GPA vs. Hours of Sleep

Report
GPA vs. Hours of Sleep
By: Allison Wilson and Victoria Fernandez
Period: 2nd
Our Study:
 Our study was the comparison between the number of
hours of sleep students receive on average every
school night vs. their GPA. We were curious to see if
these two sets of data have an impact on one another.
 We surveyed 40 random students from James Bowie
High School in the 9th-12th grade both male and female.
Math:
 Mean: The average of the numbers. To solve for the
mean you add up all the numbers, then divide by how
many numbers there are.
 Mean of the GPA: 3.17
 Mean of the Hours of Sleep: 6.77
 Median: The middle value in the list.
 Median of GPA: 3.1
 Median of hours of sleep: 7
More Math:
 Mode: The number that is repeated more often than any
other.
 Mode of the GPA: 2.8
 Mode of the Hours of Sleep: 6 and 7
 Range: The difference between the largest and smallest
values.
 Range of GPA: 4.3-1.8=2.5
 Range of the Hours of Sleep: 10-5= 5
More Math:
 Variance is the average of the squared differences from
the mean.
 Variance of hours of sleep: 72.976/40-1= 1.87
 Standard Deviation is a measure of how spread out the
numbers are.
 Standard Deviation of hours of sleep: 1.36
 Variance of GPA: 16.692/40-1=.43
 Standard Deviation of GPA: .65
Quartile and Median of GPA
 Quartile 1(lower quartile): 2.8
 Quartile 2 (middle quartile): 3.1
 Quartile 3 (upper quartile): 3.5
 Median: 3.1
Quartile and Median of Hours
of Sleep
 Quartile 1: 6
 Quartile 2: 7
 Quartile 3: 8
 Median: 7
Box Plot
Hours of sleep
6
7
8
This box plot shows the number of hours
of sleep the students get. The average
amount of sleep was seven hours.
The histogram
shows the
frequent hours
of sleep the
students got,
which was
between 6 & 7
hours .
Frequency
2 4 6 8
Histogram
Pie Chart
Percentage of GPA
0%
9%
8%
0-1
1.1-2.0
35%
2.1-3.0
3.1-4.0
48%
4.1-4.5
This pie chart correlates the
percentages of students to GPA.
The most frequent GPA range
was between 3.1-4.0, while the
least frequent was below 1.
Stem and Leaf Plot: GPA’s
Stem
Leaf
1 8,8,9,
2 2,3,7,7,8,8,8,8,8,8,9
3 0,0,1,1,1,1,2,2,2,3,3,5,5,5,5,7,8,9,9,
4 0,0,1,2,2,3
This Steam and Leaf Plot shows the GPA’s.
As you can see the majority are in the 3’s.
Bar Graph
Hours of Sleep vs. GPA
10
H
o
u
r
s
9
8
7
6
o
f
5
Hours of Sleep
4
S
l
e
e
p
3
2
1
0
4.3
4.2
4
3.9
3.8
3.5
3.5
3.3
3.2
3.2
3.1
3.1
3
2.8
2.8
2.8
2.7
2.3
1.9
GPA
This bar graph correlates the hours of sleep vs. GPA.
Surprisingly, there is no linear relationship.
1.8
Dot Plot of GPA’s
1.8
1.9
2.2
2.3
2.7
2.8
2.9
3
3.1
3.2
3.3
3.5
3.7
3.8
3.9
This Dot plot shows the number of students with each
GPA. The most common one was 2.8, while the ones
with the least common were 1.9, 2.2,2.3,2.9,3.7, 3.8,
4.1,and 4.3.
4
4.1
4.2
4.3
Scatter Plot
GPA vs. Hours of sleep
12
10
Hr.s of sleep
8
6
4
2
0
0
0.5
1
1.5
2
2.5
GPA
3
3.5
4
This scatter plot shows the correlation between
the number of hours of sleep each student
receives on average and the GPA. As you can
see there is no direct correlation between the
two.
4.5
5
Questions:
1. Did your data confirm your original thoughts about your research question?
Surprisingly, the data did not confirm my original thoughts about my research question. I
originally believed the higher the GPA the less the average amount of sleep would be due to
staying up late studying. Instead, the amount of sleep did not correlate to the GPA.
2. What was the biggest surprise?
My biggest surprise was how unrelated the GPA’s were in comparison to the amount of
sleep. There seemed to be no correlation.
3. What was the most useful information your data captured?
The most useful information was the lack of correlation between hours of sleep and GPA.
4.What additional questions arise from your research?
A question that arises from my research is if sleep is not a deciding factor in the GPA then
what is?
More Questions
5. How could you use your data persuasively?
You could use your data persuasively through the use of the various chart formats which clearly show the
lack of relationship between sleep and GPA.
6. Did you modify the sampling method you used? Why?
No, because I wanted to establish a simple cause and effect relationship.
7. How would you categorize your new sampling method?
I would categorize the data between the different grade levels and gender.
8. Explain how statistical bias could have applied to your project.
Statistical bias could have applied to my project had I thrown out data that didn’t agree with my assumption
of what I thought the results would be.
9.What type of regression do you think your data?
Relationship of grade level and gender.

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