The assignment below is focused on exploring how graph visualization assist in interpreting raw data. The dataset used for the mathematical analysis is the assumption of Ozzie (fictional person) to fill in the truck with gas and go on a road trip, further visualized in Figure 1. Moreover, the conventional math analysis is presented to investigate the maturity of decisions performed by Ozzie based on the descriptive algorithms.
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There are several points related to the graph shown in Appendix. First, one should consider a basic notation of (x, y) positioning for the coordinates to simplify the understanding of how variables are related. For the point (-3, 0) it is obvious that -3 relates to the x-axis based on the notation, while the one is not presented on the graph and therefore should be considered as irrelevant. Plotting the (4, -2) in a rectangular coordinate system assumes extending the graph to the minus points, where the y-axis will remain plotted in the same values while the x- axis should be divided in a more numerical juxtaposition to show the difference. The ordered pair is a solution to the given equation since there is a straightforward line that supports the initial idea and provides critical points for dependency analysis (Puig & Rojano, 2004). Following the notation above, the point (0, 8) is on the y-axis, since it shows the number of gallons in trucks’ gas tank.
The difference in equations is informed by the use of plot variances, where x-axis represents the number of miles driven, while the y-axis shows the number of gallons of gas in a truck. The common equation used for this model is Y = ax + b, where a is a compound, x is a number of miles, and Y is a number of gallons. The y-intercept shows that 300 gallons of a gas in a truck are required to manage the trip that Ozzie pursues.
In terms of progression, the slope of the model is downward, which suggests that the more galloons purchased, the more travel experience the Ozzie has. However, based on the line slope it is feasible that Ozzie will require frequent charge-ups, which was also previously confirmed throughout the tentacular system management process. It means that the increase in gas prices contributes to the changes in kilometers gone. This observation would specifically benefit biking activists, both from the storm or the opportunity thinking perspective.
Overall, the analysis shows that it is trustworthy in terms of the parallel lines and direct recognition. However, there is no evidence on whether one should treat the number of gallons used for the miles tripped, since there is a case of multiple obstacles on the road. Furthermore, statistical significance for such observation is required as a part of research activity to justify the case thinking. Specifically, some observational trends could be considered in terns of the significance for practice, the use of alternative works, and social awareness. The graph itself is rather simplified and could be improved with additional variables to construct data validity. However, it might require more efforts in terms of math logic and associated probability research. Still, it indicates the reasonable use of statistics to show how graph visualization assists in decision-making.
Puig L., & Rojano T. (2004) The History of Algebra in Mathematics Education. In: Stacey K., Chick H., Kendal M. (eds) The Future of the Teaching and Learning of Algebra The 12thICMI Study. New ICMI Study Series, vol 8. Springer, Dordrecht. Web.