IB Mathematical Studies 2014-Internal Assessment

Is there a correlation between the height of the 2014 University of Florida softball players and their stolen base

percentages?

Kaley RenslowCandidate Number: 001195-0067

Table of Contents

Statement of Intent………………………………………………………………………3

Raw Data………………………………………………………………………………...4

Mathematical Processes: Height Conversion……………………………………………5

Mathematical Processes: Correlation Coefficient……………………………………….6

Mathematical Processes: Correlation Coefficient Continued............................................7

Mathematical Processes: Scatter Plot.……...……………………………………………7

Mathematical Processes: Line of Best Fit.………………………………………………8

Conclusion……….………………………………………………………………………9

Works Cited……………………………………………………………………………...1

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Statement of Intent:

My aim is to discover whether or not the height of the 2014 University of Florida softball players and their stolen base percentages correlate. I am interested in this because I have played softball for the past thirteen years, and have witnessed numerous players, including myself, steal countless bases. However, I have never paid attention to whether or not height correlates with the number of times each girl steals a base, and am genuinely excited to conduct an investigation to find out.

Growing up, I dreamed of playing softball for the University of Florida, which is how I decided to use their team’s statistics in my investigation. I plan to access the University of Florida website in order to gather the names of the girls on the 2014 softball roster, their heights, and their stolen base percentages. After obtaining this data, I plan to organize it into a scatter plot, find the correlation coefficient, and draw a line of best fit. Using the correlation coefficient, I will be able to determine the strength of the correlation between the height and stolen base percentage of the 2014 University of Florida softball players. I also plan to utilize the chi-squared test in order find out whether or not their heights and stolen base percentages are independent.

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Raw Data:

Player Name Height (M) 1 Stolen Base Percentage2

Lauren Haeger 1.8034 0.429

Bailey Castro 1.7018 0.000

Jessica Damico 1.6256 0.000

Francesca Martinez 1.6510 0.000

Alyssa Bache 1.7780 0.000

Aubree Munro 1.7780 0.615

Taylor Schwarz 1.7526 0.000

Taylore Fuller 1.7018 0.333

Kristi Merritt 1.6256 0.000

Justine McLean 1.6002 0.000

Chelsea Herndon 1.7018 0.000

Hannah Rogers 1.7780 0.556

Kelsey Stewart 1.6764 0.000

Katie Medina 1.6256 0.000

Briana Little 1.6256 0.000

Stephanie Tofft 1.6510 0.000

Delanie Gourley 1.6256 0.667

1 2014 Softball Roster, http://www.gatorzone.com/softball/bios.php2 2014 Florida Softball Overall Statistics for Florida (as of Jun 04, 2014), http://www.gatorzone.com/softball/stats/cumu.pdf

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Mathematical Processes:

When researching the height of the 2014 University of Florida softball players, the data was represented by the measurements of feet and inches. In order for my findings to be more easily read on a global scale, I decided to convert the feet and inches into meters.

Height Conversion

1 inch = 2.54/100, or 0.0254 meters3

Therefore:

71 in x 0.0254 m = 1.8034 m

67 in x 0.0254 m = 1.7018 m

64 in x 0.0254 m = 1.6256 m

65 in x 0.0254 m = 1.6510 m

70 in x 0.0254 m = 1.7780 m

70 in x 0.0254 m = 1.7780 m

69 in x 0.0254 m = 1.7526 m

67 in x 0.0254 m = 1.7018 m

64 in x 0.0254 m = 1.6256 m

63 in x 0.0254 m = 1.6002 m

67 in x 0.0254 m = 1.7018 m

70 in x 0.0254 m = 1.7780 m

66 in x 0.0254 m = 1.6764 m

64 in x 0.0254 m = 1.6256 m

64 in x 0.0254 m = 1.6256 m

65 in x 0.0254 m = 1.6510 m

64 in x 0.0254 m = 1.6256 m

3 Inches to meters conversion, http://www.conversion-metric.org/length/inch-to-meter

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Correlation Coefficient

As my intent is to determine whether or not there is a correlation between the height and stolen base percentage of the 2014 University of Florida softball players, I decided to calculate the correlation coefficient of my data. Represented by the letter r, the correlation coefficient will not only determine if there is a correlation between the height and stolen base percentage, but it will also determine the strength of the correlation. If the correlation coefficient is between 0 and 0.25,then it is very weak correlation. If it is between 0.25 and 0.5, it is a weak correlation. If it between 0.5 and 0.75, it is a moderate correlation. And finally, if the correlation coefficient is between 0.75 and 1, then it is a strong correlation.

r = Sxy /Sx Sy

Sxy = Σ(x-x)(y-y)/n

Sx = √Σ(x−x) ² /n

Sy = √ Σ( y− y ) ²/n

x=1.8034+1.7018+1.6256+1.6510+1.7780+1.7780+1.7526+1.7018+1.6256+1.6002+1.7018+1.7780+1.6764+1.6256+1.6256+1.6510+1.6256 = 1.69

y=0.429+0.000+0.000+0.000+0.000+0.615+0.000+0.333+0.000+0.000+0.000+0.556+0.000+0.000+0.000+0.000+0.667 = 0.153

Sxy = (1.8034−1.69)x (0.429−0.153)

17 +

(1.7018−1.69) x (0.000−0.153)17

+

(1.6256−1.69) x (0.000−0.153)17

+ (1.6510−1.69) x (0.000−0.153)17

+

(1.7780−1.69) x (0.000−0.153)17

+ (1.7780−1.69) x (0.615−0.153)17

+

(1.7526−1.69) x (0.000−0.153)17

+ (1.7018−1.69) x (0.333−0.153)17

+

(1.6256−1.69) x (0.000−0.153)17

+ ¿¿ + (1.7018−1.69) x (0.000−0.153)17

+

(1.7780−1.69) x (0.556−0.153)17

+ ¿¿ + (1.6256−1.69) x (0.000−0.153)17

+

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(1.6256−1.69) x (0.000−0.153)17

+ (1.6510−1.69) x (0.000−0.153)/¿17

¿ +

(1.6256−1.69) x (0.667−0.153)17

= 0.00709

Sx = (1.8034-1.69)² + (1.7018-1.69)² + (1.6256-1.69)² + (1.6510-1.69)² + (1.7780-1.69)² + (1.7780-1.69)² + (1.7526-1.69)² + (1.7018-1.69)² + (1.6256-1.69)² + (1.6002-1.69)² + (1.7018-1.69)² + (1.7780-1.69)² + (1.6764-1.69)² + (1.6256-1.69)² + (1.6256-1.69)² + (1.6510-1.69)² + (1.6256-1.69)² = 0.0725; 0.0725/17 = 0.00426; √0.00426 = 0.0653

Sy = (0.429-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.615-0.153)² + (0.000-0.153)² + (0.333-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.556-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.000-0.153)² + (0.667-0.153)² = 1.0284; 1.0284/17 = 0.0605; √0.0605 = 0.246

r= 0.00709(0.0653 ) x (0.246)

=0.441

Therefore, because r is between 0.25 and 0.5, there is a weak correlation between the height and the stolen base percentages of the 2014 University of Florida softball players.

Scatter Plot

The scatter plot provides not only a visual for the raw data, but also the findings of the correlation coefficient. Because there is a weak correlation between the height and stolen base percentage of the 2014 University of Florida softball players, it will also be useful in displaying the line of best fit found on the next page.

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Line of

Best Fit

A line of best fit is

useful in representing data with the equation of a straight line in order to predict values that may not be displayed on the plot. The line of best fit is determined by the correlation between the two variables on a scatter plot, and passes through the point (x, y).

x=1.8034+1.7018+1.6256+1.6510+1.7780+1.7780+1.7526+1.7018+1.6256+1.6002+1.7018+1.7780+1.6764+1.6256+1.6256+1.6510+1.6256 = 1.69

y=0.429+0.000+0.000+0.000+0.000+0.615+0.000+0.333+0.000+0.000+0.000+0.556+0.000+0.000+0.000+0.000+0.667 = 0.153

Therefore, the line of best fit passes through the point (1.69, 0.153).

1.55 1.6 1.65 1.7 1.75 1.8 1.850

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.429

00 0 0

0.615000000000001

0

0.333000000000001

00 0

0.556

00 0

0.667000000000002

Relationship between height and stolen base percentage of the 2014 University of

Florida softball players

Height (meters)

Stol

en B

ase

Perc

enta

ges

1.55 1.6 1.65 1.7 1.75 1.8 1.850

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.429

00 0 0

0.615000000000001

0

0.333000000000001

00 0

0.556

00 0

0.667000000000002

Relationship between height and stolen base percentage of the 2014 University of

Florida softball players

Height (meters)

Stol

en B

ase

Perc

enta

ges

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1.55 1.6 1.65 1.7 1.75 1.8 1.850

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.429

00 0 0

0.615000000000001

0

0.333000000000001

00 0

0.556

00 0

0.667000000000002

Relationship between height and stolen base percentage of the 2014 University of

Florida softball players

Height (meters)

Stol

en B

ase

Perc

enta

ges

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Conclusion:

According to my calculations, there is a weak correlation between the height and stolen base percentage of the 2014 University of Florida softball players. When checking the validity of my findings with my graphing calculator, the correlation coefficient rounds to 0.428 instead of my 0.441. However, this is due to my rounding to three significant figures during each step of the mathematical process. Fortunately, this does not change the strength of the correlation; the range of a weak correlation is from 0.25 and 0.5, and both 0.428 and 0.441 are found within this range.

Converting the heights of the players from inches to meters was imperative for ensuring the most accurate interpretation of my findings. The correlation coefficient was the best technique for answering my research question because it not only determined that there was a correlation between my two data points, but it also determined the strength of the correlation. A scatter plot was the best visual aid for the raw data, and also helped display the best fit line. While some studies use a regression line, I chose to use the line of best fit because the regression line should only be calculated if there is a moderate or strong correlation coefficient. Therefore, the line of best fit was the proper process to utilize.

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Works Cited

2014 Florida Softball Overall Statistics for Florida (as of Jun 04, 2014),

http://www.gatorzone.com/softball/stats/cumu.pdf

Inches to meters conversion, http://www.conversion-metric.org/length/inch-to-meter

Peter Blythe, Jim Fensom, Jand Forrest, Paula Waldman de Tokman, Mathematical Studies

Standard Level, Oxford University Press

2014 Softball Roster, http://www.gatorzone.com/softball/bios.php