all males

Leaf of students
with Leg Length
taller than 37”
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Mean Jump
Distance of all
students 37” Leg
Length or shorter:
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.
Original Task developed by Georgia Department of Education 2008 © Math 2 – Unit 4
Modified by M. Winking e-mail: [email protected]
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Stem
Male Leg Length 37” or shorter
Leg Length (in.)
(Waist to Floor)
Stem
Collect Data:
Jump three times according to the method described above. Record the class information in the table below.
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Leaf of Females
 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.
Jump Distance
 Make a scatter plot of all of the data points of (Leg Length, Jump Distance).
Leg Length
 Describe the correlation.
Highlight L1 and press
CLEAR, ENTER
 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
bring up the following menu shown at the right.
o Press
ENTER
2nd , Y=
, which will
. Select the “On” position by moving the cursor over “On” and push
(as shown at on the last screen at the right).
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o To view the scatter plot, press ZOOM , 9 . This will select the appropriate
window range that will show the entire scatter plot.
Original Task developed by Georgia Department of Education 2008 © Math 2 – Unit 4
Modified by M. Winking e-mail: [email protected]
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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 ,
,  ,  , 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: [email protected]
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