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.