IB Math Studies Internal Assessment:

Shoe Size and Height

School Name: International School of BangkokDate: November 2010Course: IB Math Studies

Statement and Plan of Task:

In this assessment I will investigate the relationship between shoe size and height. For this topic I have collected data from students in my age group, which is 17 to 18 years old. I collected fifteen shoe sizes and height for each gender. My task to is to find patterns, which reveal how they are correlated, and the chi-squared test will prove how significant the correlation is. In the end I will compare female and male results to see how the correlation results differ or if they are exactly the same.

Hypothesis:

I believe that the relationship between shoe size and height is significant. The larger shoe size is the taller a person will be.

The Measurements:

I have converted all the height measurements to centimeters and collected all shoe sizes in by American standards.

DATA COLLECTION

MALEHeight (X)Shoe Size (Y)XYXY

173929929811557

1689.52822490.251596

19010.536100110.251995

17711.531329132.252035.5

18010324001001800

1'6810.528224110.251764

17710313291001770

17212259841442064

18211331241212002

18012324001442160

18511.534225132.252127.5

18411338561212024

17210259841001720

16510272251001650

17810.531684110.251869

4620171696.528134

FEMALE

Height (X)Shoe Size (Y)XYXY

170728900491190

172825984641376

1677.52788956.251252.5

160725600491120

160725600491120

1777.53132956.251327.5

155924025811395

170728900491190

175930625811575

160725600491120

170928900811530

170828900641360

14652131625730

15562402536930

167927889811503

409082870.518719

MAXIMUM, AVERAGE, MINUMUN & MODE

Male

Height (cm)Shoe Size

Maximum190 12

Average17710.6

Minimum1659

Mode17710

Female Height (cm)Shoe Size

Maximum1759

Average1657.5

Minimum1465

Mode1707

BothHeight (cm)Shoe Size

Maximum19012

Average1719.05

Minimum1465

Mode1709

CORRELATION & LINEAR FIT

MALE GRAPH

WORKING OF CORRELATION

SxSy

=

=

=

= 6.9

=

=

=

= 0.86

= = 2.262

Solving for R:

= = 0.38

The wokring of the correlation matches up with the results of the graph.

FEMALE GRAPH

WORKING OF CORRELATION

SxSy

=

=

=

= 8.314

=

=

=

= 1.1323

= = 10.43

Solving for R:

= = 0.33

BOTH GENDER GRAPH

SxSy

=

=

=

= 170.97

=

=

=

= 9.446

= = 1575.983

Solving for R:

= = 0.577

CHI SQUARED TEST

MALE

Null Hypothesis- Height and shoe size are independent of each other.Alternative Hypothesis- Shoe size is dependent of height.

Observed Frequency ():

Height (cm)9-9.510-10.511-11.512-12.5Total

161-17012003

171- 18014128

181-19001304

Total274215

Expected FREQUENCY ():

Height (cm)9-9.510-10.511-11.512-12.5Total

161-170(2 x 3)/15= .4(7 x 3)/15=1.4(4 x 3)/15=.8(2 x 3)/15= .43

171-180(2 x 8)/15= 1.067(7 x 8)/15=3.733(4 x 8)/15=2.133(2 x 8)/15= 1.0678

181-190(2 x 4)/15= .533(7 x 4)/15=1.867(4 x 4)/15=1.066(2 x 4)/15= .5334

Total 274215

Calculated Chi Squared

-(-)(-)/

1.4.60.360.9

21.4.60.360.9

0.8-.80.640.8

0.4-.40.160.4

11.0670.0670.00450.0042

43.733.2670.07130.0191

12.133-1.1331.2840.602

21.067.9330.8700.815

0.533-.5330.2840.533

11.867-.8670.7520.4027

31.0671.9333.7363.501

0.533-0.5330.2840.533

9.41

Degree of Freedom = (row -1) x (column -1) = (3-1) x (4-1)= 6

With the significant level of 5% Chi Squared from the table equals to 12.59. The calculated result is 9.41 while the table result is 12.59. This means that the null hypothesis is accepted, meaning that height and shoe size are independent of each other.

FEMALE:

Null Hypothesis- Height and shoe size are independent of each other.Alternative Hypothesis- Shoe size is dependent of height.

Observed Frequency ():

Height (cm)5-5.56-6.57-7.58-8.59-9.5Total

141-150100012

151-160013004

161-170003126

171-180001113

Total1172415

Expected FREQUENCY ():

Height (cm)5-5.56-6.57-7.58-8.59-9.5Total

141-1500.1330.1330.9330.2670.5332

151-1600.2670.2671.8670.5331.0674

161-1700.40.42.80.81.66

171-1800.20.21.40.40.83

Total1172415

Calculated Chi Squared

-(-)(-)/

10.1330.8670.7525.65

00.133-0.1330.0170.127

00.933-0.9330.870.932

00.267-0.2670.0710.265

10.5330.4670.2180.409

00.267-0.2670.0710.265

10.2670.7330.5372.01

31.8671.1331.2830.687

00.533-0.5330.2840.532

01.067-1.0670.2840.266

00.4-0.41.1381.067

00.4-0.5330.160.4

32.80.20.2840.101

10.80.20.040.05

21.60.40.160.1

00.2-0.20.040.2

00.2-0.20.040.2

11.4-0.40.160.114

10.40.60.360.9

10.80.20.040.05

14.325

Degree of Freedom = (4-1) x (5-1)= 12

With the significant level of 5% Chi Squared from the table equals to 21.0. The calculated result is 14.325 while the table result is 21.0. This means that the null hypothesis is accepted, meaning that height and shoe size are independent of each other.

BOTH:

Null Hypothesis- Height and shoe size are independent of each other.Alternative Hypothesis- Shoe size is dependent of height.

Observed Frequency ():

Height (cm)5-6.57-8.59-10.511-12.5Total

141-15010102

151-16013004

161-17004509

171-180026311

181-19000134

Total2913630

Expected FREQUENCY ():

Height (cm)5-6.57-8.59-10.511-12.5Total

141-1500.1330.60.8670.42

151-1600.2671.21.7330.84

161-1700.62.73.91.89

171-1800.7333.34.7672.211

181-1900.2671.21.7330.84

Total2913630

Calculated Chi Squared

-(-)(-)/

10.1330.8670.7525.65

00.6-0.60.360.6

10.8670.1330.0180.021

00.4-0.40.160.4

10.2670.7330.5372.011

31.21.83.242.7

01.733-1.7333.0031.733

00.8-0.80.640.8

00.6-0.60.360.6

42.71.31.690.626

53.91.11.210.31

01.8-1.83.241.8

00.733-0.7330.5370.733

23.3-1.31.690.512

64.7671.2331.520.319

32.20.80.640.291

00.267-0.2670.0710.267

01.2-1.21.441.2

11.733-0.7330.5370.31

30.82.24.846.05

26.933

Degree of Freedom = (5-1) x (4-1)= 12

With the significant level of 5% Chi Squared from the table equals to 21.0. The calculated result is 26.933 while the table result is 21.0. Because this result is greater than the chi squared from the table, the null hypothesis is rejected. Which means that height and shoe size are dependent of each other.

Conclusion

After analyzing the gathered date and finding the R values and Chi squared test it can be concluded that height and shoe size are correlated. It is not a very strong correlation but with results of 0.38 for male, 0.33 for female and 0.577 for both the correlation is shown. In the graphs it is also very visible to see the correlation and because the point are not extremely spread out the it is shown that the correlation is somewhat strong. Chi squared showed us that the null hypothesis was accepted for both male and female but when it came to testing both, the null hypothesis was rejected.

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