For more information contact:
THE E-JOURNAL OF STUDENT RESEARCH has been made possible through grants provided by the United States Department of Education, South Central Bell Telephone, American Petroleum Institute, Intertel Foundation, Springhouse Publishing Corporation, Graham Resources, Inc., Chevron Oil Company, Central Louisiana Electric Company, Louisiana State Department of Education, and National Science Foundation. Mandeville Middle School and the National Student Research Center thank these organizations for their generous support of education.
TABLE OF CONTENTS
1. Is The Theory of Probability Correct?
2. Is The Formula For The Area Of A Circle Pi Times Radius
Squared?
3. Probability Theory And The Flipping Of A Quarter
4. The Frequency Of Occurrence of Different Colored Skittles
TITLE: Is the Theory of Probability Correct?
STUDENT RESEARCHER: Dean Cockerham
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I would like to do a research project that tests the theory of
probability which says that an event will have specific a outcome
which may be defined prior to it's actual occurrence. My
hypothesis states that if I flip a coin nine hundred times, heads
will come up the same number of times as tails.
II. METHODOLOGY:
First, I completed my statement of purpose. Next, I conducted my
review of the literature and wrote my hypothesis. I then wrote my
methodology and list of materials, and created my data collection
form. To test this theory, I flipped a quarter nine hundred
times. I then recorded my data, wrote my analysis of data, and
accepted or rejected my hypothesis. I then wrote my summary and
conclusion and applied my findings to the real world.
III. ANALYSIS OF DATA:
On my first trial, heads came up 153 times and tails came up 147
times. On my second trial, tails came up 164 times and heads
came up 136 times. On my third trial, heads came up 157 times and
tails came up 143 times. Tails came up 454 times and heads came
up 446 times. If I were to continue flipping the coin, the number
of heads and tails which would come up would be closer to those
predicted by probability which would be fifty percent for each.
IV. SUMMARY AND CONCLUSION:
Even though tails came up slightly more times than heads, I accept
my hypothesis which states that if I flip a coin nine hundred
times, heads will come up the same number of times as tails. If I
were to continue flipping the coin the number of heads and tails
would come closer to those predicted by probability which is 50%
for each.
V. APPLICATION:
Now I know that the probability theory is correct. If I wanted to
bet I would go with the odds.
TITLE: Is The Formula For the Area Of A Circle Pi Times Radius
Squared?
STUDENT RESEARCHER: Emily Meyer
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I would like to do a scientific research project on why the
formula for a circle is Pi times radius squared and not just Pi
times radius. My hypothesis states that the actual area of a
circle will be equal to the formula Pi times radius squared.
II. METHODOLOGY:
First, I wrote my statement of purpose and review of the
literature. Next, I developed my hypothesis. Then I made my data
collection form. To test my hypothesis, I drew a circle. I then
measured it vertically and horizontally. Then I made a mark every
centimeter. Next, I drew lines in my circle according to the
centimeter marks which formed squared cm. Then I counted the
number of whole and partial square cm. in my circle. Next, I
calculated the area of the circle using the formulas Pi times
radius squared and Pi times radius. I then recorded this
information on my data collection sheet. I repeated my procedure
a total of three times using different size circles. After this I
analyzed my data and wrote my analysis of data. Then I wrote my
summary and conclusion and accepted or rejected my hypothesis.
Finally, I wrote my application and applied my findings to the
real world.
III. ANALYSIS OF DATA:
I found that in my first circle, the actual circle had 25 whole
square cm. and 25 partial square cm. According to the formula Pi
times radius squared, the area was 38.47 square cm. According to
the formula Pi times radius, the area was 10.99 square cm. I know
this is incorrect because I counted more square cm. than this
number. In my second circle, I counted sixteen whole square cm.
and sixteen partial square cm. According to the formula Pi times
radius squared, the area of the circle 28.26 cm.. According to
the formula Pi times radius, the area was 9.42 cm. I know this
number is incorrect because I counted more actual square cm. than
this number. In my third circle, I counted 77 whole square cm.
and 77 partial square cm. According to the formula Pi times
radius squared, the area was 94.99 square cm. According to the
formula Pi times radius, the area was 17.27 cm. I know this
number is incorrect because I counted more square cm. than this
number. If I had had the correct tools for actually measuring the
area of a circle, the area would have equalled the formula Pi
times radius squared.
IV. SUMMARY AND CONCLUSION:
I found that in all of my circles the actual area of the circles
was closer to the formula Pi times radius squared. Therefore, I
accept my hypothesis.
V. APPLICATION:
I found that the actual area of a circle can be found by using the
formula Pi times radius squared. When calculating the area of a
circle you should use the formula. It is easier.
TITLE: Probability Theory and Flipping a Quarter
STUDENT RESEARCHER: James Pye
SCHOOL: Pineview Middle School
Covington, Louisiana
GRADE: 6
TEACHER: M. Phillips
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I want to find out what side of a quarter has the best chance of
being flipped if I flip a quarter two hundred times. I plan to
use an American quarter of any year. I predict that if I flip a
quarter fifty times, heads will appear more frequently than tails.
II. METHODOLOGY:
First, I will take the quarter and flip it fifty times. I will
observe the results. Afterwards, I will record my results on my
data collection sheet. Then I will analyze my data.
III. ANALYSIS OF DATA:
I observed that in the first trial, heads came up 26 times and
tails 24. In the second trial, I came up with the same numbers.
In the third trial, heads came up 27 times and tails came up 23
times. In the fourth trial, heads came up 25 times and tails came
up 25 times.
IV. SUMMARY AND CONCLUSION:
After flipping a quarter 200 times (4 trials, 50 flips each) heads
came up 4% more than tails (104/96). From this experiment, I
conclude that heads comes up more frequently than tails on a
quarter. It is possible that if I continued to flip the coin many
more times, that the number of head and tail which come up will
equal what probability theory predicts which is a 50/50 split.
V. APPLICATION:
I can apply this to my life in that at the beginning of sport
events there is a coin tossed. I would like to know what side of
the coin to pick if I was going to choose.
TITLE: The Frequency of Occurrence of Different Colored Skittles
STUDENT RESEARCHER: Michael Clark
SCHOOL: Mandeville Middle School
Mandeville, Louisiana
GRADE: 6
TEACHER: John I. Swang, Ph.D.
I. STATEMENT OF PURPOSE AND HYPOTHESIS:
I would like to do a research project on the frequency of
occurrence of different colored Skittles. A frequency is a rate
of occurrence. My hypothesis states that the yellow colored
Skittle will have the highest frequency of occurrence in one bag
of regular sized Skittles.
II. METHODOLOGY:
First, I wrote my statement of purpose. Next, I conducted my
review of literature. Then I developed my hypothesis. Then I
wrote my methodology. Next, I bought two bags of regular sized
Skittles at three different stores. Then I made an observation
and data collection form. Then I opened the bags of Skittles and
separated each color into a pile. Then I counted and averaged up
the total number of different colored Skittles in each bag. Then
I figured out the frequency of each color. Then I wrote down my
results and wrote my analysis of data. I then wrote my summary
and conclusion and accepted or rejected my hypothesis. Then I
shared my results with the world and published my abstract.
III. ANALYSIS OF DATA:
There was an average of 59 and 1/2 Skittles in each pack. There
was a total of 365 Skittles all together. There were 66 reds, 78
purples, 71 oranges, 63 yellows, and 85 greens. The percent for
red is 18%, purple is 21%, orange is 19%, yellow is 17%, and green
is 23%.
IV. SUMMARY AND CONCLUSION:
Since green had the highest frequency of occurrence, I reject my
hypothesis which states that the yellow colored Skittle will have
the highest frequency of occurrence. Purple had the second
highest then orange, red, and yellow.
V. APPLICATION:
Since red is my favorite color to eat, I will not share many of
them because it has one of the lowest frequency of occurrence.
© 1994 John I. Swang, Ph.D.