The document is a 3,972 word mathematical studies project that examines the time spent after school by students who live near the school in Nichada and farther away outside of Nichada. It includes an introduction outlining the method, which involved surveying 60 students about their weekly after school hours and travel time home. Tables display the raw data collected from the students sorted by their location and time spent/travel time. The interpretation of results section analyzes the mean, median, mode and standard deviations of the data and finds that on average students in Nichada spend 7.15 hours after school with a travel time of 2.62 minutes, while those outside spend 8.48 hours with a travel time of 45.

1. Mathematical Studies Project
The Time Spent After School by
Students that Live both Near and Far
From School
James Evans
IB Candidate Number: 000307-120
Ms. S. Goghar
IB Math Studies SL
May, 2012
Number of words: 3,972
1

2. Mathematical Studies Project
Contents
Introduction and method ................................................................................................................page 3
Mathematical processes ................................................................................................................page 4
Table of students ...........................................................................................................................page 5 - 7
Interpretation of results.................................................................................................................page 8 - 20
Overall conclusion and validity....................................................................................................page 21
Appendix.......................................................................................................................................page 22
2

3. Mathematical Studies Project
Introduction:
Time is something that most students tend to spend without realizing. Students tend to complain
about being in school but not being at school. Most of the student body live in the gated community that
surrounds the school grounds, this community (known as Nichada) holds thousands of houses for students
and teachers alike, and the school is within reasonable travel distance from any of the homes within the
compound. The remainders of the students live outside of the gates to Nichada and are usually located in
the central downtown area of Bangkok and the time to get downtown from Nichada can take up to an
hour or more depending on traffic. Another factor may be the time take to get from someone’s house to
the school may affect the amount of time that they spend after school. All students have time to
themselves to spend on what they would like to do on a weekday (i.e. use their computers, hang out with
friends, etc) as well as what they have to do (i.e. homework, projects, studies, etc). This is completely up
to the student to manage accordingly. However, students regardless of their duties and location of homes
and the time take to reach them, still tend to spend time after school on several activities whether it is
school related or leisure. Thus being intrigued by this, I shall conduct an investigation to determine the
time spent after school by students that live in Nichada and students that live downtown, or any other area
outside of the gated community, and compare them together. I will also ask for the reason as to why they
decided to spend their time after school whether the reason is school related or simply just to relax and
recuperate from a day at school. A survey will be conducted that will ask not only for the time a student
spends after school and the location of their house, but also the amount of time it takes to get to their
house and the reason as to why they have stayed after hours. The question that is to be answered is: “Is
there any relation between how far a student lives and the amount of time that they spend after school?”
Method:
1. Create a survey that I will use to gather information from students with.
2. Proceed to question students based upon the questions that have been created on the survey
sheet.
3. The questions will include: The time spent after school per week, the reason, and the travel
time to get home disregarding traffic.
4. The data gathering process will be taken place throughout the school day and even after
school.
5. The data gathering process will end after a sufficient number of students from the senior
student body have been accounted for (a possible total of 60 students, 30 downtown and the
other 30 Nichada residents).
3

4. Mathematical Studies Project
Mathematical Process:
NOTE: The mathematical processes will be done separately for both sets of students.
Medians
Modes
Standard Deviations
Chi Square Tests
The Chi-square test will allow the data to be formatted so that it can be easily understood by
allowing the data to be compared from both the expected frequencies and the actual frequencies. This will
be of use because this will provide an accurate display of processed data that will show with accuracy,
how different the data is.
4

5. Mathematical Studies Project
The 60 students were sorted into two different categories. One column shows the number of
houses that a student has spent after school per week and the other column shows the travel time taken by
car (in minutes) to get home. The two types of students (those that live in Nichada and those that live
outside of Nichada) were combined together and placed into the table below.
Student Hours After School / Week Travel Time (Car) (Minutes)
1 0 2.5
2 0 2.5
3 0 3
4 0 3.5
5 2.5 0.5
6 3 2.5
7 3.5 1.5
8 4 4
9 5 0.5
10 5 1.5
11 5 2
12 5 2.5
13 5 3
14 5 3
15 5 3.5
16 5 4
17 7 2
18 7 3.5
19 7.5 3.5
20 9.5 1
21 10 0.5
5

6. Mathematical Studies Project
22 10 3
23 11 3
24 12 3
25 12.5 2.5
26 15 3
27 15 3
28 15 3
29 15 3.5
30 15 4
31 0 2.5
32 0 2.5
33 0 3
34 0 3.5
35 2.5 0.5
36 3 2.5
37 3.5 1.5
38 4 4
39 5 0.5
40 5 1.5
41 5 2
42 5 2.5
43 5 3
44 5 3
45 5 3.5
46 5 4
6

7. Mathematical Studies Project
47 7 2
48 7 3.5
49 7.5 3.5
50 9.5 1
51 10 0.5
52 10 3
53 11 3
54 12 3
55 12.5 2.5
56 15 3
57 15 3
58 15 3
59 15 3.5
60 15 4
7

8. Mathematical Studies Project
INTERPRETATION OF RESULTS
8

9. Mathematical Studies Project
The Mean, Median and Modal data
From the raw data received from fellow participants around campus, the data can first be
organized to gain a rough idea of types of answers and results can be seen.
People that live in Nichada:
Mean
The mean of the data will be found for students that live in Nichada and outside of Nichada. This
data will include the number of students that go straight home after school rather than staying afterwards.
This data will be used to easily display of the results and allow for easiness when it comes time to read
the data. By comparing the two means it can be seen what has the higher average and then see clearly
which group of students stay after school the longest.
Mean number of hours:
= 7.15
Mean time taken to get home (minutes):
= 2.62
Median:
The median will show the middle term out of the thirty students. This can be used to find the different
quartiles of the data (the lower quartile, the middle quartile, and the upper quartile). This data can then be
later used in a cumulative frequency graph to or a box and whisker graph to see the different ranges such
as the inter-quartile range and then the ranges between the other quartiles.
Median number of hours:
0, 0, 0, 0, 2.5, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7.5, 9.5, 10, 10, 11, 12, 12.5, 15, 15, 15, 15, 15
=5
Median time taken to get home (minutes):
0.5, 0.5, 0.5, 1, 1.5, 1.5, 2, 2, 2.5, 2.5, 2.5, 2.5, 2.5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3.5, 3.5, 3.5, 3.5, 3.5, 4, 4, 4
=3
9

10. Mathematical Studies Project
Mode:
The mode will simply display what the most common amount of time spent after school will be.
This will be done for both the students that live in Nichada and outside of Nichada.
Modal number of hours: 5
Modal time taken to get home (minutes): 3
People that live outside of Nichada:
Mean
Mean number of hours:
= 8.48
Mean time taken to get home (minutes):
= 45.5
Median:
Median number of hours:
0, 0, 0, 3.5, 4, 4, 5, 6, 6, 6, 7.5, 7.5, 7.5, 7.5, 7.5, 7.5, 8, 8, 10, 10, 10, 11, 12.5, 12.5, 12.5, 14, 14, 15, 15,
15, 16
= 7.5
Median time taken to get home (minutes):
2, 15, 15, 20, 20, 30, 30, 30, 30, 35, 35, 40, 45, 45, 45, 45, 45, 45, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60,
90, 90
= 45
Mode:
Modal number of hours: 7.5
Modal time taken to get home (minutes): 60
10

11. Mathematical Studies Project
The Standard Deviations
Standard deviation will prove the same as the mean will however; it will allow the data to be graphed and
to see what the correlation of the data would be. If the standard deviation is large then the correlation of
the data is not very strong and then if the standard deviation in small then that means that the data would
have a closer, stronger correlation.
People that Live in Nichada- Hours After School / Week
Number of
hours spent Midpoint ( ) Frequency
after school
0- 0.5 4 2 -8 64 256
1- 1.5 0 0 -7 49 0
2- 2.5 1 2.5 -6 36 36
3- 3.5 2 7 -5 25 50
4- 4.5 1 4.5 -4 16 16
5- 5.5 8 44 -3 9 72
6- 6.5 0 0 -2 4 0
7- 7.5 3 22.5 -1 1 3
8- 8.5 0 0 0 0 0
9- 9.5 1 9.5 1 1 1
10 10.5 2 21 2 4 8
11- 11.5 1 11.5 3 9 9
12- 12.5 2 25 4 16 32
13- 13.5 0 0 5 25 0
14- 14.5 0 0 6 36 0
15- 15.5 5 77.5 7 49 245
16- 16.5 0 0 8 64 0
Avg: 8.5 Sum: 30 Sum: 227 Sum: 728
The Standard deviation for the hours spent after school per week for people that live in Nichada is 4.926
11

12. Mathematical Studies Project
People that Live in Nichada- Time Traveled(Car) (Minutes)
Time
Traveled(Car) Midpoint ( ) Frequency
(Minutes)
0- 0.5 3 1.5 -2.5 6.25 18.75
1- 1.5 3 4.5 -1.5 2.25 6.75
2- 2.5 7 17.5 -0.5 0.25 1.75
3- 3.5 14 49 0.5 0.25 3.5
4- 4.5 3 13.5 1.5 2.25 6.75
5- 5.5 0 0 2.5 6.25 0
Avg: 3 Sum: 30 Sum: 86 Sum: 37.5
The Standard deviation for the time traveled to get to school by car (in minutes) for people that live in
Nichada is 1.12
12

13. Mathematical Studies Project
People that Live Outside of Nichada- Hours After School / Week
Number of
hours spent Midpoint ( ) Frequency
after school
0- 0.5 3 1.5 -8 64 192
1- 1.5 0 0 -7 49 0
2- 2.5 0 0 -6 36 0
3- 3.5 1 3.5 -5 25 25
4- 4.5 2 9 -4 16 32
5- 5.5 1 5.5 -3 9 9
6- 6.5 3 19.5 -2 4 12
7- 7.5 6 45 -1 1 6
8- 8.5 2 17 0 0 0
9- 9.5 0 0 1 1 0
10 10.5 3 31.5 2 4 12
11- 11.5 1 11.5 3 9 9
12- 12.5 3 37.5 4 16 48
13- 13.5 0 0 5 25 0
14- 14.5 2 29 6 36 72
15- 15.5 3 46.5 7 49 147
16- 16.5 0 0 8 64 0
Avg: 8.5 Sum: 30 Sum: 257 Sum: 564
The Standard deviation for the hours spent after school per week for people that live outside of Nichada is
4.33.
13

14. Mathematical Studies Project
Number of
hours spent Midpoint ( ) Frequency
after school
0- 5 1 5 -55 3025 3025
10- 15 2 30 -45 2025 4050
20- 25 2 50 -35 1225 2450
30- 35 6 210 -25 625 3750
40- 45 7 315 -15 225 1575
50- 55 0 0 -5 25 0
60- 65 10 650 5 25 250
70- 75 0 0 15 225 0
80- 85 0 0 25 625 0
90- 95 2 190 35 1225 2450
100- 105 0 0 45 2025 0
110- 115 0 0 55 3025 0
Avg: 60 Sum: 30 Sum: 1450 Sum: 17550
The Standard deviation for the time traveled to get to school by car (in minutes) for people that live
outside of Nichada is 24.2.
14

15. Mathematical Studies Project
People that live in Nichada:
Mean number of hours spent at school: 7.15
= -3.65 -3.65² = 13.3
= -4.65 -4.65² = 21.6
= 3.85 3.85² = 14.8
= -0.15 -0.15² = 0.0225
= -7.15 -7.15² = 51.1
=
......... .........
= -1.15 -1.15² = 1.32
Sx =
Mean time taken to get home (minutes): 2.62
1.25 +
4.49 +
- 2.62 = -1.12 1.12² = 1.25 0.144 +
- 2.62 = -2.12 -2.12² = 4.49 0.384 +
- 2.62 =0.38 0.38² = 0.144 0.144 +
......... +
- 2.62 = -0.62 -0.62² = 0.384
0.144
- 2.62 = 0.38 0.38² = 0.144
......... .........
- 2.62 = 0.38 0.38² = 0.144
Sx = 1.12
15

16. Mathematical Studies Project
People that do not live in Nichada: 0.960
Mean number of hours: 8.48 16.1
0.960
- 8.48 = -0.98 -0.98² = 0.960
30.5
- 8.48 = 4.02 4.02² = 16.1
0.960
- 8.48 = -0.98 -0.98² = 0.960
.........
- 8.48 = -5.52 -5.52² = 30.5
0.230
- 8.48 = -0.98 -0.98² = 0.960
......... .........
- 8.48 = -0.48 -0.48² = 0.230
Sx = 4.33
Mean time taken to get home: 45.5
0.25 +
240.25 +
= 0.25 650.25 +
= 240.25 210.25 +
= 650.25 0.25 +
.........
= 210.25
210.25
= 0.25
......... .........
= 210.25
Sx = 24.2
16

17. Mathematical Studies Project
Correlation coefficient Table 1: This table shows the equation for the
correlation coefficient.
1 0 30
0 0 900
0 60 0 0 3600
3 0 90
0 0 8100
4 3.5 45
157.5 12.25 2025
5 4 60 240 16 3600
6 4 60
240 16 3600
7 5 45
225 25 2025
8 6 15
90 36 225
9 6 15
90 36 225
10 6 60 360 36 3600
11 7.5 20
150 56.25 400
12 7.5 35 262.5 56.25 1225
13 7.5 45 337.5 56.25 2025
14 7.5 45
337.5 56.25 2025
15 7.5 60
450 56.25 3600
16 7.5 60 450 56.25 3600
17 8 2
17 16 64 4
18 8 35 280 64 1225

18. Mathematical Studies Project
19 10 30 300 100 900
20 10 40 400 100 1600
21 10 45
450 100 2025
22 11 30
330 121 900
23 12.5 30 375 156.25 900
24 12.5 45
562.5 156.25 2025
25 12.5 90
1125 156.25 8100
26 14 60
840 196 3600
27 14 60
840 196 3600
28 15 20
300 225 400
29 15 60
900 225 3600
30 15 60
900 225 3600
31 0 2.5 0 0 6.25
32 0 2.5 0 0 6.25
33 0 3 0 0 9
34 0 3.5 0 0 12.25
35 2.5 0.5 1.25 6.25 0.25
36 3 2.5 7.5 9 6.25
37 3.5 1.5 5.25 12.25 2.25
38 4 4 16 16 16
39 5 0.5 2.5 25 0.25
18

19. Mathematical Studies Project
40 5 1.5 7.5 25 2.25
41 5 2 10 25 4
42 5 2.5 12.5 25 6.25
43 5 3 15 25 9
44 5 3 15 25 9
45 5 3.5 17.5 25 12.25
46 5 4 20 25 16
47 7 2 14 49 4
48 7 3.5 24.5 49 12.25
49 7.5 3.5 26.25 56.25 12.25
50 9.5 1 9.5 90.25 1
51 10 0.5 5 100 0.25
52 10 3 30 100 9
53 11 3 33 121 9
54 12 3 36 144 9
55 12.5 2.5 31.25 156.25 6.25
56 15 3 45 225 9
57 15 3 45 225 9 X Average
=
58 15 3 45 225 9
7.827869
59 15 3.5 52.5 225 12.25
60 15 4 60 225 3600 Y Average =
24.43443
TOTAL 477.5 1490.5 12555.5 5089.75 80673.75
19

20. Mathematical Studies Project
Test for independence of hours spent after school and distance from school to house:
Null hypothesis: The number of hours spent after school is independent from the distance to
someone’s house from school.
Alternate hypothesis: The number of hours spent after school is not independent from the distance
to someone’s house from school.
Contingency Table:
0 ≤ 6.9 hours 7 hours and above Sum
Nichada 17 13 30
Outside Nichada 12 18 30
Sum 29 31 60
Expected Value Table:
0 ≤ 6.9 hours 7 hours and above Sum
Nichada 30
Outside Nichada 30
Sum 29 31 60
Fo Fe Fo-Fe (Fo-Fe)²
17 14.5 2.5 6.25 0.431
13 15.5 -2.5 6.25 0.403
12 14.5 -2.5 6.25 0.431
18 15.5 2.5 6.25 0.403
Sum = 1.668
The critical value for speed against gender:
Degrees of Freedom:
= At 5% significance level. By having the results of the chi-
square test, this therefore rejects the
= Critical value, χ2crit = 3.84 alternate hypothesis and accepts the
2 2
χ calc < χ crit
null hypothesis. This means that the
=1
number of hours spent after school is
1.668 < 3.84 independent from the distance to
someone’s house from school.
20

21. Mathematical Studies Project
Overall Conclusion:
From the data analyzed above, the means, medians and mode give a rough understanding as to
what is to be expected from the full spread of data. The standard deviations give a better understanding as
to the strength of the data and whether it is reliable or not and for the most part the data seems to be fairly
strong. The Chi-square test accepts the null hypothesis that proves that the number of hours spent after
school is independent from the distance to someone’s house from school. Students tend to spend a lot of
time after school regardless of where they live. Whether they’re downtown or around the block, there will
always be time for these students to spend after school, participating in several different activates.
Validity:
The experiment conducted has provided the data that has answered the question stated in the
introduction. From the data collected the question can be answered with a “NO”. The null hypothesis was
that the student’s time spent after school (measured in hours) was independent to how far they lived
(measured in minutes taken by traveling in a car). The results of the chi squared test prove that there is no
correlation and that they are in fact independent.
The method used to gather the data for this experiment took into account the necessary
requirements to answer a question like this. The survey that was conducted was simply used to gather the
reason, the time spent after school, and the time taken to get home by car. By using the time spent after
school and the time taken to get home by car, statistical math was implemented to calculate the
correlation of the data gathered to ultimately answer the question posed in the introduction.
The method of data gathering and the process as a whole did have a few points of concern even
though the results of the experiment were satisfactory and answered the research question. The method of
data gathering only justifies students in the senior year (12th grade) and does not take into account any
member of a lower grade level. That means that it is possible that the data may be different in lower grade
levels. However, one cannot say from the results shown. Another factor that the test does not asses is that
of different schools. This data is only applicable with students that attend the “International School
Bangkok” in Thailand. But it is still arguable that this data can be applied to other students as the
“International School Bangkok” students are that of an international background, so thus, it can be argued
that the data can be used in other scenarios in different typical high schools around the world. Another
problem, that flaws the experiment, is the fact that there were only 60 students in total that participated in
the experiment, and of that 60, the students were split up into two groups of 30 students. One that
represented students that live in Nichada and the other that represented the students that didn’t. This
number can be seen as very small and if there were more students surveyed then maybe more accurate
results could have been seen after the math had been conducted.
Although these problems were contributing factors that could have skewed the data, the question
was still answered and seems to be fairly certain. The validity of the experiment stands but there were
factors that could have been accounted for and ultimately create a better experiment with stronger results.
21

22. Mathematical Studies Project
Appendix
22

23. Mathematical Studies Project
People that live OUTSIDE of Nichada
Name Hours After School / Week Reason Travel Time
(Car)(Minutes)
Jennifer Purgill 7.5 Villa / Friends / Waiting for the bus 45
Pammy Thavornvanit 12.5 Dance 30
Mick Laksanakorn 7.5 Drama / Friends / Community Service 20
Greg Ah-Fenne 14 Homework / Friends 60
Ty Fernstrom 7.5 Villa / Friends 45
Rahat Madarasmi 14 Villa / Soccer Practice 60
Paddy Davis 8 Friends / Villa / Music 2
Ryohei Kimura 7.5 Community Service / Friends / Homework 60
William Joyce 10 Community Service / Working out 45
Korn Toongtong 10 Community Service 40
Mint Nithikarnphisitha 11 Lessons / Community Service / Friends 30
Pong Karatkul 7.5 Friends / Rugby 35
Toto Snidvongs 16 Soccer / Villa 60
Nancy Pakdivong 12.5 Sports / Homework / Clubs 90
Jenna Tan 12.5 Talking to teachers / Homework 45
Quint Darrow 7.5 Villa / Friends 60
Nine Singhara 5 Studying / Villa / Community Service 45
Tai Lim Kim 4 Clubs 60
Megha Ghandi 4 Clubs 60
Winner Limlahapun 0 – Goes Straight Home Preference 90
Ben Ruktantichoke 0 – Goes Straight Home Preference / Homework 30
Mint Acha 0 – Goes Straight Home Preference / Homework 60
Claudine Torres 10 Drama / Friends 30
Friend Chai 3.5 Preference / Homework 45
Geegee Burapachaisri 15 Cross Country / Villa / Friends 60
Tomohiro Urakami 15 Soccer / Softball/ Sports 60
Ian Reau 15 Tutoring / Strings / Work 20
Trent Sripolcharoen 6 Tutoring / Teaching / Clubs 60
Sirimas Fong 6 Tutoring / Teaching / Clubs 15
Siriben Fong 6 Tutoring / Teaching / Clubs 15
23

24. Mathematical Studies Project
People that live in Nichada
Name Hours After School / Week Reason Travel Time
(Car)(Minutes)
Alisha Cunzio 3.5 Drama Rehearsals 1.5
Spenser Davis 2.5 Villa 0.5
Michael Pollock 11 Cross country (3 days a week) / Villa 3
Salvador Ortega 7 Villa / Friend’s house / After school work 2
Anish King 0 – Goes Straight Home Homework / Preference 3
Grant Simens 15 Villa / Cross country (everyday) 3
Mina Edwards 7.5 Swimming 3.5
Katie Eliot 10 Drama / Friends / Counselors 0.5
Alex Dybell 5 Drama 1.5
Melanie Bunker 9.5 Dance / Dance Teaching 1
Thomas Eliot 5 Friends / Choir / School work 0.5
Brooke Schaffner 5 Friends / School work 2
Sarah Cano 5 Friends 2.5
Koen De Meyere 12.5 MUN / Swimming / Community Service 2.5
E-man Castano 12 Sports 3
Carrie Burke 10 Dance 3
Preston Fernandez 15 Swimming / Cross Country / Clubs / Work 3
Nathan Stoiber 3 Drama / Villa 2.5
Daniel Schaefer 5 Villa 3.5
Nick Davin 5 Villa 3
Josiah Spears 0 – Goes Straight Home Preference 3.5
Mitchell Li 0 – Goes Straight Home Preference / Homework 2.5
Marinda Popp 15 Volleyball 3.5
RaeAnne Smith 15 Villa / Cross Country 3
Luke Hoehn 0 – Goes Straight Home Preference 2.5
James Kim 4 Clubs / Community service 4
Michaela Schnier 7 Teachers / Clubs / Sports 3.5
Michaela Onofre 5 Friends 3
Nicolas Parent 15 Cross Country / Villa / Flextime 4
Ticha Sethapakdi 5 Clubs 4
Pratik Sharma 8 Teacher / Clubs 35
24