Rachel Lutz Statistics Project 5/30/14 Hours Dancing per Week and Unweighted GPA Introduction: The purpose of this project was to discover a correlation, or lack thereof between the amount of time a dancer spends dancing and their unweighted GPA. The population studied was made up of 30 dancers at the Onstage New York Competition in the Portland Convention Center. Data was collected through a survey, which asked for unweighted GPA and the number of hours spent dancing a week. Factors that were not taken into account, but could affect the data include sex, age, talent ,school district as well as other socioeconomic factors. Unprocessed Data (Table 1) Hours Dancing a Week 22 8 8 20 10.5 6 7 12 14.5 13 9 3.5 11 20 8 8 Unweighted High School GPA 3.675 3.8 3.8 4.0 3.9 3.5 3.5 3.5 3.5 3.9 4.0 4.0 3.8 3.9 3.8 3.75 1

9 14 18 15 10 11 12 11 13 15 11 12 12 Single Variable Analysis (Table 2) Analysis Average Median Mode Standard Deviation Range Hours Dancing Per Week 11.84 11 8, 11, 12 4.377 18.5

3.0 4.0 3.8 3.5 3.7 3.8 3.8 3.75 3.5 3.875 4.0 3.8 3.75

Unweighted GPA 3.7465 3.8 3.8 0.2168 1.0

The most notable parts of the single variable analysis are the standard deviation, the range and the average unweighted GPA. For the hours dancing per week, the range and standard deviation are significant, 18.5 hours and 4.377 hours, implying that a great spectrum of data was collected. However, for the unweighted GPA, the standard deviation is relatively small, 0.2168, and the range is only 1.0. As these values were calculated from the same population, this implies that the GPAs of the population are relatively homogenous, whereas the hours spent dancing 2

varied greatly. This data implies that there is little effect of hours dancing on GPA because even as dancing hours differed greatly, the GPA stayed about the same; it never changes more than 2.2 points above or below the average. Also very interesting is the average GPA. The average unweighted score is a 3.75, which is higher than the national average. Hours Dancing per Week and Frequency (Graph 1) This graph shows the distribution of the data collected for hours dancing per week. The data is slightly positively skewed because the mean is slightly larger than the median. This histogram implies variance in the data, as a larger spread of data occurs at lower relative frequencies. Note: There are no outliers in this data set. Unweighted GPA and Frequency (Graph 2 and Graph 3) Graph 2 is seen with outliers whereas Graph 3 shows the data without outliers. There is only one outlier (3.0). When examining graph 3, it is clear that the data has a smaller range (1.0) in comparison to the average than in graph 1. The data appears to be slightly positively skewed, but considerably less than in graph 1. This histogram does not imply much variance in the data, as the data is not spread very much and still occurs at high relative frequencies. 3

Bivariate Analysis (Graph 4)

This graph shows a very weak, almost insignificant positive relationship between hours spent dancing and the average GPA of a dancer. This means that dancers who take 3 hours of class have very similar GPAs to those who take 22, and that the GPA does not significantly increase or decrease depend on the amount of hours a dancer dances in a week. The correlation coefficient is 0.1255, which by IB standards, represents a weak positive correlation. Interpretation A very weak correlation between hours dancing and unweighted GPA is shown in Graph 4. This may have more implications than if the data did show a trend. Interestingly, the average GPA of the population is 3.75 (Table 2) which is above the national average. Unless there is another factor that is affecting the GPA, it appears that competitive dancers have higher grades in school than average. This could mean that simply by being in dance, which is a very high dedication sport and art, dancers are better prepared for school and receive high grades. This may be because time management skills and work ethic are enforced in dancers from a young age. However, because there are so many other possible variables, this data is relatively inconclusive. There may have been a disproportionate number of freshmen studied compared to seniors, which could have inflated the GPA values. I observed that more females participated in this study than males, and on average, females maintain higher GPAs than their male counterparts. There may also be socioeconomic factors that affected the data. As dance can be a very expensive 4

extracurricular, I have observed that most dancers come from the upper middle class. If the population studied here came from high economic backgrounds, they are more likely to attend higher performing school districts as well as receive higher grades in school. For further research, I would isolate the population of dancers within a single school district. Then, I would survey 100 freshmen, 100 sophomores, 100 juniors and 100 seniors within a the district. Then, I would survey as many dancers of various years in high school within the district as possible. All of the data will be collected from females for efficiency purposes. By adding these adjustments, it should be easy to see how female dancers perform at school compared to other females in their year within their district. This should produce a population with similar socioeconomic backgrounds as well as schooling.

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