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AP Statistics Correlation Project

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by

Kaya Mark

on 28 May 2014

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Transcript of AP Statistics Correlation Project

Three Questions
Data Collection Methods
We constructed a Survey Monkey with these three questions
We distributed the survey on Facebook and collected 100 responses
Potential Bias
Only within CRLS community
Given through Facebook; only our specific FB friends can see it (most of our FB friends have similar GPAs, family sizes, & travel experiences as us)
Only people who have a FB
Only people who want to take the survey and are willing to take it
Immature people on FB --> write random answers
Could only collect 100 responses max b/c we used Survey Monkey
Possible misinterpretation of the questions; people could have analyzed differently
Question #3
Question #1
Correlation Between Q1 & Q2
# of people in family & current GPA
Question #2
AP Statistics Correlation Project
By Kaya Ludtke and Maya Mark
1. How many people are in your family (including yourself)?
2. What is your current GPA (not scaled)?
3. How many countries have you been to (including the US)?
We wanted to see if there is a correlation between
1. Family size (# of people in immediate family) & GPA (approximate range)
2. GPA & travel experience (outside U.S.)
3. Family size & travel experience
# of People in Family
n = 100
mean = 4.1
S.D. = 0.985
Q1= 4 Q3= 5
IQR = 1
6.5< outliers <2.5
number of outliers:6
median= 4
Our Survey!!!
n = 100
mean = 3.23
median = 3
S.D. = 0.6172
Q1= 3 Q3= 4
IQR = 1
5.5< outliers< 1.5
number of outliers:up to 2
skewed left
n = 100
mean = 7.1764
S.D. = 4.6781
Q1= 4 Q3= 14
IQR = 10
29< outliers< -11
number of outliers:0
skewed right(-20+ group)
This was pretty much expected. The majority of families within CRLS and Cambridge have family sizes of about 4, and the majority of our friend groups have family sizes of 4 people total. It is not likely for a high school student to live alone or live with five or more siblings. This data did not surprise us.

The results did match most of our expectations. Most people had been to 2-5 countries, and it was less likely for students to have gone to more than 13 countries. However, we were surprised that 15/100 people reported that they had been to 20+ countries. We felt that this was strange and there may have been a mistake. Perhaps people read the question wrong or there is a large bias.
The results do match what we expected. Students will likely have a GPA around a 3, with some deviation. It is impossible to have a GPA above a 4.5 and unlikely to have one below a 1.5. However there may be bias given the audience and method of our survey.
Correlation Between Q2 & Q3
Current GPA & # of countries traveled to
Correlation Between Q1 & Q3
# of people in family & # of countries traveled to
Impact of Outlier
Conclusion
correlation: Weak negative
r= 0.0963
Variance= 0.929%

correlation: weak negative correlation
Linear regression line:
r= 0.0732
Variance= 0.536
correlation: strong positive correlation!
r= 0.8217
Variance= 67.528%

With outlier:
Without 2 outliers:
Can you guess
what we're trying
to find out???
The data was not very surprising in terms of the numerous amounts of high GPAs, considering the majority of our FB friends receive good grades; however, we did not expect that everyone from large families would have such high GPAs or that many people from smaller sized families would have such low GPAs. The data was almost opposite from what we had originally predicted. The large the family size, the higher the GPA--this was very surprising!
1: 1.1-2.0
2: 2.1-3.0
3: 3.1-4.0
4: 4.1-5.0
GPA Range
Can't be 100% sure on anything b/c so much bias & small sample size :(
Based off data collected, the larger the family size, the higher the GPA
Unexpected
No obvious correlation between GPA & countries visited
Unexpected
Slight correlation between countries visited and family size: the larger the family size, the less countries visited
Expected
The number of people in a family accounts for 67.528% of varying GPA's. This is a fairly strong correlation.
The number of people in a family account for 0.536% of varying number of countries traveled to. This a fairly weak correlation.
The data does slightly support our original hypothesis that having more people in a family decreases the number of countries they have traveled to. This makes sense because more people means more money. However, we were surprised that so many people had been to over 20 countries. There is likely a difference between individual travel and family travel.
r^2= 0.67528
Y= 0.5214+1.1293
r^2= 0.00929
Y= 0.7648+8.5503
The results are not what we expected. There is a weak correlation showing that a higher GPA means the person has traveled to a smaller number of countries. We had predicted that a higher GPA would correlate with more countries because a family may have more resources, and the student more learning opportunities. However traveling to more countries might mean less time focusing on school. But, there is a wide range of data.
We removed two outliers. One was a person with a low GPA who had been to a large number of countries (15) and the other was a person with a very high GPA who had been to more than 20 countries. Before removal the data had a very small negative correlation, and removing these two points showed less of a correlation- r^2 is smaller. GPA does not correlate with traveling to a higher or lower amount of countries.
Citations
Survey Monkey
Excel
Prezi
Dictionary.com
Ms. Breyer
http://www.imathas.com/stattools/boxplot.html
http://www.meta-chart.com/pie
"I like this."

-Ms. Breyer, Friday during class

Ms. Breyer likes our Prezi!!!!!!
WHY did we choose these questions?
WHAT were our original hypotheses?
What We Would Have Changed...
More "official" survey
Not via FB
Not such a biased crowd
More random
Larger sample size
Provided more clearly-worded questions
Asked a few more specific questions
Travel alone vs. travel with family
Specify countries traveled to
Family in house vs. close family
Classes taken (CP, HN, AP)
ahah yess!!
What could we have expected with less bias?
Tree of Data
Frequency
Special S/O to Ralph Waldo Emerson & Rachel Louise Carson! Happy birthweek!
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